Dielectric spectroscopy of single cells: time domain analysis using Maxwell's mixture equation

Dielectric spectroscopy is a powerful tool for investigating the dielectric properties of biological particles in suspension. For low volume fractions, the dielectric properties of the particles are related to the measured properties of the suspension by Maxwell's mixture equation. A number of different techniques can be used to measure the dielectric spectrum in the frequency domain or the time domain. In time domain dielectric spectroscopy, data can be converted into the frequency domain using convolution or Fourier transform, prior to data analysis. In this paper, we present a general method for transforming Maxwell's mixture equation from the frequency domain to the time domain allowing analysis of cell dielectric properties directly in the time domain. The derivation is based on the Laplace transform of the single shell model for a spherical particle, and can be extended to the multi-shell model. For a single shelled cell two characteristic relaxation time constants are derived. The results are compared with published analytical models. We show that the original frequency dependent mixture equation can be recovered by Fourier transform back to the frequency domain. As a result, a general relationship for the dielectric response of a mixture of particles is presented which links the frequency and time domains.