Modeling extracellular field potentials and the frequency-filtering properties of extracellular space.
Claude Bédard, Helmut Kroger and Alain Destexhe

Biophysical Journal 86: 1829-1842, 2004.

Copy of the full paper (PDF)
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.
A NEURON program that simulates this model is also available.
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.

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