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

We examine the properties of the transfer function FT = Vm / VLFP between the intracellular membrane potential (Vm) and the local field potential (VLFP) 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 FT. The calculation of FT 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 Vm and VLFP during desynchronized states in rat barrel cortex in vivo. The experimentally derived FT matches the one derived theoretically, only if one assumes that the impedance of the extracellular medium is frequency-dependent, and varies as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1/\sqrt{\omega}$\end{document} (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.