# Evidence for frequency-dependent extracellular impedance from the transfer function between extracellular and intracellular potentials

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## Abstract

We examine the properties of the transfer function *F* _{ T } = *V* _{ m } / *V* _{LFP} between the intracellular membrane potential (*V* _{ m }) and the local field potential (*V* _{LFP}) in cerebral cortex. We first show theoretically that, in the subthreshold regime, the frequency dependence of the extracellular medium and that of the membrane potential have a clear incidence on *F* _{ T }. The calculation of *F* _{ T } from experiments and the matching with theoretical expressions is possible for desynchronized states where individual current sources can be considered as independent. Using a mean-field approximation, we obtain a method to estimate the impedance of the extracellular medium without injecting currents. We examine the transfer function for bipolar (differential) LFPs and compare to simultaneous recordings of *V* _{ m } and *V* _{LFP} during desynchronized states in rat barrel cortex *in vivo*. The experimentally derived *F* _{ T } matches the one derived theoretically, only if one assumes that the impedance of the extracellular medium is frequency-dependent, and varies as \(1/\sqrt{\omega}\) (Warburg impedance) for frequencies between 3 and 500 Hz. This constitutes indirect evidence that the extracellular medium is non-resistive, which has many possible consequences for modeling LFPs.

## Keywords

Computational models Local field potentials EEG Extracellular resistivity Intracellular recordings Maxwell equations## Notes

### Acknowledgements

Research supported by the Centre National de la Recherche Scientifique (CNRS, France), Agence Nationale de la Recherche (ANR, France) and the Future and Emerging Technologies program (FET, European Union; FACETS project). Additional information is available at http://cns.iaf.cnrs-gif.fr.

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