Spectroscopic imaging of a dilute cell suspension

Habib Ammari ETH Zürich Josselin Garnier Université Paris VII Laure Giovangigli University of California at Irvine Wenjia Jing Tsinghua University Jin-Keun Seo Yonsei University

Analysis of PDEs mathscidoc:1702.03080

J. Math. Pures Appl., 105, (5), 603-661, 2016
The paper aims at analytically exhibiting for the first time the fundamental mechanisms underlying the fact that effective biological tissue electrical properties and their frequency dependence reflect the tissue composition and physiology. For doing so, a homogenization theory is derived to describe the effective admittivity of cell suspensions. A new formula is reported for dilute cases that gives the frequency-dependent effective admittivity with re- spect to the membrane polarization. Different microstructures are shown to be distinguish- able via spectroscopic measurements of the overall admittivity using the spectral properties of the membrane polarization. The Debye relaxation times associated with the membrane polarization tensor are shown to be able to give the microscopic structure of the medium. A natural measure of the admittivity anisotropy is introduced and its dependence on the frequency of applied current is derived. A Maxwell-Wagner-Fricke formula is given for concentric circular cells, and the results can be extended to the random cases. A randomly deformed periodic medium is also considered and a new formula is derived for the overall admittivity of a dilute suspension of randomly deformed cells.
electrical impedance spectroscopy, stochastic homogenization, Maxwell-Wagner-Fricke formula, Debye relaxation time
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  title={Spectroscopic imaging of a dilute cell suspension},
  author={Habib Ammari, Josselin Garnier, Laure Giovangigli, Wenjia Jing, and Jin-Keun Seo},
  booktitle={J. Math. Pures Appl.},
Habib Ammari, Josselin Garnier, Laure Giovangigli, Wenjia Jing, and Jin-Keun Seo. Spectroscopic imaging of a dilute cell suspension. 2016. Vol. 105. In J. Math. Pures Appl.. pp.603-661. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170222084112300708484.
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