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

TL;DR

This study provides evidence that the extracellular medium's impedance in the brain varies with frequency, affecting the transfer function between intracellular and extracellular potentials, with implications for neural modeling.

Contribution

The paper introduces a method to estimate extracellular impedance from transfer functions without current injection and demonstrates its frequency dependence in vivo.

Findings

Extracellular impedance follows a Warburg (1/√ω) frequency dependence.

The transfer function matches theoretical predictions only with frequency-dependent impedance.

Evidence suggests the extracellular medium is non-resistive, impacting neural signal modeling.

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.