Dielectric spectra of biological cells and tissues simulated by three-dimensional finite difference method

Abstract

For understanding dielectric spectra of biological cells and tissues, their modelling at cellular and subcellular levels is essential. Available analytical solutions, however, are limited to cells with simple geometry. To simulate the Maxwell- Wagner effect of biological cells and tissues with complex geometry, a numerical technique based on the three-dimensional finite difference method has been developed. The technique has a simple algorithm and is easy to generate three-dimensional models. It solves the electric potential distribution in a parallel plate capacitor including a cell or cells and calculates the effective complex permittivity of the system from the electric potential distribution. Its application was verified with a spherical cell model by comparing the numerical results with analytical ones. Thus, dielectric spectra were simulated for cells with a hole (as a model of erythrocyte ghosts), cells in cell division, erythrocyte aggregates and tissues in which cells are connected by gap junctions. The simulations provided good explanations for the related experimental results, namely, the α- dispersion of erythrocyte ghosts, the oscillation of permittivity during yeast cell division, the spectrum change by erythrocyte aggragation, and the α-dispersion of tissues with gap junctions.