Evaluation of adjacent and opposite current injection patterns for a wearable chest electrical impedance tomography system

In order to ensure a desirable and stable contact between electrodes and skin during EIT data acquisition, disposable and self-adhesive Ag/AgCl electrodes (3M, USA) were used and equally attached around the thorax at the level of the 4–5th intercostal space. The procedures of EIT electrode placement for each subject were as follows. First, the chest circumference of each subject, denoted as M, was measured to calculate the distance L between two adjacent electrodes by L = M/16. Next, Electrode #1 and #16 were equally placed on the two sides of the sternum with a distance of L/2, and Electrode #8 and #9 on the two sides of the spine to avoid the bony parts (sternum and spine) with high impedance hindering the excitation current into the thorax. Third, the remaining electrodes were equidistantly attached in sequence. Finally, an elastic belt comprising 16 electrode buckles (MidasMED Biomedical technology, Suzhou, China) was connected to all the electrodes to improve electrode stability (figure 1(a)) prior to connection to the EIT data acquisition system through an electrode wire.

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A wireless and wearable EIT system (MidasMED Biomedical technology, Suzhou, China) for pulmonary ventilation was used to carried out EIT data measurement (Yang et al 2023). This system can work at 50 kHz with an acquisition rate of 20 frame per second and a wide current range from 100 uA to 1 mA. The measurement stability can be up to 0.1% relative change for a long-term measurement of 3 h and its measurement SNR is greater than 70 dB, as tested with a resistor phantom. The wearable system occupies a total volume of 10 × 8 × 3 cm³ and can wirelessly transmit data to the host computer through Bluetooth. The whole system is powered by a small lithium battery (+3.7 V).

Throughout the whole data acquisition period, the participants were asked to maintain a sitting position with calm breathing. The opposite current injection pattern was selected by the host computer and four amplitudes of current (1 mA, 500 uA, 250 uA and 125 uA) were configured sequentially. For each current injection, EIT data was recorded for ∼2 min. Subsequently, the adjacent current injection pattern was chosen and the identical current amplitudes and sequence were conducted.

The time-series EIT images were reconstructed with the GREIT (Graz consensus Reconstruction algorithm for EIT) algorithm, which was specially designed for lung imaging (Adler et al 2009). To improve the accuracy of EIT images, a realistic thorax model was established to produce the reconstruction matrix. First, the contours of thorax and lungs were extracted from an CT image of an adult in the EIDORS toolbox (https://eidors3d.sourceforge.net/). After setting the positions of the 16 electrodes corresponding to the realistic locations, a 2.5D FEM (finite element method) model consisting of 24 505 triangular elements was produced by an automatic mesh generator NETGEN 5.3, as shown in figure 1(b). Then, to avoid reconstruction bias introduced by conductivity change in the lung regions, we determined to set a homogeneous conductivity distribution within the thorax to perform EIT images reconstruction for all subjects, which have been adopted by the commercial EIT systems, such as PulmoVista 500 (Teschner et al 2015) and Pulmo EIT-100 (Qu et al 2021). Next, using identical algorithm parameters such as noise figure (NF) of 0.5, the two patterns of current injection were configured to calculate reconstruction matrices (${{\bf{R}}}_{ad}$ and ${{\bf{R}}}_{op}$ for adjacent and opposition injection, respectively). In this study, the reconstructed matrix was resized to the dimension 1024*${N}_{V},$ in which 1024 denoted the EIT image size (32 × 32 pixels) and ${N}_{V}$ denoted the number of one frame of EIT data (192 for opposite injection and 208 for adjacent injection). The purpose of obtaining EIT images with a resolution of 32 × 32 pixels is to facilitate analysis of regional ventilation (Leonhäuser et al 2018, Brabant et al 2022, Larrabee et al 2023).

