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Impedance of tissue-mimicking phantom material under compression

Barry Belmont
Barry Belmont
, 
Robert E. Dodde
Robert E. Dodde
 e 
Albert J. Shih
Albert J. Shih
   | 27 feb 2013
Journal of Electrical Bioimpedance's Cover Image
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Article Category: Articles
Pubblicato online: 27 feb 2013
Pagine: 2 - 12
Ricevuto: 27 nov 2012
DOI: https://doi.org/10.5617/jeb.443
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© 2013 Barry Belmont, Robert E. Dodde and Albert J. Shih, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

The basic schematic diagram of many bioimpedance models consisting of parallel branches representing the suspended elements and the suspension in which they rest. In this case Rext and Cext would be the resistance and capacitance of the suspending fluid, respectively and Rint, Cm, and CPE would be the internal resistance of the suspended elements, the membrane capacitance and a constant phase element of the suspended elements, respectively. However, any components could be used along these branches.
The basic schematic diagram of many bioimpedance models consisting of parallel branches representing the suspended elements and the suspension in which they rest. In this case Rext and Cext would be the resistance and capacitance of the suspending fluid, respectively and Rint, Cm, and CPE would be the internal resistance of the suspended elements, the membrane capacitance and a constant phase element of the suspended elements, respectively. However, any components could be used along these branches.

Fig. 2

The mechanical analog of the Maxwell model of viscoelasticity.
The mechanical analog of the Maxwell model of viscoelasticity.

Fig. 3

A graphical representation of the experimental setup with each of the important elements labeled.
A graphical representation of the experimental setup with each of the important elements labeled.

Fig. 4

The relationship between the change in mass (ΔMass), the change in impedance (ΔZ), and the compression (ε0) were found to be linear (R2 > 0.95) across all samples indicating that the change in impedance is linked with the fluid exiting the sample, which in turn is a function of compression. The values reported here were found by taking the initial and final masses and impedances of the samples.
The relationship between the change in mass (ΔMass), the change in impedance (ΔZ), and the compression (ε0) were found to be linear (R2 > 0.95) across all samples indicating that the change in impedance is linked with the fluid exiting the sample, which in turn is a function of compression. The values reported here were found by taking the initial and final masses and impedances of the samples.

Fig. 5

Stress vs. time at four levels of compression. Using a standard moving average fitting technique the stress measurements were smoothed out and averaged within compression levels (n = 12). The initial time is set to the moment when the linear stage ceases to compress the samples.
Stress vs. time at four levels of compression. Using a standard moving average fitting technique the stress measurements were smoothed out and averaged within compression levels (n = 12). The initial time is set to the moment when the linear stage ceases to compress the samples.

Fig. 6

The relaxation curve of the samples as represented by normalized stress vs. time plot. The stress has been normalized through the full range of values by finding the ratio of the values to the peak value observed at the initial point of relaxation. The graph highlights the relaxation mechanism of tofu observed is essentially the same in all samples.
The relaxation curve of the samples as represented by normalized stress vs. time plot. The stress has been normalized through the full range of values by finding the ratio of the values to the peak value observed at the initial point of relaxation. The graph highlights the relaxation mechanism of tofu observed is essentially the same in all samples.

Fig. 7

Peak stress (σmax) as a function of initial compression. The relationship was found to be approximately linear and was fit via linear regression (R2 = 0.91). Given the assumptions of the chosen model, this result is in line with what was expected.
Peak stress (σmax) as a function of initial compression. The relationship was found to be approximately linear and was fit via linear regression (R2 = 0.91). Given the assumptions of the chosen model, this result is in line with what was expected.

Fig. 8

The (a) average change in impedance over time and the (b) admittance normalized to the maximum value over time seen for each level of compression. Twelve individual runs comprise each of the curves. Time was set to zero at the point compression ceased.
The (a) average change in impedance over time and the (b) admittance normalized to the maximum value over time seen for each level of compression. Twelve individual runs comprise each of the curves. Time was set to zero at the point compression ceased.

Fig. 9

Normalized admittance plotted as a function of stress and linear regression fit for each strain level. Also presented are the equations of the fit data.
Normalized admittance plotted as a function of stress and linear regression fit for each strain level. Also presented are the equations of the fit data.

Fig. 10

Admittance vs. stress vs. time for four strain levels. The correlation between admittance and stress comes more sharply into focus when viewed in this manner.
Admittance vs. stress vs. time for four strain levels. The correlation between admittance and stress comes more sharply into focus when viewed in this manner.

Fig. 11

Resting admittance (normalized) as a function of strain. This relationship was necessary for the admittance relaxation curve proposed in Eq. (12).
Resting admittance (normalized) as a function of strain. This relationship was necessary for the admittance relaxation curve proposed in Eq. (12).

Fig. 12

Admittance vs. stress vs. time for each strain level and portions of their corresponding relaxation curves. Though the fit is not perfect, it is an appropriate first approximation that yields a high level of correlation (R2 > 0.95 in all cases).
Admittance vs. stress vs. time for each strain level and portions of their corresponding relaxation curves. Though the fit is not perfect, it is an appropriate first approximation that yields a high level of correlation (R2 > 0.95 in all cases).

Fig. 13

The empirical model derived for (a) normalized admittance as a function of time and initial strain, (b) normalized admittance as a function of time and stress, (c) stress as a function of time and compression, and (d) normalized admittance as function of stress. Each relationship shown here fit the data well (in all cases R2 > 0.95). From empirical models presented above and the theoretical modeling presented in equations (), the underlying physical changes of the phantom can be determined and predicted with a high degree of certainty through passive electric properties measured via impedance techniques.
The empirical model derived for (a) normalized admittance as a function of time and initial strain, (b) normalized admittance as a function of time and stress, (c) stress as a function of time and compression, and (d) normalized admittance as function of stress. Each relationship shown here fit the data well (in all cases R2 > 0.95). From empirical models presented above and the theoretical modeling presented in equations (), the underlying physical changes of the phantom can be determined and predicted with a high degree of certainty through passive electric properties measured via impedance techniques.
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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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