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Estimating electrical properties and the thickness of skin with electrical impedance spectroscopy: Mathematical analysis and measurements

U. Birgersson
U. Birgersson
, 
E. Birgersson
E. Birgersson
 y 
S. Ollmar
S. Ollmar
   | 22 oct 2012
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Article Category: Articles
Publicado en línea: 22 oct 2012
Páginas: 51 - 60
Recibido: 06 sept 2012
DOI: https://doi.org/10.5617/jeb.400
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© 2012 U. Birgersson, E. Birgersson, S. Ollmar, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Schematic overview of the non-invasive electrode applied on (a-b) stratum corneum, viable skin and adipose tissue and (c) details of the mathematical Ansatz. The boundary conditions are denoted with roman numerals. Dimensions are given in Table 1.
Schematic overview of the non-invasive electrode applied on (a-b) stratum corneum, viable skin and adipose tissue and (c) details of the mathematical Ansatz. The boundary conditions are denoted with roman numerals. Dimensions are given in Table 1.

Fig. 2

(a) The magnitude (▘) and phase (▾) from the numerical solution of the full set of equations and the analytical counterparts (lines); (b) the relative error for the analytical solution relative to the full set of equations for the magnitude (—) and phase (---).
(a) The magnitude (▘) and phase (▾) from the numerical solution of the full set of equations and the analytical counterparts (lines); (b) the relative error for the analytical solution relative to the full set of equations for the magnitude (—) and phase (---).

Fig. 3

The individual currents, Ik, in terms of their (a) real and (b) imaginary parts for the numerical solution of the full set of equations (symbols) and the analytical counterpart (lines); here, ( ⋆) I4,(▴) I2, (▘) I1, and (▾) I3.
The individual currents, Ik, in terms of their (a) real and (b) imaginary parts for the numerical solution of the full set of equations (symbols) and the analytical counterpart (lines); here, ( ⋆) I4,(▴) I2, (▘) I1, and (▾) I3.

Fig. 4

Magnitude and phase of the of the numerical solution (...), analytical solution (−−) and the experimental data (symbols) at five depth settings αn= (▘ 0.1, ▴ 0.27, ▾0.58, ⋆ 0.81, ▘ 1).
Magnitude and phase of the of the numerical solution (...), analytical solution (−−) and the experimental data (symbols) at five depth settings αn= (▘ 0.1, ▴ 0.27, ▾0.58, ⋆ 0.81, ▘ 1).

Fig. 5

The ratio of the impedance to the numerical solution (...), analytical solution (−−) and the experimental data (symbols) at five depth settings αn= (▘ 0.1, ▴ 0.27, ▾ 0.58, ⋆ 0.81, ▘ 1).
The ratio of the impedance to the numerical solution (...), analytical solution (−−) and the experimental data (symbols) at five depth settings αn= (▘ 0.1, ▴ 0.27, ▾ 0.58, ⋆ 0.81, ▘ 1).

Fig. 6

The median predicted (a) resistivity and (b) relative permittivity for the full set of equations (▘) with 1 standard deviation (▴), ±2 standard ±±deviations (▾) and the closed-form expressions (−) with ±1 standard deviation (−−), ±2 standard deviations (...).
The median predicted (a) resistivity and (b) relative permittivity for the full set of equations (▘) with 1 standard deviation (▴), ±2 standard ±±deviations (▾) and the closed-form expressions (−) with ±1 standard deviation (−−), ±2 standard deviations (...).

Fig. 7

The estimated thickness distributions for stratum corneum based on the real and imaginary part from EIS measurements and a combination of the two.
The estimated thickness distributions for stratum corneum based on the real and imaginary part from EIS measurements and a combination of the two.

Dimensions for the electrode and skin layers [8].

Model objectAcronymDimensions
Current detectionw11 mm
Ceramicw2,w4,w60.15, 0.15, 1.9 mm
Guard ringw30.3 mm
Secondary injectw50.5 mm
Primary injectw70.5 mm
Total width for domainw20 mm
Electrode thicknesshE0.1 mm
Stratum corneum thicknesshSC14 μm
Viable skin thicknesshVS1.2 mm
Adipose tissue thicknesshAT1.2 mm

Cofficients for the material properties.

j(SC) cj(VS) cj(AT) cj(SC) 𝔡j(VS) 𝔡j(AT) 𝔡j
0-1.1803×1012.3688×1011.7402×1001.7570×1016.7610×1017.5844×100
12.1404×101-2.7471×1010-1.7961×101-7.0466×101 8.3142×10-2
2-9.9955×1001.2952×10108.5278×1003.2847×101 -7.7214×10-1
32.2537×100-3.0088×1000-2.0255×100-7.7649×1001.1797×10-1
4-2.5509×10-1 3.4167×10-10 2.3953×10-1 9.2429×10-1-4.0926×10-4
51.1516×10-2-1.5178×10-20-1.1319×10-2-4.4465×10-2-5.2423×10-4
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Engineering, Bioengineering and Biomedical Engineering, Biomedical Electronics, Life Sciences, Biophysics, Medicine, Biomedical Engineering, Physics, Spectroscopy and Metrology
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