Optimizing the Measurement Frequency in Electrical Impedance Tomography

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1 POSTER 2017, PRAGUE MAY 23 1 Optimizing the Measurement Frequency in Electrical Impedance Tomography Jakob ORSCHULIK 1, Tobias MENDEN 1 1 Philips Chair for Medical Information Technology, Helmholtz Institute for Biomedical Engineering, RWTH Aachen University, Pauwelsstr. 20, Aachen, Germany orschulik@hia.rwth-aachen.de, menden@hia.rwth-aachen.de Abstract. In electrical impedance tomography (EIT), a small alternating current is injected into the patient and the resulting voltages are measured at the body surface. From this, images are reconstructed that can be used for ventilation and cardiac monitoring. In modern EIT systems and in prototypes, the frequency of the injected current can be varied in a range between typically 50 khz and 250 khz. In this paper, we investigate the effect of the current injection frequency on EIT measurements. 76 logarithmically distributed frequencies between 1 khz and 1 MHz are simulated. The influence is investigated on both the raw data and the images. Keywords Electrical impedance tomography, current injection, bioimpedance, finite element modeling. 1. Introduction In recent years, electrical impedance tomography (EIT) moved closer from research towards clinical use. Currently, two commercial devices are available for clinical use: the Draeger PulmoVista 500 and the Swisstom BB 2. The general idea of EIT is to reconstruct images that are capable of displaying the impedance change inside the body from voltage measurements at the body surface. Even though the spatial resolution of these images is low compared to CT or MRI, high frame rates of up to 50 images per second allow an identification of dynamic processes such as breathing or cardiac activity. Currently, both commercial systems are used for ventilation monitoring allowing the setting of ventilation parameters based on regional information instead of global parameters such as the compliance. In addition to the clinical availability, research in the field of lung EIT increased over the past years addressing nearly every step of the EIT measurement chain: the positioning of the electrode belt [1], the influence of the injection and measurement pattern [2] and, in addition to the currently used linear GREIT reconstruction algorithm [3], nonlinear D-bar methods for image reconstruction [4] are investigated. This paper deals with the current injection frequency: all EIT systems inject a small, alternating current into the patient. The Pulmo- Vista 500 uses an adjustable frequency range from 80 khz to 130 khz while the Swisstom BB 2 injects current at 150 khz. However, the effect of the current frequency on both the measurement results and the reconstructed images is not clear. It is known that the conductivity of biological tissue is dependent on the measurement frequency. Additionally, the injection depth of the applied current varies with the frequency. Thus, the aim of this paper is to investigate the influence of the current frequency on EIT measurements. A simulation study is performed and the results are evaluated in both the raw data and the reconstructed images. A detailed finite element model of the human thorax is used and a total of 76 logarithmically distributed frequencies is used for evaluation. Additionally, the effect of noise on the EIT data is investigated. 2. Materials and Methods In this section, the materials and methods are introduced. After a brief introduction into the EIT measurement principle and the dielectric properties of body tissues, some general information on impedance measurements at different current frequencies are given. Finally, the simulation setup and the evaluation methods are introduced Electrical Impedance Tomography Electrical impedance tomography (EIT) is a biomedical imaging modality. The general idea is to reconstruct impedance changes inside the body from multiple impedance measurements at the body surface. Current EIT systems use an electrode belt with 16 electrodes, which is placed around the thorax. For each frame, 208 voltage or impedance measurements v i are recorded. The impedance change image Z with respect to a reference measurement v ref can then be reconstructed using the so-called GREIT algorithm [3]: Z = R M (v i v ref ), (1) where R M is the reconstruction matrix which maps voltage difference to an image. R M is calculated from a finiteelement model and is constant for one specific model. Typ-

