Department of Computational Science and Engineering, Advanced Science and Technology Center (ASTC), Yonsei University, 50 Yonsei-Ro, 134 Sinchon-dong, Seodaemun-gu, Seoul 120 749, Republic of Korea.
Comput Math Methods Med. 2013;2013:353849. doi: 10.1155/2013/353849. Epub 2013 Apr 16.
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.
生物组织的电学特性可以用一个复杂张量来描述，这个张量由有效电导率的简单表达式组成。生物组织的有效电导率取决于尺度、施加的频率、细胞内外液的比例以及膜结构。生物组织的有效电导率谱可以作为一种描述与生物细胞悬浮液有关的组织结构信息的手段，因此测量频率相关的有效电导率对于了解组织的生理状态和结构非常重要。尽管有效电导率的概念已经被广泛应用，但它的精确定义似乎被忽视了。我们考虑如何为具有几种不同生物相关成分的立方体物体确定有效电导率。这些有效电导率的精确定义可能会提示我们如何从边界电流和电压数据中测量它。与均匀化理论一样，可以通过求解麦克斯韦方程组从逐点电导率计算有效电导率。我们从数学公式出发，计算了简单模型的有效电导率作为频率的函数，以获得 Maxwell-Wagner 界面效应和 Debye 弛豫。最后，使用层位势得到了稀疏散布的椭圆和覆盖有膜的球体的 Maxwell-Wagner-Fricke 表达式。
