Three-dimensional pulmonary monitoring using focused electrical impedance measurements

The conducted research is not related to either human or animals use.

In bioimpedance measurements, a tetrapolar electrode setup is typically used to measure an electrical impedance. In this setup, two electrodes are used to inject a small, alternating current into the body while two separate electrodes are measuring the resulting voltage drop across those electrodes. In contrast to impedance-based imaging techniques such as Electrical Impedance Tomography, where multiple measurements are performed at different electrode locations, single tetrapolar measurements typically do not contain any spatial information, especially if the electrodes are placed far away from each other, for example in hand-to-hand or hand-to-foot configurations. However, when optimizing the electrode positions to specific placement strategies, measurements can be focused to desired regions of interest [16]. In particular, we showed in earlier work that impedance measurements can be focused to specific lung regions [6, 7]. For better understanding and readability of this article, the criteria will be repeated in this section.

In general, the measured impedance of a tetrapolar impedance measurement can be described using eq. (1):

where Z is the measured impedance, J→LE(v)andJ→LI(v)$${{\vec{J}}_{LE}}\left( v \right)\,\,\operatorname{and}\,\,{{\vec{J}}_{LI}}\left( v \right)$$are the current density of the injecting and sensing electrode pair, respectively, and σ(ν) is the conductivity in a given location ν [17, 18, 19]. It should be noted that Z is not the physical impedance of the body or between one electrode pair, but should be interpreted rather as a local transfer function given an input injected current and an output measured voltage drop. Thus, while analyzing Z does not necessarily allow an interpretation of the dielectric properties of the investigated body part, an analysis of the impact of certain locations on Z can be estimated.

In particular, we extract two measures from eq. (1): The sensitivity S(ν) and the local impedance contribution ζ(ν):

The sensitivity S(ν) describes the impact of a local conductivity change on the measured impedance, while the local impedance contribution ζ(ν) describes the contribution of a specific location ν to the measured transfer impedance Z. Both the sensitivity and the local impedance contribution can be both positive and negative. A local conductivity increase in areas with positive local sensitivity will result in a decrease of the measured impedance, whereas in areas with negative local sensitivity, a local increase in conductivity will increased the measured impedance. For local impedance contribution, the behavior is similar: areas with a positive local impedance contribution increase the measured impedance, while areas with a negative contribution decrease the measured transfer impedance.

Now, in order to evaluate a tetrapolar electrode configuration with respect to its capability to focus on a specific region of interest (ROI) inside the lung, criteria were defined which are beneficial for focused impedance measurement [6, 7]: Let L_ROI be the ROI inside the lung. Let further L_ROI be the remainder of the lung. Then, the following criteria can be defined:

The selectivity measures the mean sensitivity inside the ROI compared to the mean sensitivity in the remainder of the lung. Thus, it is a measure on how much a conductivity change inside the ROI will be visible in the measured impedance compared to a sensitivity change in the remainder of the lung. The higher the sensitivity, the higher the impact of an impedance change inside ROI on the measurement data.

The homogeneity measures the distribution of the sensitivity inside the ROI. A high homogeneity value means that changes in the complete ROI have a similar impact on the measured impedance.

The Impedance Contribution Ratio shows, how much the ROI contributes to the measured impedance. The higher I_%, the higher the impact of the ROI on the actual impedance value. If for example I_% = 50%, the ROI accounts for half of the measured impedance value. However, I_% does not measure the impact of an impedance change in this ROI.

Fig. 1 shows sample sensitivity distributions and their impact on the criteria. Here, the ROI is highlighted with the dashed circle in the center. Fig. 1 a.) shows the ideal distribution, where a high sensitivity is present inside the ROI while the sensitivity is zero outside the ROI. This ideal case, however, cannot be achieved by single tetrapolar measurements, as the sensitivity will not be zero everywhere outside the ROI, especially if the electrodes are placed outside the ROI, as the current density is highest close to the electrodes. Fig. 1 b.) shows a distribution, where a high sensitivity peak is visible inside the ROI. This distribution possesses a high Selectivity, but a low Homogeneity value. In Fig. 1 c.), the sensitivity is spread homogeneously inside the ROI and drops slowly outside the ROI. In this distribution, the Homogeneity value is high while the Selectivity is low. The local impedance contribution can be determined by multiplying the Sensitivity and the local conductivity. Thus, while only areas with a nonzero sensitivity contribute to the measured impedance, also areas with a low sensitivity may have a significant contribution to the measured impedance, if they occur in areas with a low local conductivity.

