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Miceli, S., Ness, T.V., Einevoll, G.T. and Schubert, D. (2017) Impedance S pectrum in Cortical Tissue: Implications for Propagation of LFP Signals on the Microscopic Level. eNeuro, 4, e0291.

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• TITLE: Kramers-Kronig Relations and the Properties of Conductivity and Permittivity in Heterogeneous Media

  AUTHORS: Claude Bédard, Alain Destexhe

  KEYWORDS: Inhomogeneous Materials, Impedance, Mean-Field, Maxwell Equations, Hilbert Transform

  JOURNAL NAME: Journal of Electromagnetic Analysis and Applications, Vol.10 No.2, February 13, 2018

  ABSTRACT: The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an analogous paradigm applies to the macroscopic electric conductivity. If the causality principle is taken into account, there exist Kramers-Kronig relations for conductivity, which are mathematically equivalent to the Hilbert transform. These relations impose strong constraints that models of heterogeneous media should satisfy to have a physically plausible frequency dependence of the conductivity and permittivity. We illustrate these relations and constraints by a few examples of known physical media. These extended relations constitute important constraints to test the consistency of past and future experimental measurements of the electric properties of heterogeneous media.