2 2 J. ORSCHULIK, T. MENDEN, OPTIMIZING THE MEASUREMENT FREQUENCY IN ELETRICAL IMPEDANCE TOMOGRAPHY 2.3. Impedance measurements at different frequencies Fig. 1. Current path through biological tissue at low and high frequencies and electrical equivalent circuit (from [7]). The change of the current injection frequency has multiple effect on bioimpedance measurements. First of all, the maximal root mean square of the injection current is regulated in the standard IEC [8]: 100 µa f 1 khz f i RMS,max (f) = 100 µa 1 khz 1 khz < f < 100 khz. 10 ma f 100 khz (2) Thus, at an injection frequency of 1 khz, only 100 µa RMS are allowed while at higher frequencies above 100 khz, 10 ma RMS are permitted. The second effect on bioimpedance measurements is in the higher framerate that is possible at higher frequencies. In current systems, an IQ- Demodulation is performed to measure the impedance. Furthermore, a fixed number of oscillations, typically 10, is used for analog to digital conversion. At higher frequencies, the time needed for this oscillations is shorter. As 208 voltage measurements are performed for each EIT frame, the framerate grows linearly with the injection frequency Simulation Setup Fig. 2. Conductivity of different tissues between 1 khz and 1 MHz. ically, the images Z have a dimension of pixels and the information is used for ventilation and cardiac monitoring Dielectric properties of body tissues In general, the impedance of biological tissue is frequency dependent. Typically, biological tissue is modeled as a suspension of cells in a conductive fluid. While the extra- and intracellular fluids have a mostly resistive behavior, the cell membrane acts as an electrical isolator. Thus, the current paths through body tissue vary with the current frequency. At low frequencies, the current flows mainly around the cells through the extracellular fluid, whereas at high frequencies the current flows through both the extra- and the intracellular fluid as depicted in Fig. 1. This behavior can be modeled with the equivalent circuit as depicted in Fig. 1, right and is known as the Cole-Model [5]. In 1996, Gabriel et al. performed a characterization of the conductivity of different biological tissues in the frequency range between 10 Hz and 10 GHz [6]. In this paper, the conductivity values of deflated and inflated lung tissue, muscle and heart tissue from the Gabriel study will be integrated into a model. Fig. 2 shows the conductivity of these four tissues in the frequency range between 1 khz and 1 MHz. The simulation study in this paper was performed in Matlab using the Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EI- DORS) [9]. First, a finite element model of the human thorax was created as shown in Fig. 3. The shape of this model is available in EIDORS and has been published in a previous study by Grychtol et al. [10]. The model consists of four main parts: First, the lungs are modeled as two trimmed ellipsoids. Second, the heart is modeled as a smaller ellipsoid. Third, the remainder of the FE-model is modeled as muscle tissue. Finally, 16 electrodes are placed around the thorax. The conductivites for the different tissues are modeled to be frequency dependent as introduced in Section 2.2. From this model, an EIT measurement frame v i can be simulated. Furthermore, a reconstruction matrix R M can be calculated. In this study, we aim to simulate breathing activity. We do this by changing the conductivity of the lungs from deflated to inflated lung as provided in the Gabriel database (see Section 2.2). A total of 76 logarithmic distributed injection frequencies between 1 khz and 1 MHz is simulated. For each frequency, the following simulation steps are performed: 1. Calculate the reconstruction matrix R M for the given FE-model. 2. Set the conductivities for muscle and heart with respect to the frequency as shown in Fig Set the lung conductivity to deflated. 4. Simulate the reference voltage measurement v ref of an EIT frame. 5. Set the lung conductivity to inflated.

3 POSTER 2017, PRAGUE MAY 23 3 noise is known, the noise can be easily extracted by subtracting the real image from the noisy image. In order to obtain robust results, this process is performed 5000 times for each SNR level, which is set between 0 db and 50 db. Then, the mean resulting SNR in the images is calculated for each noise level. Note, that the exact same noise is added to the voltage difference at all frequencies. Thus, the SNR value is only true for 1 khz. The step is repeated for the voltages acquired when applying the maximal allowed current as shown in 2.3. Fig. 3. Finite Element Model of the human thorax. 6. Simulate the voltage v i of an EIT frame. Based on the simulated voltages, the impedance change image can be reconstructed by applying Z = R M (v i v ref ), which displays the impedance change due to the conductivity change of the lungs during breathing activity. A sample result is shown in the top left part of Fig Evaluation Criteria In this paper, we aim to investigate the effect of the current injection frequency on EIT. We do this by analyzing the effect in two key points of the EIT measurement chain: First, we analyze the raw data v i v ref. As introduced in Section 2.1, the images of the conductivity change are reconstructed from this voltage difference. Thus, we calculate the root mean square of this signal at a specific injection frequency. This is done both for a constant current amplitude of 100 µa RMS and for the maximal current amplitude as introduced in Section 2.3. The second key point is the reconstructed images. First, we analyze the reconstruction quality. This is done using the evaluation chain introduced in Fig. 4: For all frequencies, we extract the lung shape from the reconstructed images by performing a binarization of the images. All pixels that have a value greater then 25% of the maximum value are set to 1 while all other pixels are set to zero. As the biggest conductivity change occurs due to the changes in lung conductivity, this results in an estimate of the lung shape. Then, this image is compared to the true setup from the underlying model and the wrong pixels are counted. Second, we analyze the robustness to noise of the image reconstruction. This is done by adding white gaussian noise of a given signal-to-noise ratio to the voltage difference v i v ref. The following steps are performed: 1. Calculate white gaussian noise at a given SNR with respect to the voltage difference v i v ref. The voltage difference at 1 khz is used to determine the signal energy. 