A unified resistor-capacitor model for impedance, dielectrophoresis, electrorotation, and induced transmembrane potential

Abstract

Dielectric properties of suspended cells are explored by analysis of the frequency-dependent response to electric fields. Impedance (IMP) registers the electric response, and kinetic phenomena like orientation, translation, deformation, or rotation can also be analyzed. All responses can generally be described by a unified theory. This is demonstrated by an RC model for the structural polarizations of biological cells, allowing intuitive comparison of the IMP, dielectrophoresis (DP), and electrorotation (ER) methods. For derivations, cells of prismatic geometry embedded in elementary cubes formed by the external solution were assumed. All geometrical constituents of the model were described by parallel circuits of a capacitor and a resistor. The IMP of the suspension is given by a meshwork of elementary cubes. Each elementary cube was modeled by two branches describing the current flow through and around the cell. To model DP and ER, the external branch was subdivided to obtain a reference potential. Real and imaginary parts of the potential difference of the cell surface and the reference reflect the frequency behavior of DP and ER. The scheme resembles an unbalanced Wheatstone bridge, in which IMP measures the current-voltage behavior of the feed signal and DP and ER are the measuring signal. Model predictions were consistent with IMP, DP, and ER experiments on human red cells, as well as with the frequency dependence of field-induced hemolysis. The influential radius concept is proposed, which allows easy derivation of simplified equations for the characteristic properties of a spherical single-shell model on the basis of the RC model.