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.

Mechanistic multilayer model for non-invasive bioimpedance of intact skin

“…The potential distribution, current density and measured impedance in cylinder coordinates [ 3 ] in the skin can be written as…”

“…Note that we do not solve for the potential distribution in the electrodes, because the potential drop there is negligible [ 3 ].…”

“…Besides natural variations between individuals that result in differing thicknesses and electrical properties, other factors come into play such as aging, skin moisture and variation of blood flow due to ambient conditions. In our earlier work, we derived a mathematical model based on conservation of charge for EIS measurements of human skin [1][2][3] between 1 kHz and 1 MHz by grouping the skin layers into three layers: viz., stratum corneum (SC), viable skin (VS) and adipose tissue (AT). The model, which was calibrated and validated with experimental EIS measurements, was solved numerically [1][2][3] and semianalytically [3] in the entire frequency domain and analytically [2,3] at around 1 kHz.…”

“…In our earlier work, we derived a mathematical model based on conservation of charge for EIS measurements of human skin [ 1 , 2 , 3 ] between 1 kHz and 1 MHz by grouping the skin layers into three layers: viz., stratum corneum (SC), viable skin (VS) and adipose tissue (AT). The model, which was calibrated and validated with experimental EIS measurements, was solved numerically [ 1 , 2 , 3 ] and semianalytically [ 3 ] in the entire frequency domain and analytically [ 2 , 3 ] at around 1 kHz. Similar continuous models have also been solved numerically [ 4 , 5 , 6 , 7 , 8 ].…”

Dielectrical properties of living epidermis and dermis in the frequency range from 1 kHz to 1 MHz

“…It might be possible to add at least the latter by also exploiting the experimental measurements at depth settings 2 and 4, which were not used in this study. We did not model the subcutaneous layer, because we have shown through a current-distribution analysis [10] that the amount of current passing through the adipose tissue in the subcutaneous layer is negligible for our frequencies. Any current passing through the muscle tissue should therefore also be negligible.…”