Mechanistic multilayer model for non-invasive bioimpedance of intact skin

Abstract

An approximate semi-analytical solution based on a Hankel transform of a mechanistic model for electrical impedance spectroscopy (EIS) is derived for a non-invasive axisymmetric concentric probe with m electrodes measuring the response of n layers of human skin. We validate the semi-analytical solution for the case when the skin is treated as a three-layer entity - (i) stratum corneum, (ii) viable skin comprising living epidermis and dermis and (iii) adipose tissue – on the volar forearm in the frequency range 1 kHz to 1 MHz with experimental EIS measurements of 120 young subjects. Overall, we find good agreement for both the mean magnitude and phase of the impedance as well as the natural variability between subjects. Finally, the semi-analytical solution is verified with the full set of equations solved numerically: Good agreement is found for the point-wise potential distribution in the three skin layers.

Modeling Stratum Corneum Swelling for the Optimization of Electrode-Based Skin Hydration Sensors

“…Therefore, in the final skin model, the SC layer employs hydration dependency for the dielectric parameters and thickness. As previous work showed, the deeper skin layers cannot be neglected [10,14,22].…”

“…Various publications characterize biological tissues [7][8][9] and report the measurement of dielectric properties of the human skin [10][11][12][13]. A semi-analytic solution for a three-layer model of stratum corneum, viable skin, and adipose tissue is proposed [14]. In [15], a model is presented to calculate the effective dielectric properties for each skin layer from numerical cellular structures parametrized by sub-cellular and cellular compounds.…”

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

“…1a-b); its main disadvantage, however, is the significant computational overhead since a complex-valued partial differential equation (PDE) needs to be solved numerically in several domains. We have recently managed to secure approximate analytical solutions [ 10 , 11 ] that reduce the multidomain PDE to a set comprising improper integrals and closed-form equations. This reduction is key when we here fit the dielectric properties of both living epidermis and dermis at the same time, because it becomes significantly more computationally difficult to fit four parameters at once—as compared to fitting only two for viable skin [ 9 ].…”

“…The layout of the paper is as follows: First, we summarize the experiments from our earlier study [ 9 ] and estimate the thicknesses of living epidermis and dermis from a literature survey. We then work through the main steps in the derivation towards the approximate analytical solution, which combines the idea of model reduction [ 10 ] and the generic, multi-electrode and -layer approximate solution [ 11 ]. After an outline of the parameter fitting, we discuss the experimental measurements at the three depth settings as well as the fitted dielectric parameters.…”