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Positive phase error from parallel conductance in tetrapolar bio-impedance measurements and its compensation

Martina F. Callaghan
Martina F. Callaghan
, 
Torben Lund
Torben Lund
, 
Ivan M. Roitt
Ivan M. Roitt
 and 
Richard H. Bayford
Richard H. Bayford
   | Dec 01, 2010
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Article Category: Articles
Published Online: Dec 01, 2010
Page range: 71 - 79
Received: Nov 05, 2010
DOI: https://doi.org/10.5617/jeb.142
Keywords
© 2010 Martina F. Callaghan, Torben Lund, Ivan M. Roitt and Richard H. Bayford, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

A parallel conductive pathway with resistance, RP, in the measurement circuit reduces the current reaching the sample, iS, by an amount, iP, corresponding to the current flowing through this extraneous pathway. The full injected current, I, is used to calculate the sample resistance leading to measurement error.
A parallel conductive pathway with resistance, RP, in the measurement circuit reduces the current reaching the sample, iS, by an amount, iP, corresponding to the current flowing through this extraneous pathway. The full injected current, I, is used to calculate the sample resistance leading to measurement error.

Fig.2

Schematic cross-section of the EndOhm-12 device (left) used to acquire impedance spectra and the corresponding 2D model geometry (right) that is symmetric about the r = 0 axis allowing parameters to be evaluated over the full 3D volume. The nodal points demark the extent of geometry elements.
Schematic cross-section of the EndOhm-12 device (left) used to acquire impedance spectra and the corresponding 2D model geometry (right) that is symmetric about the r = 0 axis allowing parameters to be evaluated over the full 3D volume. The nodal points demark the extent of geometry elements.

Fig. 3

Micrograph of a non-confluent transwell membrane (left) and the proposed equivalent electrical circuit (right) for the EndOhm device with the transwells in situ. RSOL represents the solution resistance above and below the transwell membrane. RGAP represents the areas of the transwell on which no cells have grown. The pathway through the cells is represented by the conventional Cole model.
Micrograph of a non-confluent transwell membrane (left) and the proposed equivalent electrical circuit (right) for the EndOhm device with the transwells in situ. RSOL represents the solution resistance above and below the transwell membrane. RGAP represents the areas of the transwell on which no cells have grown. The pathway through the cells is represented by the conventional Cole model.

Fig. 4

In these simulations of the circuit shown in figure 1, the true sample impedance is purely resistive with no phase component (□). Artefact caused by electrode polarisation effects (+) is characterised by negative phase and decreasing impedance magnitude with frequency. In contrast, artefact due to a parallel conductive pathway (o) is characterised by positive phase and increasing impedance magnitude with frequency. The parallel conductance is 750#. Each electrode is characterised by a charge transfer resistance of 800# and a double-layer capacitance of 0.1μF.
In these simulations of the circuit shown in figure 1, the true sample impedance is purely resistive with no phase component (□). Artefact caused by electrode polarisation effects (+) is characterised by negative phase and decreasing impedance magnitude with frequency. In contrast, artefact due to a parallel conductive pathway (o) is characterised by positive phase and increasing impedance magnitude with frequency. The parallel conductance is 750#. Each electrode is characterised by a charge transfer resistance of 800# and a double-layer capacitance of 0.1μF.

Fig. 5

The double layer capacitance, charge transfer resistance and parallel resistance are set to 1nF, 1kΩ and 5kΩ respectively for the “high” condition and to 100nF, 100# and 500# respectively for the “low” condition. The true sample impedance is purely resistive at 500#.
The double layer capacitance, charge transfer resistance and parallel resistance are set to 1nF, 1kΩ and 5kΩ respectively for the “high” condition and to 100nF, 100# and 500# respectively for the “low” condition. The true sample impedance is purely resistive at 500#.

Fig. 6

Blank transwell membrane data with and without a chloride layer on the surface of the lower CC electrode. Without the chloride layer, the electrode impedance is increased and the effect of a parallel conductance pathway is accentuated.
Blank transwell membrane data with and without a chloride layer on the surface of the lower CC electrode. Without the chloride layer, the electrode impedance is increased and the effect of a parallel conductance pathway is accentuated.

Fig. 7

Fitting is performed on the impedance spectra of three known conductivity solutions. Artefact consistent with the existence of a parallel conductance is seen in each spectrum and is more pronounced for the lower conductivity solutions.
Fitting is performed on the impedance spectra of three known conductivity solutions. Artefact consistent with the existence of a parallel conductance is seen in each spectrum and is more pronounced for the lower conductivity solutions.

Fig. 8

The sensitivity map for the EndOhm device shows considerable spatial variation. The sensitivity is large and positive between the PU electrodes. The sensitivity is large and negative between the PU and CC electrodes. Elsewhere the sensitivity tends to zero.
The sensitivity map for the EndOhm device shows considerable spatial variation. The sensitivity is large and positive between the PU electrodes. The sensitivity is large and negative between the PU and CC electrodes. Elsewhere the sensitivity tends to zero.

Fig. 9

Micrographs of three transwell membranes show differences in the final patterns of cell coverage (a). Acquired impedance spectra for these transwells are shown in (b). The solid lines depict the result of fitting this data to the cellular model with parallel conductance. The extracted impedance spectra from within the rig are shown in (c). The characteristic !-dispersion of the cells becomes visible and is more pronounced for the most densely seeded transwell (-o-).
Micrographs of three transwell membranes show differences in the final patterns of cell coverage (a). Acquired impedance spectra for these transwells are shown in (b). The solid lines depict the result of fitting this data to the cellular model with parallel conductance. The extracted impedance spectra from within the rig are shown in (c). The characteristic !-dispersion of the cells becomes visible and is more pronounced for the most densely seeded transwell (-o-).

Fig. 10

The magnitude of the dispersion from the low frequency limit to the high frequency limit rises as the number of cells present on the transwell membrane increases.
The magnitude of the dispersion from the low frequency limit to the high frequency limit rises as the number of cells present on the transwell membrane increases.

The transfer resistance as calculated using the sensitivity, RSEN; numerical implementation of the measuring procedure, RFEM; through fitting the acquired data to the EEC model, RS. The final row shows the pseudo geometric factor calculated for each approach through linear regression.

Conductivity (S/m)RSEN (Ω)RFEM (Ω)RS (Ω)
0.1305101.90122.80119.72
0.461728.8034.7036.10
1.191011.1713.4514.51
Geometric factor13.3m-116.0m-115.7m-1

The variability of the impedance magnitude is calculated with the range expressed as a percentage of the mean. The mean error of the magnitude is with respect to the true sample impedance.

CaseVariability (%)Mean Error (%)
High ZCC High RP17.0020.35
High ZCC Low RP80.5371.14
Low ZCC High RP1.809.98
Low ZCC Low RP9.5752.53
eISSN:
1891-5469
Language:
English
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Volume Open
Journal Subjects:
Engineering, Bioengineering and Biomedical Engineering, Biomedical Electronics, Life Sciences, Biophysics, Medicine, Biomedical Engineering, Physics, Spectroscopy and Metrology
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