MATHEMATICAL MODELING OF NON-INVASIVE ELECTRICAL IMPEDANCE SPECTROSCOPY OF INTACT HUMAN SKIN

Abstract

This dissertation aims to develop and solve mathematical models of electrical impedance spectroscopy (EIS) for intact human skin. In the first part, we develop the analytical framework by developing a mechanistic mathematical model for EIS measurements of human skin, leading to a reduced model and approximate solutions. The reduced model, which only needs to be solved numerically for the viable skin with modified boundary conditions, is verified. Thereafter, a Hankel transform of the reduced model allows for approximate solutions of not only the measured impedance but also the point-wise potential distribution in the skin. Subsequently, an extended generalized model is developed for n skin layers and m electrodes. In the second part on model applications, we determine the in-vivo dielectric properties – resistivity and relative permittivity – of living epidermis and dermis of human skin between 1 kHz and 1 MHz; and demonstrate guidelines for probe design for specific applications.