The effects of the amount of liquid applied to the electrode as well as the effect of the NaCl concentration on the skin-electrode impedance were analyzed, divided into analysis of the complex impedance followed by an equivalent circuit modelling. Generalized linear model analyses (GLM) were performed to determine the statistical relevance of all factors.
Frequency influence
The skin-electrode impedances were measured over a frequency range of 0.1 Hz – 1 MHz. Figure 6 exemplarily shows the impedance responses to wetting with deionized water and with physiological saline solution at different frequencies, depending on the electrolyte volume. An inverse frequency-impedance relation was found for all performed measurements with a significance of p(f) = 0.000, which was shifting the curve on the log(y)-axis but not changing the curves’ shapes. Hence, the same trends for the influence of the electrolyte could be observed at all frequencies while only the magnitude of impedance depended on the frequency. Therefore, the following analysis was performed using a single frequency to represent the entire frequency range. The impedance at 39 Hz was chosen as this is a common frequency used in NMES. [41-43]
Wetting and drying impedance
The ‘wetting impedance’ at 39 Hz depending on the NaCl concentration and electrolyte volume is presented in Figure 7a+c. The skin-electrode impedance decreased significantly for higher liquid amounts with p(V) = 0.000. The biggest change in impedance was found between the completely dry electrode (7.5 MΩ) and the first added liquid drop, i.e., 5 µL, reaching impedances of 1.6 – 3.1 MΩ (decrease by 58.8 % up to 78.7 %) for the NaCl solutions and 6.5 MΩ (decrease by 13.33 %) for deionized water. Afterwards, the impedance continued decreasing with a flatter slope until reaching impedances of 36.6 – 154.4 kΩ for the NaCl solutions and 409.8 kΩ for deionized water at 320 µL of electrolyte. Further, overall greater differences in impedance variation could be observed for deionized water compared to the NaCl solutions.
Corresponding observations were made for the ‘drying impedance’, presented in Figure 7b+d depending on the NaCl concentration and the drying time. After initially applying 20 µL of electrolyte, the impedance stagnated at around 0.4 – 0.5 MΩ for the two NaCl solutions and 2.3 MΩ for deionized water. After ca. 800 s (≈ 13 min) the curves started rising until after about 2200 s (= 37 min) where the curves stopped clearly increasing and instead fluctuated around 7-8 MΩ, which corresponds to the impedance of a completely dry electrode also found in the ‘wetting procedure’. Here, the impedance data measured for all concentrations was overlapping to a big extent. Overall, an increase in impedance over time, i.e., upon drying, was visible with p(t) = 0.000.
In the beginning of the drying procedure, no clear difference was visible between the mean impedances of the NaCl solutions while deionized water showed a clearly higher impedance. Once the electrodes started drying, differences between impedance means became visible for the two NaCl solutions. However, as seen in the box plot, the measured impedances were still overlapping to some extent at most times wherefore they were not considered significant.
In both the drying and wetting procedure, 20 µL of electrolyte were present at some point in the experiments. Thus, both should give the same impedance value in case the only significant influence on the impedance was the present moisture content. In the ‘wetting procedure’, a total amount of 20 µL was reached after about 600 s after applying the first drop of liquid to the electrode. The impedance here is theoretically corresponding to the impedance after 600 s in the ‘drying procedure’, when assuming that drying out was equivalent in both procedures. This was confirmed in the performed experiment even though mean impedances were differing to some extent due to high underlying variations in impedance data. In the ‘wetting procedure’ an impedance of 0.8 (± 0.6) MΩ was found for the NaCl solutions and 3.8 (± 2.7) MΩ for deionized whereas the ’drying procedure’ showed impedances of 0.4 (± 0.2) MΩ for the two NaCl solutions and 2.2 (± 1.6) MΩ for deionized water.
