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  • Author: U. Birgersson x
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Estimating electrical properties and the thickness of skin with electrical impedance spectroscopy: Mathematical analysis and measurements

Abstract

Electrical impedance spectroscopy (EIS) allows for the study and characterization of tissue alterations and properties associated with the skin. Here, the potential application of EIS to estimate the thickness of the stratum corneum is explored in the form of a mathematical model for EIS, which is analyzed in the limit of 1 kHz and closed-form analytical solutions derived. These analytical expressions are verified with the numerical solution of the full set of equations and validated with an EIS study comprising 120 subjects: overall, good agreement is found in the frequency range 1-100 kHz, where the impedance is governed by the stratum corneum. Combining the closed-form expression for the thickness of the stratum corneum predicted by the model with the experimental EIS measurements, a distribution for the stratum corneum thickness of the subjects is found with a mean and standard deviation that agree well with reported stratum corneum thicknesses from other experimental techniques. This, in turn, suggests that EIS could be employed to measure the thickness of the stratum corneum with reasonable accuracy. In addition, the electrical properties relevant to EIS – conductivity and relative permittivity – of the stratum corneum can be estimated with the closed form expressions if the stratum corneum thickness is known.

Open access
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.

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

Abstract

We determine the in-vivo dielectric properties—resistivity and relative permittivity—of living epidermis and dermis of human skin soaked with a physiological saline solution for one minute between 1 kHz and 1 MHz. This is done by fitting approximate analytical solutions of a mechanistic model for the transport of charges in these layers to a training set comprising impedance measurements at two depth settings on stripped skin on the volar forearm of 24 young subjects. Here, the depth settings are obtained by varying the voltage at a second inject on the electrical-impedance-spectroscopy probe. The model and the dielectric properties are validated with a test set for a third depth setting with overall good agreement. In addition, the means and standard deviations of the thicknesses of living epidermis and dermis are estimated from a literature review as 61±7 μm and 1.0±0.2 mm respectively. Furthermore, extensions to resolve the skin layers in more detail are suggested.

Open access
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.

Open access