Modeling Extracellular Field Potentials and the Frequency-Filtering Properties of Extracellular Space
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.
- Publication:
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Biophysical Journal
- Pub Date:
- March 2004
- DOI:
- 10.1016/S0006-3495(04)74250-2
- arXiv:
- arXiv:physics/0303057
- Bibcode:
- 2004BpJ....86.1829B
- Keywords:
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- Physics - Biological Physics;
- Quantitative Biology
- E-Print:
- text (LaTeX), 6 figs. (ps)