The Dielectric Behavior of Nonspherical Biological Cell Suspensions: An Analytic Approach

The influence of the cell shape on the dielectric and conductometric properties of biological cell suspensions has been investigated from a theoretical point of view presenting an analytical solution of the electrostatic problem in the case of prolate and oblate spheroidal geometries. The model, which extends to spheroidal geometries the approach developed by other researchers in the case of a spherical geometry, takes explicitly into account the charge distributions at the cell membrane interfaces. The presence of these charge distributions, which govern the trans-membrane potential Delta V, produces composite dielectric spectra with two contiguous relaxation processes, known as the alpha-dispersion and the beta-dispersion. By using this approach, we present a series of dielectric spectra for different values of the different electrical parameters (the permittivity epsilon and the electrical conductivity sigma, together with the surface conductivity gamma due to the surface charge distribution) that define the whole behavior of the system. In particular, we analyze the interplay between the parameters governing the alpha-dispersion and those influencing the beta-dispersion. Even if these relaxation processes generally occur in well-separated frequency ranges, it is worth noting that, for certain values of the membrane conductivity, the high-frequency dispersion attributed to the Maxwell-Wagner effect is influenced not only by the bulk electrical parameters of the different adjacent media, but also by the surface conductivity at the two membrane interfaces.