TITLE:
Mean-Field Formulation of Maxwell Equations to Model Electrically Inhomogeneous and Isotropic Media
AUTHORS:
Claude Bédard, Alain Destexhe
KEYWORDS:
Macroscopic Model, Theoretical Analysis, Electromagnetic Signals, Local Field Potential
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.6 No.10,
September
25,
2014
ABSTRACT: Maxwell
equations were originally designed to describe classic electromagnetic
phenomena in any type of medium. In particular, to describe electromagnetic
phenomena under the quasistatic electric approximation in
media that are electrically inhomogeneous and isotropic, such as for example when
there are strong spatial variations of conductivity, the formalism must be
adapted according to the problem considered. We review here two approaches to
this problem, first a “microscopic” model, where the spatial variations of
conductivity and permittivity are explicitly taken into account. In a second
“macroscopic” model, these spatial variations are taken on average by using a
mean-field formulation of Maxwell equations. Both of these models can describe
the electromagnetic behavior of inhomogeneous media. We illustrate this
formalism to describe the electric behavior of biological media, such as brain
tissue, which is typically very inhomogeneous. We show that the theory predicts
that for the typical frequency range of biological phenomena (lower than about
1000 Hz), the inhomogeneous nature of the medium has a determinant influence.