Effective Admittivity of Biological Tissues as a Coefficient of Elliptic PDE

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.

Frequency‐dependent anisotropic modeling and analysis using mfEIT: A computer simulation study

“…It has been proven in Ammari et al and Zhang et al that the boundary voltages are highly frequency dependent because of the existence of thin insulating objects; thus, we are considering exploiting mfEIT methods to determine the anisotropy direction of the proposed model. To start with, for a better understanding of the frequency behavior of the constructed model, a simplified 2‐dimensional model is explained, detailed, and analyzed to show the effective admittivity distribution of B with respect to various frequencies …”

“…We have numerically computed and visualized the current streamlines through the frequency‐dependent anisotropic object at 3 current frequencies when currents are injected at both vertical and horizontal directions. Those additional simulations offer a more intuitive interpretation of the effects of current frequency, and the inverse process is conducted through a linear reconstruction by using sensitivity matrix approach . Various numerical simulations will be conducted to show that mfEIT is feasible to visualize the direction of anisotropy at certain frequencies with the expectation that anisotropy will vanish at high frequencies.…”

Spectroscopic conductivity imaging of a cell culture

“…Organization of the cells in the cartilage tissue. [11,17,18], we describe the conductivity of the medium by a scalar field…”

A battery-based constant current source (Bb-CCS) for biomedical applications

“…Electrical impedance of biological tissues [1][2][3] and their other electrical properties [4][5][6][7][8][9] such as resistivity [4][5], conductivity [6], permittivity [7][8] and admittivity [9] all have their own complex frequency responses and all are found as the function of tissue composition and signal frequency [4][5][6][7][8][9][10]. The frequency response of the electrical impedance of the biological tissues varies with physiological and physiochemical health status.…”

“…Frequency response of the bioelectrical impedance varies from subject to subject [10][11][12][13][14][15][16][17] and it may also vary from one tissue part to another tissue part within a particular subject. Moreover, the bioelectrical impedance of biological tissues varies with the measurement directions for the same tissue called anisotropic tissues [9]. As the bio-impedance changes with the variations in tissue health status [1,[18][19], the frequency response studies of bioelectrical impedance can provide a lot of information about the anatomy and physiology of the tissue under test.…”