The GLM found a significant influence of the NaCl concentration on the impedance with p(c) = 0.000 for both procedures as well as a significant interaction of concentration and volume for the ‘wetting procedure’. However, visual analysis showed that smaller differences between NaCl concentrations were visible without showing a clear trend, whereas bigger differences could be seen between the impedances with deionized water and with NaCl solutions in general. Therefore, multiple comparisons of the NaCl concentrations were performed, see Table 1. Here it emerged that only the difference between deionized water and any NaCl solution was statistically significant whereas the NaCl concentrations did not differ significantly to each other with p > 0.05 for the ‘wetting impedance’.
Table 1. Multiple comparisons of concentrations for ‘wetting impedance’ and ’drying impedance’ over different time spans.
|
|
Wetting
|
Drying for t = 2700 s
|
Drying for t ≤ 2000 s
|
c in %
|
c in %
|
sign.
|
p
|
sign.
|
p
|
sign.
|
p
|
0.0
|
0.9
|
*
|
0.000
|
*
|
0.000
|
*
|
0.000
|
|
1.5
|
*
|
0.000
|
|
---
|
|
---
|
|
5.0
|
*
|
0.000
|
*
|
0.000
|
*
|
0.000
|
|
35.0
|
*
|
0.000
|
|
---
|
|
---
|
0.9
|
1.5
|
|
0.981
|
|
---
|
|
---
|
|
5.0
|
|
0.970
|
*
|
0.032
|
|
0.169
|
|
35.0
|
|
0.226
|
|
---
|
|
---
|
1.5
|
5.0
|
|
0.757
|
|
---
|
|
---
|
|
35.0
|
|
0.541
|
|
---
|
|
---
|
5.0
|
35.0
|
|
0.054
|
|
---
|
|
---
|
Statistical significance between means marked with * for confidence level of 0.05.
In terms of the ‘drying impedance’, when analyzing the entire measured time range of the procedure (t = 2700 s), all three concentrations were significantly differing from each other. However, visual comparison of the curves suggested that the results from the multiple comparison analysis were distorted by the factor ‘NaCl concentration’ not being applicable for a dry electrode. Therefore, the analysis was performed for a reduced time range for which the electrode was not considered completely dry yet. This point was determined to be at t ≤ 2000 s. The multiple comparison of concentrations for this time span, presented in Table 1, showed that the impedances of the two NaCl solutions did not differ significantly from each other, only the presence of ions led to a significant change. These observations match with the results from the ‘wetting procedure’. Hence, differences in impedance for wetted electrodes were caused by whether or not ions were present, while the NaCl concentration did not have a considerable influence.
The Bode and Nyquist plots are exemplarily presented for three volumes of 0.9 % NaCl solution and deionized water, respectively, see Figure 8, retrieved from the ‘wetting procedure’. In the Bode plots in Figure 8a+b, picturing the complex impedance Z and the phase angle θ, a clear plateau at the low frequency end should appear in the Z curve which corresponds to a value of Rs+Rp and at the high frequency end corresponding to the value of Rs. This was not clearly visible for the impedances of lower electrolyte volumes, but started getting visible for the higher volumes, especially for the NaCl solutions, as the phase angle curve was lower for higher liquid amounts. At the low frequency end of the measured range, the phase angle decreased for all electrolyte volumes, though not fully reaching zero. The lowest values were found for the highest electrolyte volumes with -θ = 13.9° for 0.9% NaCl solution and -θ = 19.3° for deionized water.
In the Nyquist plots in Figure 8c-e, presenting the resistance Z’ and the reactance –Z’’, a (depressed) semicircle was expected to be visible with two intersections at -Z’’= 0 (or shifted below the x-axis for a depressed semicircle) representing Z’= Rs and Z’= Rs+Rp. This semicircle was not visible for the dry electrode or for low volumes (10µL) of deionized water, and the intersections with the x-axis were not reached. Especially in the low frequency end (i.e., at high Z’ values) the reactance –Z’’ did not show an indication for a beginning decrease. For the 0.9 % NaCl solution, an indication for a beginning semicircle started appearing at 10 µL but was not yet decreasing at low frequencies. For 320 µL of both 0.9 % NaCl solution and deionized water, the semicircle was clearly visible. Here, the reactance decreased for low frequencies and almost reached an intersection.
