Analysis of a mechanistic model for non-invasive bioimpedance of intact skin
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 pointwise potential distribution in the skin. In addition, the dimensionless numbers governing the EIS are elucidated and discussed.