2. Add this noise to the voltage difference at all 76 frequencies. 3. Reconstruct the noisy EIT image. 4. Calculate the signal to noise ratio of the reconstructed EIT image. Since the reconstruction result without 3. Results In this section, we present the results of the simulation study. First, we show the influence of the injection frequency on the raw data. Then, we analyze the effect on the images Raw Data As mentioned in Section 2.1, the images are reconstructed from the difference of two voltage measurements. Thus, the higher the energy of the difference data, the lower the sensitivity additive to noise. Fig. 5(a) shows the root mean square of the difference data at a given injection frequency. Interestingly, the highest V RMS is achieved at f = 35 khz. For higher frequencies, the root mean square of the voltage difference drops significantly. However, this is only true when keeping the injection current amplitude constant for all frequencies. When applying the maximal allowed current amplitude, the result is different as shown in Fig. 5(b). Here, the highest V RMS is achieved at 100 khz. Thus, with respect to the raw data, the frequency should be set depending on the amplitude of the injected current. When choosing a current amplitude of 100 µa, f = 35 khz should be chosen while at higher currents 100 khz should be used. Higher frequencies, however, do not improve the raw signal Image data As introduced in Section 2.5, the evaluation of the image data was performed in two steps. The result of the reconstruction quality is shown in Fig. 6. At higher frequencies, the number of wrong pixels decreases. Thus, the frequency should be as high as possible. However, the improvement in the reconstruction is small as the number of wrong pixels is still in the same range. The noise sensitivity, shows a different relation. In Fig. 7(a), the signal to noise ratio in the images is shown at four different noise levels while keeping the amplitude of the injection current constant. First of all, the signal to noise ratio in the images is worse than in the raw data. On average, a 6 db drop in the signal to noise ratio is caused by the image reconstruction. Interestingly, however, the best signal to noise ratio is achieved at the lowest frequencies. This is especially surprising as the root mean square of the raw difference data is highest at 35 khz. However, the reconstruction maps the voltage measurements to

4 4 J. ORSCHULIK, T. MENDEN, OPTIMIZING THE MEASUREMENT FREQUENCY IN ELETRICAL IMPEDANCE TOMOGRAPHY Image Lung shape Difference Reconstructed True Fig.4. Evaluation chain. The lung shape is extracted from both the reconstructed image and the true FE-model. Then, the shapes are compared to each other. Fig. 6. Number of wrong pixels in reconstructed images as introduced in Section 2.5. (a) Constant current. the image plane, so that parts of the measured signal are amplified and other parts are attenuated. For the maximal permitted current, the result is shown in Fig. 7(b). Here, the best signal to noise ratio is achieved for a frequency of 100 khz. Fig. 5. (b) Maximal allowed current. Root mean square of the measured voltage difference v i v Ref at different injection frequencies. In 5(a), the current was held constant to 100 µa RMS while, in 5(b), it set to be the maximum allowed by EN (see Section 2.3). 4. Discussion and Conclusions In this paper, we investigated the impact of the current injection frequency on EIT measurements in a simulation study. 76 logarithmically distributed frequencies were simulated and the effect on both the raw measurement data and the image was evaluated. Unfortunately, the results do not provide a clear outcome, as different frequencies are best for the different evaluation steps. When observing the raw data, an injection frequency of 35 khz works best. However, when applying the maximal permitted current with respect to the standard IEC , an injection frequency of 100 khz should be used. When examining the reconstructed images, higher frequencies provide a better reconstruction result. However, the sensitivity for noise is also higher for high frequencies. At 100 µa, the best signal to noise ratio in the images was achieved at low frequencies, while at maximal current amplitudes, the result was best at 100 khz. In summary, we recommend a current frequency of 100 khz with the highest permitted current amplitude of 10 ma.

