Spectroscopic imaging of a dilute cell suspension

Habib Ammari, Josselin Garnier, Laure Giovangigli, Wenjia Jing, Jin Keun Seo

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


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 respect to the membrane polarization. Different microstructures are shown to be distinguishable 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.

Original languageEnglish
Pages (from-to)603-661
Number of pages59
JournalJournal des Mathematiques Pures et Appliquees
Issue number5
Publication statusPublished - 2016 May 1

Bibliographical note

Funding Information:
This work was supported by the ERC Advanced Grant Project MULTIMOD-267184 .

Publisher Copyright:
© 2015 The Authors.

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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