EC analysis
An EC takes the entire frequency range into account; thus, EC modelling is a more universal way to analyze the electrical behavior of a system than analyzing impedance values at specific frequencies. Therefore, EC modelling was carried out for the analyzed system for the ‘wetting procedure’ to evaluate the influence of the liquid amount and the NaCl concentration on the values of the individual circuit elements.
The error of fit χ2, presented in Figure 9, describes how well the calculated EC models the measured impedance curves. The figure shows that χ2 was depending on the electrolyte volume with p(V) = 0.000 and the presence of ions in the performed experiments. For the dry electrode, a value of 6.99 was found which is extraordinarily high and it showed a very high variation in data. However, when liquid was added to the electrode, the error of fit decreased to values of 0.34 ≤ χ2 ≤ 3.59 for the NaCl solutions and 1.36 ≤ χ2 ≤ 6.71 for deionized water, and the systems with NaCl solution were all having lower variation within the data than the dry electrode. It is striking that the error of fit was considerably lower for the NaCl solutions than for deionized water for which in turn the mean χ2 never reached values below one. This was confirmed in the multiple comparison analysis, presented in Table 2, where the ion presence led to significant differences in error of fit. As a consequence, the modelled ECs for the system with deionized water had a limited fit in general.
Table 2. Multiple comparisons of concentrations for influence on χ2.
c in %
|
c in %
|
χ2
|
sign.
|
p
|
0.0
|
0.9
|
*
|
0.000
|
|
1.5
|
*
|
0.000
|
|
5.0
|
*
|
0.000
|
|
35.0
|
*
|
0.000
|
0.9
|
1.5
|
|
0.816
|
|
5.0
|
|
0.998
|
|
35.0
|
|
0.089
|
1.5
|
5.0
|
|
0.941
|
|
35.0
|
|
0.602
|
5.0
|
35.0
|
|
0.183
|
Statistical significance between means marked with * for confidence level of 0.05.
The skin and electrolyte resistance Rs is presented in Figure 10. As also found for the complex impedances, Rs depended on the electrolyte volume with p(V) = 0.000 and the presence of ions whereas the NaCl concentration was not a significant factor, as shown in the multiple comparisons analysis in Table 3, with one exception for the comparison of 35 % and 5 % NaCl solution being significant. For the dry electrodes, Rs was simulated to be 722 Ω which then decreased upon higher liquid volumes until reaching 173 Ω - 204 Ω for 320 µL of liquid. Within this, the decrease in Rs upon adding more deionized water was flatter than upon the application of more NaCl solution. Further, the NaCl solutions showed less variation in the data than the values calculated for deionized water.
Table 3. Multiple comparisons of concentrations for influence on Rs.
c in %
|
c in %
|
Rs wetting
|
sign.
|
p
|
0.0
|
0.9
|
*
|
0.000
|
|
1.5
|
*
|
0.000
|
|
5.0
|
*
|
0.000
|
|
35.0
|
*
|
0.000
|
0.9
|
1.5
|
|
0.998
|
|
5.0
|
|
0.110
|
|
35.0
|
|
0.964
|
1.5
|
5.0
|
|
0.051
|
|
35.0
|
|
0.996
|
5.0
|
35.0
|
*
|
0.019
|
Statistical significance between means marked with * for confidence level of 0.05.
The charge transfer resistance Rp, presented in Figure 11, was significantly affected by the electrolyte volume and the presence of ions, see also Table 4. Rp showed a decrease upon higher electrolyte volumes for all tested electrolytes with a big drop in the beginning from 85.8 MΩ for the dry electrode to Rp ≤ 23.2 MΩ for the NaCl solutions and to 54.7 MΩ for deionized water. After 320 µL of liquid were added, the system with deionized water had a resistance Rp of 2.8 MΩ whereas the NaCl solutions had resistances of 47.3 kΩ (for 35% NaCl) to 753 kΩ (for 0.9% NaCl). Again, higher variation in data was present for the systems wetted with deionized water compared to the NaCl solutions.
