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.

text (LaTeX), 6 figs. (ps)

Cited by in corpus (15)

• Does the 1/f frequency-scaling of brain signals reflect self-organized critical states?
• Macroscopic models of local field potentials and the apparent 1/f noise in brain activity
• Frequency dependence of signal power and spatial reach of the local field potential
• Model of Low-pass Filtering of Local Field Potentials in Brain Tissue
• The effect of ionic diffusion on extracellular potentials in neural tissue
• A generalized theory for current-source density analysis in brain tissue
• Perspective: Organic electronic materials and devices for neuromorphic engineering
• Generalized cable theory for neurons in complex and heterogeneous media
• Quasistatic approximation in neuromodulation
• A Comparison of Computational Models for the Extracellular Potential of Neurons
• A framework to reconcile frequency scaling measurements, from intracellular recordings, local-field potentials, up to EEG and MEG signals
• Analysis of claims that the brain extracellular impedance is high and non-resistive
• Efficient Micro-electrode Recording Modeling using a Filtered Point Process
• Electrothermal equivalent three-dimensional Finite Element Model of a single neuron
• Multiscale modeling via split-step methods in neural firing