The theory of the frequency response of ellipsoidal biological cells in rotating electrical fields

In this paper we have presented in as compact a form as possible the theoretical formalism that is needed to predict the frequency response of a biological cell of arbitrary ellipsoidal shape to a frequency dependant rotating external field. The formalism is much more complicated than that for a spherical or cylindrical cell where the radial vector is always parallel to the surface normal at each point of the surface. In addition to providing the theory we have demonstrated that the spin rate and its frequency dependance is very intimately related to the electrical properties of the cell interior and to that of the suspending fluid. It is possible to probe these properties of the cell and its environment by utilizing this technique. This aspect has been demonstrated by examining rotational changes as a function of the conductivity of both the cell interior and its suspending liquid. We also have shown, by considering a very simple model for the cell and the two dielectric constants, that the frequency spectrum is shape dependant. All our calculations have been carried out for "lossy" systems with frictional dissipation where energy minimization methods are no longer applicable. The invariant form of the Poynting vector forms the basis of the method.