In this study, difference imaging was used to reconstruct the time-series EIT images ventilation over time. For each current injection of each subject, the recorded EIT data at the end of expiration of the first respiratory cycle was designated as the reference ${{\bf{v}}}_{ref}$ to calculate time-series EIT images ${\rm{\Delta }}{\boldsymbol{\rho }}$ at all moments with 2 min by using the reconstruction matrix ${\bf{R}}$(${{\bf{R}}}_{ad}$ or ${{\bf{R}}}_{op}$): ${\rm{\Delta }}{{\boldsymbol{\rho }}}_{t}={\bf{R}}\cdot ({{\bf{v}}}_{t}-{{\bf{v}}}_{ref}),$ where ${\rm{\Delta }}{{\boldsymbol{\rho }}}_{t}$ and ${{\bf{v}}}_{t}$ were the EIT image and the EIT data at the instant $t,$ respectively.

In addition, the time-series thorax impedance $s$ was calculated with ${s}_{t}=\displaystyle {\sum }_{i=1}^{1024}{\rm{\Delta }}{{\boldsymbol{\rho }}}_{t}^{i},$ where ${s}_{t}$ was the thorax impedance at the instant $t$ and ${\rm{\Delta }}{{\boldsymbol{\rho }}}_{t}^{i}$ was the $i{\rm{th}}$ pixel of ${\rm{\Delta }}{{\boldsymbol{\rho }}}_{t}.$

For subsequent analysis, functional EIT (fEIT) images were generated by applying the time-series EIT images ${\rm{\Delta }}{\boldsymbol{\rho }}$ to measure the specific regional ventilation characteristics. Because the fEIT-regression method was very robust to signals with different phase information (Zhao et al 2018), it was used to calculate the fEIT image ${\bf{B}},$ in which each pixel was a regression coefficient of the following linear regression formula:

$$\begin{eqnarray}&&{\rm{\Delta }}{{\boldsymbol{\rho }}}^{i}(t)={\alpha }_{i}\cdot \displaystyle \sum _{i=1}^{1024}{\rm{\Delta }}{{\boldsymbol{\rho }}}_{t}^{i}+{\beta }_{i}+{\varepsilon }_{i}={\alpha }_{i}\cdot {s}_{t}+{\beta }_{i}+{\varepsilon }_{i},\end{eqnarray} \tag{ 1 }$$

where ${\rm{\Delta }}{{\boldsymbol{\rho }}}^{i}(t)$ denotes time-dependent relative impedance value of the $i{\rm{th}}$ pixel in the time-series EIT images; $\displaystyle {\sum }_{i=1}^{1024}{\rm{\Delta }}{{\boldsymbol{\rho }}}_{t}^{i}$ denotes the time-dependent impedance value of the whole thorax; $\alpha$ and $\beta$ are regression coefficients and $\varepsilon$ is the fitting error. As a result, ${\alpha }_{i}$ will be the value plotted in the $i{\rm{th}}$ pixel in the fEIT image ${\bf{B}}.$ ${\alpha }_{i}$ represents a statically measure which is used to measure the average functional relationship between the global lung impedance and the $i{\rm{th}}$ pixel impedance. The positive ${\alpha }_{i}$ indicates that the $i{\rm{th}}$ pixel impedance increases with the global lung impedance while the negative ${\alpha }_{i}$ indicates that the $i{\rm{th}}$ pixel impedance decreases with the global lung impedance. Therefore, the pixels with positive value in the fEIT image could be considered as the ventilation regions while the pixels with negative value represented the reconstruction artifacts.

SNR was chosen as a quality metric of the EIT signal, namely the time-series thorax impedance $s$ in this study. The main reason is that the SNR is directly related to the level of noise present in the EIT signal and the estimate of SNR values can be calculated directly with appropriate methods. To achieve precise calculation of SNR of the EIT signal, we first defined noise as all components except for the respiratory component and then employed the discrete wavelet transform (DWT) to separate the respiratory component from the noise component (Yang et al 2022).

