### Abstract

The electrical properties of biological tissues can be described by a complex tensor comprising a simple expression of the effective admittivity. The effective admittivities of biological tissues depend on scale, applied frequency, proportions of extra- and intracellular fluids, and membrane structures. The effective admittivity spectra of biological tissue can be used as a means of characterizing tissue structural information relating to the biological cell suspensions, and therefore measuring the frequency-dependent effective conductivity is important for understanding tissue's physiological conditions and structure. Although the concept of effective admittivity has been used widely, it seems that its precise definition has been overlooked. We consider how we can determine the effective admittivity for a cube-shaped object with several different biologically relevant compositions. These precise definitions of effective admittivity may suggest the ways of measuring it from boundary current and voltage data. As in the homogenization theory, the effective admittivity can be computed from pointwise admittivity by solving Maxwell equations. We compute the effective admittivity of simple models as a function of frequency to obtain Maxwell-Wagner interface effects and Debye relaxation starting from mathematical formulations. Finally, layer potentials are used to obtain the Maxwell-Wagner-Fricke expression for a dilute suspension of ellipses and membrane-covered spheres.

Original language | English |
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Article number | 353849 |

Journal | Computational and Mathematical Methods in Medicine |

Volume | 2013 |

DOIs | |

Publication status | Published - 2013 May 13 |

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### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Applied Mathematics

### Cite this

*Computational and Mathematical Methods in Medicine*,

*2013*, [353849]. https://doi.org/10.1155/2013/353849

}

*Computational and Mathematical Methods in Medicine*, vol. 2013, 353849. https://doi.org/10.1155/2013/353849

**Effective admittivity of biological tissues as a coefficient of elliptic PDE.** / Seo, Jin Keun; Bera, Tushar Kanti; Kwon, Hyeuknam; Sadleir, Rosalind.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Effective admittivity of biological tissues as a coefficient of elliptic PDE

AU - Seo, Jin Keun

AU - Bera, Tushar Kanti

AU - Kwon, Hyeuknam

AU - Sadleir, Rosalind

PY - 2013/5/13

Y1 - 2013/5/13

N2 - The electrical properties of biological tissues can be described by a complex tensor comprising a simple expression of the effective admittivity. The effective admittivities of biological tissues depend on scale, applied frequency, proportions of extra- and intracellular fluids, and membrane structures. The effective admittivity spectra of biological tissue can be used as a means of characterizing tissue structural information relating to the biological cell suspensions, and therefore measuring the frequency-dependent effective conductivity is important for understanding tissue's physiological conditions and structure. Although the concept of effective admittivity has been used widely, it seems that its precise definition has been overlooked. We consider how we can determine the effective admittivity for a cube-shaped object with several different biologically relevant compositions. These precise definitions of effective admittivity may suggest the ways of measuring it from boundary current and voltage data. As in the homogenization theory, the effective admittivity can be computed from pointwise admittivity by solving Maxwell equations. We compute the effective admittivity of simple models as a function of frequency to obtain Maxwell-Wagner interface effects and Debye relaxation starting from mathematical formulations. Finally, layer potentials are used to obtain the Maxwell-Wagner-Fricke expression for a dilute suspension of ellipses and membrane-covered spheres.

AB - The electrical properties of biological tissues can be described by a complex tensor comprising a simple expression of the effective admittivity. The effective admittivities of biological tissues depend on scale, applied frequency, proportions of extra- and intracellular fluids, and membrane structures. The effective admittivity spectra of biological tissue can be used as a means of characterizing tissue structural information relating to the biological cell suspensions, and therefore measuring the frequency-dependent effective conductivity is important for understanding tissue's physiological conditions and structure. Although the concept of effective admittivity has been used widely, it seems that its precise definition has been overlooked. We consider how we can determine the effective admittivity for a cube-shaped object with several different biologically relevant compositions. These precise definitions of effective admittivity may suggest the ways of measuring it from boundary current and voltage data. As in the homogenization theory, the effective admittivity can be computed from pointwise admittivity by solving Maxwell equations. We compute the effective admittivity of simple models as a function of frequency to obtain Maxwell-Wagner interface effects and Debye relaxation starting from mathematical formulations. Finally, layer potentials are used to obtain the Maxwell-Wagner-Fricke expression for a dilute suspension of ellipses and membrane-covered spheres.

UR - http://www.scopus.com/inward/record.url?scp=84877255601&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877255601&partnerID=8YFLogxK

U2 - 10.1155/2013/353849

DO - 10.1155/2013/353849

M3 - Article

C2 - 23710251

AN - SCOPUS:84877255601

VL - 2013

JO - Computational and Mathematical Methods in Medicine

JF - Computational and Mathematical Methods in Medicine

SN - 1748-670X

M1 - 353849

ER -