Table 4. Multiple comparisons of concentrations for influence on Rp.
c in %
|
c in %
|
Rp wetting
|
sign.
|
p
|
0.0
|
0.9
|
*
|
0.000
|
|
1.5
|
*
|
0.000
|
|
5.0
|
*
|
0.000
|
|
35.0
|
*
|
0.000
|
0.9
|
1.5
|
|
0.837
|
|
5.0
|
|
1.000
|
|
35.0
|
|
0.060
|
1.5
|
5.0
|
|
0.876
|
|
35.0
|
|
0.473
|
5.0
|
35.0
|
|
0.075
|
Statistical significance between means marked with * for confidence level of 0.05.
The values for the constant phase element were divided into the capacitance parameter Y0 and the empirical constant N, both pictured in Figure 12. The mean Y0 increased with a higher liquid amount, however not being statistically significant due the comparably high underlying variation. The dry electrode had a capacitance of 1.4 nMho*s^N which increased to 5.9 – 8.9 nMho*s^N for the NaCl solutions and to 2.0 nMho*s^N for deionized water once 5 µL of liquid were added. Y0 then continued increasing with higher liquid amounts until reaching 102.6 – 166.9 nMho*s^N for the NaCl solutions and 65.6 nMho*s^N for deionized water once 320 µL of liquid were present. Further, the NaCl concentration did not have a significant influence on the capacitance Y0.
The empirical constant N, on the other hand, showed a significant influence of the electrolyte volume and the NaCl concentration as well as an interaction of both, even though only varying in a small range with values between 0.75 – 0.86, which are typical values for biomedical electrodes. [34] A drop was visible between the dry electrode and the first added liquid from 0.86 to 0.81 for the NaCl solutions and to 0.85 for deionized water, after which the means for the NaCl solutions became rather steady once 40 µL of liquid were applied. For deionized water, the curve continued decreasing even for higher volumes, however the box plot showed that the data of most curves was overlapping to a big extent. To statistically evaluate this observation, a multiple comparisons analysis was performed for the influence of the liquid volume on N. The found Tukey groups are presented in Table 5. It became eminent that the dry electrode was significantly differing from all wet electrodes. Once liquid was added, the change in N slowed down. Between 5 – 40 µL differences were still visible, even if not with the ‘direct neighbor’ wherefore the Tukey groups were not clearly statistically significant. However, after having applied 40 µL N did not change significantly anymore when adding more liquid which led to all higher volumes being in the same Tukey group.
Table 5. The Tukey groups.
V (µL)
|
Subset
|
1
|
2
|
3
|
4
|
5
|
320
|
0.7621
|
|
|
|
|
160
|
0.7655
|
|
|
|
|
80
|
0.7220
|
|
|
|
|
40
|
0.7785
|
0.7785
|
|
|
|
20
|
|
0.7926
|
0.7926
|
|
|
10
|
|
|
0.8023
|
0.8023
|
|
5
|
|
|
|
0.8147
|
|
0
|
|
|
|
|
0.8624
|
p
|
0.100
|
0.238
|
0.716
|
0.401
|
1.000
|
Means of the homogeneous subsets included for the influence of the liquid volume on the empirical constant N using a statistical significance of 0.05.
Even though the mean N curve of deionized water looked noticeably different than the ones of the NaCl solutions, the multiple comparisons of concentrations did not show clear differences arising from the presence of additional ions, see Table 6. Here, only the 35 % NaCl solution was evaluated as significantly different to the other electrolytes leading to a more capacitive behavior.
Table 6. Multiple comparisons of NaCl concentrations for influence on the empirical constant N.
c in %
|
c in %
|
N wetting
|
sign.
|
p
|
0.0
|
0.9
|
|
1.000
|
|
1.5
|
|
0.524
|
|
5.0
|
|
0.808
|
|
35.0
|
*
|
0.000
|
0.9
|
1.5
|
|
0.649
|
|
5.0
|
|
0.895
|
|
35.0
|
*
|
0.000
|
1.5
|
5.0
|
|
0.990
|
|
35.0
|
*
|
0.038
|
5.0
|
35.0
|
*
|
0.009
|
Statistical significance between means marked with * for confidence level of 0.05.