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Mean-Field Formulation of Maxwell Equations to Model Electrically Inhomogeneous and Isotropic Media

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DOI: 10.4236/jemaa.2014.610029    4,344 Downloads   4,863 Views   Citations


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.

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Bédard, C. and Destexhe, A. (2014) Mean-Field Formulation of Maxwell Equations to Model Electrically Inhomogeneous and Isotropic Media. Journal of Electromagnetic Analysis and Applications, 6, 296-302. doi: 10.4236/jemaa.2014.610029.


[1] Angel, C.A. (1992) Mobile Ions in Amorphous Solids. Annual Review of Physical Chemistry, 43, 693-717.
[2] Peters, A., Palay, S.L. and Webster, H.F. (1991) The Fine Structure of the Nervous System. Oxford University Press, Oxford.
[3] Bedard, C., Kroger, H. and Destexhe, A. (2004) Modeling Extracellular Field Potentials and the Frequency-Filtering Properties of Extracellular Space. Biophysical Journal, 86, 1829-1842.
[4] Bedard, C., Kroger, H. and Destexhe, A. (2006) Model of Low-Pass Filtering of Local Field Potentials in Brain Tissue. Physical Review E, 73, 051911.
[5] Bedard, C., Kroger, H. and Destexhe, A. (2006) Does the 1/f Frequency Scaling of Brain Signals Reflect Self-Organized Critical States? Physical Review Letters, 97, Article ID: 118102.
[6] Bedard, C. and Destexhe, A. (2009) Macroscopic Models of Local Field Potentials and the Apparent 1/f Noise in Brain Activity. Biophysical Journal, 96, 2589-2603.
[7] Jackson, J.D. (1999) Classical Electrodynamics. 3rd Edition, John Wiley Sons, New York.
[8] Bedard, C. and Destexhe, A. (2011) A Generalized Theory for Current-Source Density Analysis in Brain Tissue. Physical Review E, 84, Article ID: 041909.
[9] Planck, M. (1932) Theory of Electricity and Magnetism. Macmillan and co: 80441143.
[10] Bedard, C. and Destexhe, A. (2013) Generalized Cable Theory for Neurons in Complex and Heterogeneous Media. Physical Review E, 88, Article ID: 022709.
[11] Foster, K.R. and Schwan, H.P. (1989) Dielectric Properties of Tissues and Biological Materials: A Critical Review. Critical Reviews in Biomedical Engineering, 17, 25-104.
[12] Kronig, R.D.L. (1926) On the Theory of Dispersion of X-Rays. Journal of the Optical Society of America, 12, 547-556.
[13] Landau, L.D. and Lifshitz, E.M. (1981) Electrodynamics of Continuous Media. Pergamon Press, Moscow.
[14] Gabriel, S., Lau, R.W. and Gabriel, C. (1996) The Dielectric Properties of Biological Tissues: II. Measurements in the Frequency Range 10 Hz to 20 GHz. Physics in Medicine and Biology, 41, 2251-2269.
[15] Linden, H., Pettersen, K.H. and Einevoll, G.T. (2010) Intrinsic Dendritic Filtering Gives Low-Pass Power Spectra of Local Field Potentials. Journal of Computational Neuroscience, 29, 423-444.
[16] Choy, T.C. (1999) Effective Medium Theory. Clarendon Press, Oxford.

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