A non-invasive characterization of a biological cell using impedance spectroscopy

Abstract

This dissertation studies the electric characterization of biological cells by proposing an analytical model describing the electrical properties of a cell. This model is mathematically derived from electromagnetic phenomena of polarizable substances in electric field. It can provide the insight how the properties of each area, such as cell membrane, cytoplasm, nuclear envelope, effect the overall properties. Since biological cells tend to have a spherical shape in a cell suspension, it is modeled as a sphere or ellipsoid, containing a cell membrane, a cytoplasm, a nuclear envelope, and a nucleoplasm. The analytical equation for explaining the effects of a cell in electric field and the response of a cell in electric field is mathematically derived. This model can be applied in several areas, such as electroporation, dielectrophoresis and impedance spectroscopy. Impedance spectroscopy has been widely used as a characterization method for electrochemical systems and starting to be used in the biomedical area as a characterization tool, since it can facilitate a non-invasive characterization, which is not possible in a traditional biochemical method. The characterization of a cell using impedance spectroscopy requires an electrical circuit model or mathematical model describing the whole system. The proposed model can suggest more detailed and realistic mathematical and circuit model for a biological cell. The mathematical model for the impedance of a cell suspension is obtained by solving Laplace’s equation and Maxwell-Wagner’s equation. From the mathematical impedance model, a new equivalent circuit model is proposed to represent a cell suspension. The electric properties of a cell are calculated using the complex nonlinear least square method, which minimizes the square error between the measured impedance and the theoretically predicted impedance. This model is applied to study the conductivities and permittivities of the nucleoplasm, the nuclear envelope, the cytoplasm and the cell membrane of human embryonic stem cells (HSF-6) and induced pluripotent stem cells. Additionally, this model can be used in manipulation techniques, such as electroporation, electrofusion and dielectrophoresis. The transmembrane potential, which is the key factor in electroporation and electrofusion, and the Clausius-Mossotti factor, which determines the magnitude and the direction of dielectrophoretic force, are evaluated in detail.