Analysis of a Mechanistic Model for Non-invasive Bioimpedance of Intact Skin

Abstract

A mechanistic mathematical model for electrical impedance spectroscopy (EIS) measurements of human skin is analyzed, leading to a reduced model and approximate solutions. In essence, the model considers a complex-valued Laplace equation in the frequency domain for the alternating current from a circular EIS probe passing through the layers – stratum corneum, viable skin and adipose tissue – of human skin in the frequency range 1 kHz – 1 MHz. The reduced model, which only needs to be solved numerically for the viable skin with modified boundary conditions, is verified with the full set of equations (non-reduced model): good agreement is found with a maximum relative error of less than 3%. 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. In addition, the dimensionless numbers governing the EIS are elucidated and discussed.

Keywords

• mathematical model
• electrical impedance
• stratum corneum
• viable skin
• equivalent circuit