5 POSTER 2017, PRAGUE MAY 23 5 Fig. 7. (a) Constant current. (b) Maximal allowed current. Signal to noise ratio in the images at four different noise levels of the voltage difference at 1 khz. Note, that the exact same noise was added to the voltage difference at all frequencies. B., DIXON, P., FAES, T.J.C., FRERICHS, I., GAGNON, H., GÄRBER, Y., GRYCHTOL, B., HAHN, G., LIONHEART, W.R.B., MALIK, A., PATTERSON, R.P., STOCKS, J., TIZZARD, A., WEILER, N., WOLF, G.K., Greit: a unified approach to 2d linear eit reconstruction of lung images., Physiological Measurement, 2009, vol. 30, no. 6, pp. S35 S55. [4] HERRERA, C.N.L., VALLEJO, M.F.M., MUELLER, J.L., LIMA, R.G., Direct 2-d reconstructions of conductivity and permittivity from EIT data on a human chest, IEEE Transactions on Medical Imaging, 2015, vol. 34, no. 1, pp [5] COLE, K.S., COLE, R.H., Dispersion and absorption in dielectrics i. alternating current characteristics, The Journal of Chemical Physics, 1941, vol. 9, no. 4, pp [6] GABRIEL, C., GABRIEL, S., CORTHOUT, E., The dielectric properties of biological tissues: I. literature survey., Phys Med Biol, 1996, vol. 41, no. 11, pp [7] SCHLEBUSCH, T., RÖTHLINGSHÖFER, L., KIM, S., KÖNY, M., LEONHARDT, S., On the road to a textile integrated bioimpedance early warning system for lung edema, 2010 International Conference on Body Sensor Networks, Institute of Electrical and Electronics Engineers (IEEE), [8] DIN, Medical electrical equipment - part 1: General requirements for basic safety and essential performance (iec : cor. : cor. : a1:2012);. [9] ADLER, A., LIONHEART, W.R.B., Uses and abuses of eidors: an extensible software base for eit., Physiological Measurement, 2006, vol. 27, no. 5, pp. S25 S42. [10] GRYCHTOL, B., MÜLLER, B., ADLER, A., 3d EIT image reconstruction with GREIT, Physiological Measurement, 2016, vol. 37, no. 6, pp About the Authors However, certain limitations apply to this study which will be addressed in future work. First, the finite element model only consists of three different tissues. No bones, fat or other organs are included into this model. Furthermore, the ventilation is modeled only with a conductivity change. No movement or dynamics are included into the model. The noise model used in this study was purely additive. Nevertheless, the results show that the current frequency has an important role in EIT measurements. Acknowledgements Research described in the paper was supervised by Prof. Dr.-Ing. Dr. med. Steffen Leonhardt and Dr.-Ing. Marian Walter. Jakob Orschulik gratefully acknowledges financial support provided by the German Research Foundation (DFG), grant no. LE 817/20-1. References [1] BUZKOVA, K., ROUBIK, K., The effect of electrode belt size selection upon evaluation of the distribution of ventilation using electrical impedance tomography, 2015 E-Health and Bioengineering Conference (EHB), IEEE, [2] ADLER, A., GAGGERO, P.O., MAIMAITIJIANG, Y., Adjacent stimulation and measurement patterns considered harmful., Physiological Measurement, 2011, vol. 32, no. 7, pp [3] ADLER, A., ARNOLD, J.H., BAYFORD, R., BORSIC, A., BROWN, Jakob ORSCHULIK was born in Mikolow, Poland and received the B.Sc. and M.Sc. degrees from RWTH Aachen University, Aachen, Germany in 2011 and 2013, respectively. He is currently a research associate and Ph.D. student at the Philips Chair for Medical Information Technology, Helmholtz-Institute for Biomedical Engineering at RWTH Aachen University. His research interests include bioimpedance spectroscopy and electrical impedance tomography. Tobias MENDEN was born January 25th, 1990 in Bad Honnef, Germany. In June 2016 he received the M.Sc. degree in Electrical Engineering with specialisation on Biomedical Engineering from the RWTH Aachen University, Germany. Currently he is working as a research associate and Ph.D. student at the Philips Chair for Medical Information Technology, Helmholtz-Institute for Biomedical Engineering at RWTH Aachen University. His research interests include electrical impedance tomography with a focus in the hardware measurement chain.