Fig. 1

In this paper, we use the results obtained in [6] as a basis, where guidelines for electrode placement were established in a simulation study. We use these guidelines in order to perform simulations in Matlab and a water tank experiment.

In order to avoid results that are only valid in a specific model, the simulation setup in this study is different to the simulation setup used for our previous optimization of the electrode configurations [6, 7]. While in the previous study CST has been used for simulation, the simulations in this study were performed in Matlab (MathWorks Inc., USA) using the EIDORS framework [20] and NETGEN [21]. Furthermore, a female model has been used in the previous study while the geometry of a male human thorax from [14] was used in this study. Only the derived electrode positions were applied to this study leading to the assumption that the results shown in this paper are not limited to the finite element model or simulation environment.

The lung was split into eight regions of interest (right/left, back/front, bottom/top) and for each ROI, a specific tetrapolar electrode setup was placed at the body surface based on the aforementioned guidelines. Fig. 2 shows the model, including the lung and the heart, and the tetrapolar configuration for the left, back bottom and the right, front, top region of interest. The respective ROI is highlighted in yellow. The values for the complex, frequency-dependent conductivity of the different organs were set according to the Gabriel database [22]. The background was set to the conductivity value of muscle tissue. Breathing was simulated by varying the conductivity of the lung between the conductivity value of deflated lung (0% inflated) and the conductivity value for inflated lung (100% inflated). For one breathing cycle, 21 breathing levels were simulated. Fig. 3 demonstrates the breathing activity for one cycle.

Fig. 2

Fig. 3

Three different pathologies were simulated in this study: atelectasis, pneumonia and edema [23]. In atelectasis, parts of the lungs are collapsed. Thus, in order to simulate an atelectasis, the ROI of the lung which suffers from atelectasis was set to 0% inflated while the other lung parts performed a normal breathing step as described above. In pneumonia, typically, parts of the lungs become inflamed. Thus, an combination of blood and pus is accumulated in the affected regions. Pus is characterized by the high amount of cells. As no conductivity value for pus is available in the Gabriel database, the conductivity of the affected regions was set to the conductivity value of the spleen, which has similar properties regarding cell structure, in order to simulate pneumonia. In edema, body fluid is accumulated inside the affected lung regions. Hence, the respective lung regions were simulated to be filled with isotonic saline solution to simulate lung edema. All simulations were performed at each of the 21 respiration levels. Additionally, in order to provide both a temporal and a spectroscopic analysis, simulations of the complex, frequency-dependent impedance measurements from 10 kHz to 1MHz were also performed at each of the 21 lung states.

In order to validate the focusing capability of the electrode configurations, an experimental measurement using a water tank phantom was performed. The tank consists of four individual lung lobes, which are represented by balloons. Fig. 4 shows an image of the water tank.

Fig. 4

The tank is filled with saline solution. Each lung lobe can be activated and deactivated manually by adjusting the connecting valve. Impedance measurements were performed using the Draeger EEK2 EIT device. To compare the experimental results to the simulation, both conventional 16 electrode single belt EIT measurements and impedance measurements focused on the regions left bottom and right top were performed. After a 30 s baseline measurement, each lung lobe was separately disabled for 30 s.

The simulations results in this chapter will be presented for two exemplary regions of interest: The region left, back, bottom (lbb) and the region right, front, top (rft). This is motivated by different clinical scenarios: Typically, the back regions are affected by atelectasis, especially in mechanically ventilated patients when lying on the back. One way of addressing this issue is to turn the patient around, which might lead to atelectasis in the then dependent front region. Furthermore, front top regions are typically associated with pneumothorax, where no ventilation activity will be present as an accumulation of air inside the pleural cave prevents the ventilation in this regions.

The evaluation criteria introduced in the Materials and Methods section were applied to the respective region of interest. The numerical results for both regions are shown in Tab. 1.

In both regions, the selectivity is greater than one, which means that conductivity changes inside the ROI have a higher impact on the measured impedance than conductivity changes elsewhere. Furthermore, the contribution of the ROI in the measured impedance is approx. 3% in the lbb region and approx. 7.5% in the rft region. While this may not seem much, one should keep in mind that other parts of the thorax contribute to the measured impedance itself. Typically, however, these parts, such as the muscles or bones, do not change their conductivity during a breathing cycle so that the selectivity is the most important criterion to detect local conductivity changes.