It was assumed that the thorax impedance $s[t]$ is an additive mixture of respiratory component $r[t]$ and noise component $n[t],$ leading to the equation $s[t]=r[t]+n[t].$ The DWT method involved a two-stage practice: decomposition and rebuilding. In the first stage, the so-called wavelet functions and scaling functions were used to decompose the thorax impedance $s[t]$ and thus the low-varying signal ${a}_{i}[t]$ (approximation coefficient) and the fast-varying signal ${d}_{i}[t]$ (detail coefficient) could be obtained at each level, where $i$ denotes the $i{\rm{th}}$ level. Theoretically, ${a}_{i}[t]$ included the respiratory component $r[t],$ because $r[t]$ could be considered as a low-varying signal and independent $r[t]$ could be obtained at an appropriate level. In this study, we empirically selected db4 as the mother wavelet and set decomposition level to 4 by comparison. Conversely, in the second stage, by transforming the coefficient ${a}_{i}[t]$ (${a}_{4}[t]$ in this study) back to the time domain through inverse wavelet functions, the denoised signal estimation $\tilde{r}[t]$ was obtained. On the other hand, the estimated noise $\tilde{n}[t]$ was computed by subtracting the noise-free signal estimate $\tilde{r}[t]$ from the thorax impedance $s[t],$ i.e. $\tilde{n}[t]=s[t]-\tilde{r}[t].$ Finally, the SNR of the EIT signal $SNR[t]$ was calculated in decibels according to the classical format as follows:

$$\begin{eqnarray}&&SNR[t]=10\cdot {\mathrm{log}}_{10}\left(\frac{\displaystyle {\sum }_{t=1}^{T}{(\tilde{r}[t])}^{2}}{\displaystyle {\sum }_{t=1}^{T}{(\tilde{n}[t])}^{2}}\right)\mathrm{dB},\end{eqnarray} \tag{ 2 }$$

where $T$ denotes the time duration of data acquisition.

Three metrics were proposed to evaluate the change of functional EIT image with varying conditions for current injection:

2.3.2.1. Lung separation

This metric is designed to describe the degree of separation of the ventilated regions of both lungs, which was measured by the difference of the peak values in the ventilated regions and the minimum between these two ventilated regions, as shown in figure 2. It was calculated by the following formula:

$$\begin{eqnarray}&&\left|{c}_{\max }^{L}-{c}_{\min }\right|/{c}_{\max }^{L}+\left|{c}_{\max }^{R}-{c}_{\min }\right|/{c}_{\max }^{R},\end{eqnarray} \tag{ 3 }$$

where $c,$ calculated by the mean of the pixel values in line 16 and 17 of the fEIT image ${\bf{B}}$ (32 × 32 pixels), was the impedance distribution contour along the coronal axis; ${c}_{\min }$ was the minimum of $c;$ ${c}_{\max }^{L}$ and ${c}_{\max }^{R}$ were the peak values of $c$ in the left and right lung, respectively.

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Larger lung separation represents better lung separation.

2.3.2.2. Inverse artifacts

This metric represents the degree of reconstructed artifacts as well as the noise of the area outside the lungs, which was measured by the ratio of the sum of negative pixel values and the sum of positive pixel values in the fEIT image:

$$\begin{eqnarray}&&\left(\displaystyle \sum _{i=1}^{M}abs({{\bf{B}}}_{i})\right)/\left(\displaystyle \sum _{j=1}^{N}abs({{\bf{B}}}_{i})\right),\end{eqnarray} \tag{ 4 }$$

where $M$ was the number of pixels with ${{\bf{B}}}_{i}\lt 0;$ $N$ was the number of pixels with ${{\bf{B}}}_{i}\geqslant 0;$ $M+N=1024.$

Smaller inverse artifacts represents less inverse artifacts.

