Modeling extracellular field potentials and the frequency-filtering
properties of extracellular space.
Claude Bedard, Helmut Kroger and Alain Destexhe
Biophysical Journal 86: 1829-1842, 2004.
Abstract
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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