In Fig. 5a, a simulation result for an impedance measurement focused on the ROI lbb during one breathing cycle is shown. The measurements were simulated at a frequency of 10 kHz and the absolute value of the complex impedance is presented. In blue, the healthy state where all lung regions are ventilated is shown. In red, an atelectasis is simulated inside the ROI. It is apparent, that the impedance curve is highly affected by the lack of ventilation inside the region of interest. Furthermore, in green, an atelectasis is simulated in the left front bottom (lfb) region of the lung, which is adjacent to the lbb focus region. During this simulation, almost no impact on the measurement result can be observed. This corresponds to the high selectivity of the electrode configuration of 31.3 for the lbb region. The impedance change inside the ROI has a much higher impact on the measurement result than an impedance change in other lung regions.

In Fig. 5b, the impact of the different pathologies on the measurement during one breathing cycle is presented. It is apparent that the impedance change during the breathing cycle decreases compared to the impedance change in healthy state. This is not surprising, as the affected lung region does not participate in the ventilation activity. It can be also observed that the baseline of the measurement is dependent on the type of pathology. This pathology dependent impedance is visualized in Fig. 5c, where the complex impedance spectrum in the frequency range between 10 kHz and 1MHz is shown. It is apparent that each pathology has a different impact on the measured spectrum. Especially when comparing the healthy state to the pneumonia, it is visible that a pathological lobe does not only change the magnitude, but also the phase and frequency behavior of the measured impedance.

For the right, front, top region, the result during one breathing cycle is shown in Fig. 6a, Here, in order to show that the concept is valid for the complete frequency range, the current injection frequency was simulated to be 1 MHz. Again, the healthy reference data is shown in blue. In red, atelectasis was simulated inside the ROI (rft) and in green, the pathology was simulated outside the ROI in an adjacent lung lobe (rbt). In principle, the result for this ROI is similar to the result of the lbb region in Fig 5a: A pathology inside the ROI has a higher impact on the measured impedance than a pathology in a different region. However, there are two differences between the lbb and rft result: While in the lbb case, almost no ventilation is visible in the focused pathological case (red curve in Fig 5a), ventilation is still visible in the rft case (red curve in Fig 6a). Furthermore, the difference between the healthy state and the pathological state in a different region of the ROI is higher (difference between the blue and green curve in Fig 5a and Fig. 6a). This, however, is not surprising as the selectivity of the focusing configuration for the rft region is smaller than the selectivity for the lbb region (9.15 vs. 31.3). In the pathological state, the ventilation activity is limited to the non-pathological lung regions which are not focused by the electrode configuration. The lower the selectivity, the more of these changes outside the ROI will be represented in the impedance data. Thus, the temporal data shows the expected behavior.

Fig. 5

Nevertheless, the lower selectivity configurations still amplify conductivity changes inside the ROI. This is demonstrated in Fig. 6b and Fig. 6c. In Fig. 6b, the impact of the different pathologies inside the ROI on the temporal data at 1MHz is shown. In Fig. 6c, the respective impedance spectra are presented. Again, the impact of the pathology is clearly visible in both the temporal and the spectroscopic data.

Fig. 6

As mentioned in the Introduction, the general idea of EIT is to reconstruct conductivity changes inside the body from multiple impedance measurements at the body surface. Typically, this is done in a single plane. Thus, in order to compare the focused tetrapolar results to EIT, simulations were performed in the exact same model using a simulated electrode belt of 16 electrodes. For image reconstruction, the GREIT algorithm was used [13] (settings: number of targets = 500, target-size = 0.03, noise-figure = 0.5). As EIT typically reconstructs conductivity changes with respect to a given reference, the inhaled state is referenced to the exhaled state.

In Fig. 7, the resulting EIT images for the healthy reference and the pathological scenarios are presented. In the top row, the pathology is present in the left, back, bottom region of the lung. The resulting image is similar for all three pathological cases. This is not surprising, as the pathological lobe does not contribute to the ventilation and thus does not change its conductivity between the exhaled and inhaled state. As EIT seeks to display conductivity changes, a time-invariant conductivity change inside a specific lobe does not have a high impact on the reconstructed images. Nevertheless, an analysis of the images allows the conclusion that ventilation activity is restricted in the back, left region. However, no three dimensional information can be extracted.

Fig. 7

The images for a pathology in the right, front, top region are shown in the bottom row. Interestingly, a pathology inside this region has almost no impact on the reconstructed EIT images. The main reason for this is that the bottom regions of the lung have a higher volume than the top lung regions. This leads to a ventilation in the right front lung region, although only the bottom part of the front lung region is actually ventilated. A pure analysis of the EIT images would lead to the conclusion that the ventilation is homogeneously distributed, which is not the case in the pathological scenario.

