Modeling extracellular field potentials and the frequency-filtering properties of extracellular space

Details Modeling extracellular field potentials and the frequency-filtering properties of extracellular space Modeling extracellular field potentials and the frequency-filtering properties of extracellular space

2003-03-14

arxiv.org/abs/physics/0303057v1

Biophysics Journal 86 (2004) 1829-1842

Physics

Biological Physics

text (LaTeX), 6 figs. (ps)

Scientific paper

10.1016/S0006-3495(04)74250-2

Extracellular local field potentials (LFP) are usually modeled as arising from a set of current sources embedded in a homogeneous extracellular medium. Although this formalism can successfully model several properties of LFPs, it does not account for their frequency-dependent attenuation with distance, a property essential to correctly model extracellular spikes. Here we derive expressions for the extracellular potential that include this frequency-dependent attenuation. We first show that, if the extracellular conductivity is non-homogeneous, there is induction of non-homogeneous charge densities which may result in a low-pass filter. We next derive a simplified model consisting of a punctual (or spherical) current source with spherically-symmetric conductivity/permittivity gradients around the source. We analyze the effect of different radial profiles of conductivity and permittivity on the frequency-filtering behavior of this model. We show that this simple model generally displays low-pass filtering behavior, in which fast electrical events (such as Na$^+$-mediated action potentials) attenuate very steeply with distance, while slower (K$^+$-mediated) events propagate over larger distances in extracellular space, in qualitative agreement with experimental observations. This simple model can be used to obtain frequency-dependent extracellular field potentials without taking into account explicitly the complex folding of extracellular space.

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