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.
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
A NEURON program that simulates this model is
This demo simulates a model of local field potentials (LFP) with
variable resistivity. This model reproduces the low-pass frequency
filtering properties of extracellular potentials. The model
considers inhomogeneous spatial profiles of conductivity and
permittivity, which result from the multiple media (fluids,
membranes, vessels, ...) composing the extracellular space around
neurons. Including non-constant profiles of conductivity enables the
model to display frequency filtering properties, ie slow events such
as EPSPs/IPSPs are less attenuated than fast events such as action
potentials. The demo simulates Fig 6 of the paper.
For further instructions, see the README file.
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