Evidence for frequency-dependent extracellular impedance from the transfer function between extracellular and intracellular potentials.
Claude Bédard, Serafim Rodrigues, Noah Roy, Diego Contreras and Alain Destexhe

Journal of Computational Neuroscience 29: 389-403, 2010. (Special issue “Modeling Extracellular Potentials”).

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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 linear 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 monopolar 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.