2.3.2.3. Boundary artifacts

This metric evaluates the degree of reconstructed artifacts within the boundary region near the electrodes, which was measured by the ratio of sum of pixel values within the boundary area and the total pixel values in the fEIT image:

$$\begin{eqnarray}&&\left(\displaystyle \sum _{i=1}^{A}abs({{\bf{B}}}_{i})\right)/\left(\displaystyle \sum _{j=1}^{N}abs({{\bf{B}}}_{i})\right),\end{eqnarray} \tag{ 5 }$$

where $A$ was the number of pixels (less than 2 pixels away from the edge) within boundary area; $N$ was the number of pixels with ${{\bf{B}}}_{i}\geqslant 0.$

Smaller boundary artifacts represents less boundary artifacts.

Four EIT-based parameters of common use, including center of ventilation (CoV), dorsal fraction of ventilation (V_D), global inhomogeneity (GI) index, and standard deviation of regional ventilation delay index (RVD_SD) were employed to evaluate the influence of varying current injections on clinical application (Yang et al 2021a). CoV, VD and GI were calculated from the fEIT image.

CoV depicts the ventilation distribution influenced by gravity or lung diseases, which is calculated by the relative impedance weighted by the pixel's location in the anteroposterior coordinate:

$$\begin{eqnarray}&&CoV=\displaystyle \sum _{i=1}^{1024}\left({{\bf{B}}}_{i}\cdot {h}_{i}\right)/\displaystyle \sum _{i=1}^{1024}\left({{\bf{B}}}_{i}\right)\cdot 100 \% ,\end{eqnarray} \tag{ 6 }$$

where ${h}_{i}$ is the height of the $i{\rm{th}}$ pixel with scaled value so that the bottom of the fEIT image (dorsal side) is 100% and the top (ventral side) is 0%.

V_D reflects the ventilation distribution in the dorsal side, which is calculated as the sum of all pixel values in the dorsal side of the fEIT image over the sum of all pixel values of the fEIT image:

$$\begin{eqnarray}&&{V}_{D}=\displaystyle \sum _{i=513}^{1024}{{\bf{B}}}_{i}/\displaystyle \sum _{i=1}^{1024}{{\bf{B}}}_{i}\cdot 100 \% .\end{eqnarray} \tag{ 7 }$$

GI indicates the heterogeneity of lung ventilation, which is calculated as the degree of deviation of all pixel values from the median values in the fEIT image:

$$\begin{eqnarray}&&GI=\displaystyle \sum _{l\in \mathrm{lung}}\left|{{\bf{B}}}_{l}-\mathrm{Median}({{\bf{B}}}_{\mathrm{lung}})\right|/\displaystyle \sum _{l\in \mathrm{lung}}{{\bf{B}}}_{l}\cdot 100 \% ,\end{eqnarray} \tag{ 8 }$$

where ${{\bf{B}}}_{l}$ denotes the pixel in the identified lung area, ${{\bf{B}}}_{\mathrm{lung}}$ represents all the pixels in the lung area, and pixel $l$ is considered to belong to a lung region if ${{\bf{B}}}_{l}\gt 10 \% \cdot \,\max ({\bf{B}}).$ A high GI index indicates large variation among pixel values; therefore, this parameter is used as an indicator of heterogeneity.

RVD_SD represents the distribution of regional ventilation delay (RVD) which is calculated as the time percentage of pixel impedance increase in the global impedance curve:

$$\begin{eqnarray}&&{\mathrm{RVD}}_{l}={t}_{l,40 \% }/{T}_{\mathrm{inspiration},\mathrm{global}}\cdot 100 \% ,\end{eqnarray} \tag{ 9 }$$