In reality, of course, it is very unlikely that a specific lung region does not contribute to the ventilation while the other lobes are completely healthy. Nevertheless, some pathologies, such as lobar pneumonia, are primarily located in specific lobes. If misinterpretations due to reconstruction occur even in the simulated extreme case, there is a high possibility that EIT-image based criteria such as the ventilation inhomogeneity might over- or underestimate the real condition inside the lungs.

This result is not surprising, as EIT maps a three dimensional problem to one specific, two-dimensional image plane. The off plane sensitivity region of EIT is described to be a lens shaped region, which extends to approx. of the body diameter [24, 25]. The exact sensitivity region is, however, dependent on the geometry, the conductivity distribution inside the body, and the current injection and voltage measurement strategy. Furthermore, in single belt EIT, changes below and above the electrode plane can not be distinguished from each other. The proposed focused impedance measurement strategies overcomes this issue by addressing specific lung regions with individual electrode configurations. This, however, comes at the price of a decreased spatial resolution, as only regions can be analyzed, and a potentially higher effort in hardware, as four electrodes are needed for each region of interest.

In order to validate the simulation results in an experimental setup, a water tank experiment was performed. The Draeger EEK2 EIT device was attached to the water tank phantom as described in the Materials and Methods section. To remove noise, the data was filtered with a simple mean-median filter. Electrodes were placed both in a single plane for EIT measurements and in configurations focusing the bottom left and top right region. In Fig. 8, the result of the experimental study is shown. The measurements are split into five phases. In phase I, all balloons were ventilated. The EIT image shows a typical result with an impedance change in both the left and right lung. Also, the raw data of the configurations focused on the bottom left and top right region shows normal ventilation.

Fig. 8

At 30 s, the valve to the bottom left lobe was closed so that on the left side ventilation was only present in the top region while the right side was homogeneously ventilated in both the bottom and top region (phase II). In the EIT image, a decrease in impedance change in the left lung can be observed. In the raw data of the focused impedance measurement, almost no ventilation activity can be seen in the left bottom focusing configuration. In contrast, the right top focusing configuration shows a similar behavior as during the baseline measurement.

In phase III, the top left region is disabled while the other regions are normally ventilated. Similar to phase II, the impedance change in the EIT image decreases compared to the baseline. When comparing phase II and

phase III to each other, the EIT image shows a shift in impedance activity towards the center. In reality, however, no ventilation is present in the center but the ventilation occurs in distinct regions on the left and right side. In the raw data, the left bottom configuration shows a similar signal as in the baseline measurement. In the right top region, however, a small shift in the base impedance can be observed, while the amplitude of the impedance change remains constant.

In phase IV, the right bottom region is disabled. In the EIT image, the expected result is visible as the impedance change in the right lung appears to be decreased. In the raw data, again, almost no impact on the signal of the configuration focusing the left bottom region can be seen. In the signal in the right top configuration, however, a change in both baseline and ventilation amplitude is visible.

Finally, in phase V, the top right region is disabled. The EIT image is very similar to the image in phase IV, so that a decrease in impedance activity is present in the right lung region. When observing the raw data, the left bottom focusing configuration is not changed by the lack of ventilation in the right top region. The bottom right configuration, however, shows a big signal change. Both the baseline and the change in amplitude due to ventilation are decreased significantly. Nevertheless, ventilation activity is still visible in this data even though no ventilation is present in the focus region.

Overall, the experimental results confirm the simulations. In EIT, a general decrease in ventilation inside the left and right lung can be detected. However, it is unclear at which height the lack of ventilation exists. Furthermore, it cannot be distinguished, if the ventilation is decreased in the top and bottom region by 50% or if one region is completely collapsed. In contrast, in the raw data, the affected region can be identified. In the experiment the data focused on the left bottom region showed a much better result than the configuration focused on the right top region. This, however, can be explained by the physical realization of the water tank: First, the electrode positions are fixed and cannot be adjusted. Thus, it was not possible to place the electrodes optimally, especially in the right top region. Nevertheless, a high selectivity was achieved for the left bottom region while the right top region apparently has a lower selectivity, so that impedance changes in other regions have an impact on the measured data as well. Second, the inflation and deflation of the balloons causes the water level to change as well. This has a higher impact on the top regions than on the bottom regions. In total, however, even in the less focusing right top configuration the non-ventilated case is clearly visible. Even more, by combination of multiple measurements (for example top and bottom right), a more precise localization should be possible.