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Analysis of a Mechanistic Model for Non-invasive Bioimpedance of Intact Skin Cover

Analysis of a Mechanistic Model for Non-invasive Bioimpedance of Intact Skin

Journal of Electrical Bioimpedance
Volume 8 (2017): Issue 1 (January 2017)
By: B. Tsai,  H. Xue,  E. Birgersson,  S. Ollmar and  U. Birgersson  
Open Access
|Dec 2017

Figures & Tables

Fig.1

Schematic overview of the non-invasive two-electrode EIS probe and adjacent stratum corneum, viable skin and adipose tissue (a-b). The model reduction from the scaling analysis is illustrated in b-f.
Schematic overview of the non-invasive two-electrode EIS probe and adjacent stratum corneum, viable skin and adipose tissue (a-b). The model reduction from the scaling analysis is illustrated in b-f.

Fig.2

Dimensionless number, Π, for SC (–), VS (– –), AT (-⋅-) and EL (⋅⋅⋅).
Dimensionless number, Π, for SC (–), VS (– –), AT (-⋅-) and EL (⋅⋅⋅).

Fig.3

Dimensionless number, Ξ$\Xi $Ξ, for SC (–), VS (– –), AT (-⋅-) and EL (⋅⋅⋅).
Dimensionless number, Ξ$\Xi $Ξ, for SC (–), VS (– –), AT (-⋅-) and EL (⋅⋅⋅).

Fig.4

The magnitude (▲) and phase (●) of the impedance from the numerical solution of the complete set of equations, the reduced set of equations, Zred (–); the Hankel counterpart, ZH (+); and the approximate analytical counterpart, Z₁ (– –).
The magnitude (▲) and phase (●) of the impedance from the numerical solution of the complete set of equations, the reduced set of equations, Zred (–); the Hankel counterpart, ZH (+); and the approximate analytical counterpart, Z₁ (– –).

Fig.5

Verification of the magnitude and the phase of the approximate solutions with the full set of equations for the large parametric study: (a-b) reduced model, Zred, solved numerically; (c-d) solution, ZH, from the Hankel transform; (e-f) solution, Z₁, for ℭ≪1.
Verification of the magnitude and the phase of the approximate solutions with the full set of equations for the large parametric study: (a-b) reduced model, Zred, solved numerically; (c-d) solution, ZH, from the Hankel transform; (e-f) solution, Z₁, for ℭ≪1.

Fig.6

The absolute value of the local potential distribution at z=0 m on the base case for the frequencies 1 kHz (▲), 0.328 MHz (■) and 1 MHz (▼); the reduced numerical model (–) and the Hankel counterpart (o). (N.B.: The verification points have been shifted slightly along r to prevent overlap.)
The absolute value of the local potential distribution at z=0 m on the base case for the frequencies 1 kHz (▲), 0.328 MHz (■) and 1 MHz (▼); the reduced numerical model (–) and the Hankel counterpart (o). (N.B.: The verification points have been shifted slightly along r to prevent overlap.)

Fig.7

The absolute value of the potential distribution at 1 MHz for the base case in the viable skin: (a) the complete model; (b) the reduced model; and (c) the approximate solution from the Hankel transform.
The absolute value of the potential distribution at 1 MHz for the base case in the viable skin: (a) the complete model; (b) the reduced model; and (c) the approximate solution from the Hankel transform.

Parameter combinations_

ν(1, 2.1, 4.6, 10, 22, 46)×103, (1, 2.2, 4.6, 10)×105 Hz
w10.5, 1, 2, 3 mm
w20.1, 0.5, 1.2, 2, 3 mm
w30.5, 1, 2, 3 mm
hSC8, 14, 20 μm
hVS0.8, 1.2, 1.6 mm

Base-case dimensions and material parameters for the probe and skin layers_

Current detection width, w12 mm
Ceramic width, w21.2 mm
Inject width, w31 mm
Outer radius of the probe, R4.2 mm
Outer radius of the skin, Rskin10 mm
Electrode thickness, hEL0.1 mm[18]
Stratum corneum thickness, hSC14 μm[18]
Viable skin thickness, hVS1.2 mm[18]
Adipose tissue thickness, hAT1.2 mm[18]
Inject voltage, V00.05 V
Electrical permittivity in vacuum, ɛ08.85 x107[19]
Fm-1
Relative permittivity of electrodes,1[20]
εrEL${{\varepsilon }_{r}}^{EL}$
Electrode conductivity, σEL4.56 x107[20]
Sm-1

Coefficients for the conductivity and relative permittivity of the skin layers for 1 kHz to 1 MHz; the skin has been soaked with a 0_9% NaCl solution for 1 minute [17]_

jcjSC${{\mathfrak{c}}_{j}}^{SC}$djSC${{\mathfrak{d}}_{j}}^{SC}$
0-1.1803×1011.7570×101
12.1404×101-1.7961×101
2-9.9955×1008.5278×100
32.2537×100-2.0255×100
4-2.5509×10-12.3953×10-1
51.1516×10-2-1.1319×10-2
jcjVS${{\mathfrak{c}}_{j}}^{VS}$djVS${{\mathfrak{d}}_{j}}^{VS}$
02.3688×1016.7610×101
1-2.7471×101-7.0466×101
21.2952×1013.2847×101
3-3.0088×100-7.7649×100
43.4167×10-19.2429×10-1
5-1. 5178×10-2-4.4465×10-2
jcjAT$\mathfrak{c}_{j}^{AT}$djAT$\mathfrak{d}_{j}^{AT}$
01.7402×1007.5844×100
108.3142×10-2
20-7.7214×10-1
301.1797×10-1
40-4.0926×10-4
50-5.2423×10-4
DOI: https://doi.org/10.5617/jeb.4826 | Journal eISSN: 1891-5469
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Language: English
Page range: 84 - 96
Submitted on: Aug 1, 2017
Published on: Dec 8, 2017
Published by: University of Oslo
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Mathematical model,
electrical impedance,
stratum corneum,
viable skin,
equivalent circuit
Related subjects:
Engineering,
Bioengineering and biomedical engineering,
Biomedical electronics,
Life sciences,
Biophysics,
Medicine,
Biomedical engineering,
Physics,
Spectroscopy and metrology

© 2017 B. Tsai, H. Xue, E. Birgersson, S. Ollmar, U. Birgersson, published by University of Oslo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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