where ${t}_{l,40 \% }$ denotes the time needed for pixel $l$ to reach 40% of its maximum inspiratory impedance; pixel $l$ belongs to the lung ventilation regions if $T{V}_{l}\gt \,\max (TV)\times 10 \%$ and $TV$ represents the tidal breathing variation, $TV={\rm{\Delta }}{{\boldsymbol{\rho }}}_{{\rm{end}}-{\rm{ins}}}-{\rm{\Delta }}{{\boldsymbol{\rho }}}_{{\rm{end}}-\exp },$ in which ${\rm{\Delta }}{{\boldsymbol{\rho }}}_{{\rm{end}}-{\rm{ins}}}$ and ${\rm{\Delta }}{{\boldsymbol{\rho }}}_{{\rm{end}}-\exp }$ denotes the raw EIT images at the end-inspiration and end-expiration, respectively; ${T}_{\mathrm{inspiration},\mathrm{global}}$ represents the inspiration time calculated from the global impedance curve. For the time-series EIT images of each current injection of each subject, RVD of each pixel within the lung ventilation regions at each respiratory cycle was first calculated and then the mean value of RVD of each pixel over all respiratory cycle was computed, as denoted by ${\overline{RVD}}_{l}.$ Further, RVD_SD was calculated as the standard deviation of RVD of all pixels within the lung area: $RV{D}_{SD}=std(\ldots ,\,{\overline{RVD}}_{l},\ldots ).$

In addition, the relative change of each parameter was also calculated as follows: ${\rm{\Delta }}{X}_{n}=abs\left({X}_{n}-{X}_{ref}\right)/{X}_{ref},$ where ${X}_{ref}$ represents the reference/baseline and was defined as the value at 1 mA, $X$ denotes an EIT-based parameter, and $n$ indicates the current with a specified amplitude, including 1 mA, 500 uA or 250 uA.

The noise level relative to chest impedance increased with the decreasing current for both injection patterns (figures 3 and 5(a)), suggesting that current amplitude could significantly affect the noise level of the measured impedance. This may be related to the characteristics of chest impedance and noise. In EIT measurement, the respiratory impedance could be considered as differential signals proportional to current amplitude, and thus the decreased current directly reduced the amplitude of respiratory impedance. However, noise belongs to common-mode signal, and thus did not decrease proportionally to the current reduction (Li et al 2019b). Additionally, compared with opposite injection, adjacent injection had smaller SNR with the same amplitude of current (figure 5(a)) and SNR of adjacent injection decreased faster than that of opposite injection (figure 5(b)), which suggested better SNR performance of opposite injection within a small current. This may be attributed to the difference in the measurement principle of the two injection patterns. In the potential field of EIT, current is distributed dominantly near the excitation electrodes and thus the resulting potential decreases as the measurement electrode is located further away from the excitation electrodes (Wu et al 2021), as shown in figure 9. Because the voltmeter has the same noise power, SNR of the measured impedance at the far-end electrode becomes smaller compared to that at the near-end electrode (Li et al 2023). In terms of the distance between electrodes of measurement and electrodes, there are more electrodes far from the excitation electrodes in adjacent injection than those in opposite injection; therefore, the impedance obtained from these measurement channels was much smaller than that with opposite injection (figure 9). As a result, SNR of the whole chest impedance with adjacent injection was smaller than that with opposite injection when current of the same amplitude was applied.

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A significantly higher value of lung separation at the same amplitude of current (p < 0.01) was found in the fEIT images acquired with adjacent injection than those with opposite injection, suggesting that adjacent injection had improved resolution within the central area of the chest. This may be due to the difference in sensitivity distributions inside the chest with the two injection patterns. Figure 10 shows the image reconstruction of simulated lung ventilation for adjacent and opposite injection and their sensitivity distributions inside the chest. Similar to the reconstructed images of humans using the GREIT algorithm (NF = 0.5), adjacent injection had better lung separation compared to opposite injection (figure 6). Sensitivity distribution indicated that the sensitivity of opposite injection within the central area of the chest was higher than that of adjacent injection, i.e., the boundary potentials of the opposite injection were more sensitive to impedance change within the central area of the chest. In addition, because of the essential characteristics of low spatial resolution of EIT (Hentze et al 2021), the reconstructed values within the central area of the chest in the EIT image of opposite injection were larger than those of adjacent injection, which exhibited the relatively worse lung separation of opposite injection (Adler and Zhao 2023).

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For inverse artifacts at the same amplitude of current, a significant higher value (p < 0.01) was observed in the fEIT image when adjacent injection was applied instead of opposite injection, which indicates greater inverse artifacts produced by adjacent injection. The most plausible explanation for this phenomenon is the property of reconstruction algorithm together with the specific sensitivity distribution of adjacent injection. Ring artifacts are inevitable in EIT image reconstruction, which appear as areas with opposite sign surrounding lung ventilation regions, like the yellow area in the ventilation image of figure 10. Ring artifacts are typical of linear filter and also be called 'overshoot' for second-order systems ${\parallel {\bf{x}}\parallel }^{2},$ such as Gauss-Newton reconstruction approaches and the GREIT algorithm used in this study (Adler et al 2009, Adler et al 2011). Further, for ventilation imaging, the magnitude of ring artifacts between two lungs was enhanced by the superposition of ring artifacts derived from the ventilation regions on both sides because the bilateral lung ventilation could be viewed as two large imaging targets. Nevertheless, the lower sensitivity of adjacent injection within the central area of the chest could result in a smaller change of reconstructed impedance compared with opposite injection. Eventually, in the case of adjacent injection, ring artifacts of larger magnitude might exceed smaller impedance change, which showed up more inverse artifacts in ventilation images with adjacent injection. EIT is a functional imaging technique, not a structural imaging method like CT. The important reason is that during the EIT data collection process, the electrical current applied to the human thorax through surface electrodes does not flow in a straight line within the thorax. Furthermore, different patterns of current injection will form different current paths, which results in different sensitivity distributions. In other words, the different current injection patterns have different sensitivity to the same impedance change. As shown in figure 10 of the manuscript, the sensitivity distribution between opposite and adjacent current injections were different, so the locations of lungs between two injection patterns were different.

In terms of boundary artifacts at the same amplitude of current, the fEIT image of adjacent injection has a significantly higher value than that of opposite injection, indicating that adjacent injection could cause more boundary artifacts. Particularly for this pattern of injection, significant differences in boundary artifacts were found between the 125 uA group and the other three groups for adjacent injection as well. The probable explanation for this may be that adjacent injection had a lower SNR, that is to say, there was a relatively higher level of noise in the EIT measurement, which may originate from the intrinsic of internal components of the hardware system, the high-frequency noise caused by distributed capacitance formed by the circuit wiring of the hardware system, or external electromagnetic interference through electrode wires or human body coupling (Hong et al 2015, Li et al 2019b, Wu et al 2019). From the perspective of EIT image reconstruction, these measurement noises could be regarded as equivalent to the impedance change within regions near electrodes, which would be finally converted to boundary artifacts in the reconstructed images. Therefore, the lower SNR, the more boundary artifacts.

For opposite injection, except for ${\rm{\Delta }}RVD$ between the 125 uA group and the other two groups, the rest of the clinical parameters did not change significantly with the amplitude of current. For adjacent injection, $CoV,$ ${V}_{D}$ and $GI$ had significant changes when the amplitude of current decreased to 125 uA, and $RVD$ changed significantly once the current varied. These results suggested that the pattern of opposite injection performed better to maintain stable clinical parameters with the small currents compared with adjacent injection. In addition, $RVD$ was found to be the most sensitive parameter for current amplitude for both current injection patterns.

Because $CoV,$ ${V}_{D}$ and $GI$ were obtained from the fEIT image calculated by using the time-series EIT images throughout the respiratory cycle, these three parameters were determined by the respiratory phase. $RVD$ was obtained from the time-series EIT images in the inspiratory phase, so it was determined by the inspiratory phase. In this study, the participants were asked to maintain a sitting position with calm breathing throughout the whole data acquisition period. Accordingly, the time-series EIT images for each subject were periodically stable and thus the four clinical parameters were also stable.