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Optimizing the Measurement Frequency in ElectricalImpedance Tomography

Jakob ORSCHULIK1, Tobias MENDEN1

1Philips Chair for Medical Information Technology, Helmholtz Institute for Biomedical Engineering,RWTH Aachen University, Pauwelsstr. 20, 52074 Aachen, Germany

orschulik@hia.rwth-aachen.de, menden@hia.rwth-aachen.de

Abstract. In electrical impedance tomography (EIT), asmall alternating current is injected into the patient and theresulting voltages are measured at the body surface. Fromthis, images are reconstructed that can be used for ventila-tion and cardiac monitoring. In modern EIT systems and inprototypes, the frequency of the injected current can be var-ied in a range between typically 50 kHz and 250 kHz. In thispaper, we investigate the effect of the current injection fre-quency on EIT measurements. 76 logarithmically distributedfrequencies between 1 kHz and 1 MHz are simulated. The in-fluence is investigated on both the raw data and the images.

KeywordsElectrical impedance tomography, current injection,bioimpedance, finite element modeling.

1. IntroductionIn recent years, electrical impedance tomography (EIT)

moved closer from research towards clinical use. Currently,two commercial devices are available for clinical use: theDraeger PulmoVista 500 and the Swisstom BB2. The gen-eral idea of EIT is to reconstruct images that are capableof displaying the impedance change inside the body fromvoltage measurements at the body surface. Even though thespatial resolution of these images is low compared to CT orMRI, high frame rates of up to 50 images per second al-low an identification of dynamic processes such as breathingor cardiac activity. Currently, both commercial systems areused for ventilation monitoring allowing the setting of ven-tilation parameters based on regional information instead ofglobal parameters such as the compliance. In addition tothe clinical availability, research in the field of lung EIT in-creased over the past years addressing nearly every step ofthe EIT measurement chain: the positioning of the electrodebelt [1], the influence of the injection and measurement pat-tern [2] and, in addition to the currently used linear GREITreconstruction algorithm [3], nonlinear D-bar methods forimage reconstruction [4] are investigated. This paper dealswith the current injection frequency: all EIT systems injecta small, alternating current into the patient. The Pulmo-

Vista 500 uses an adjustable frequency range from 80 kHz to130 kHz while the Swisstom BB2 injects current at 150 kHz.However, the effect of the current frequency on both themeasurement results and the reconstructed images is notclear. It is known that the conductivity of biological tissueis dependent on the measurement frequency. Additionally,the injection depth of the applied current varies with the fre-quency.

Thus, the aim of this paper is to investigate the influ-ence of the current frequency on EIT measurements. A sim-ulation study is performed and the results are evaluated inboth the raw data and the reconstructed images. A detailedfinite element model of the human thorax is used and a to-tal of 76 logarithmically distributed frequencies is used forevaluation. Additionally, the effect of noise on the EIT datais investigated.

2. Materials and MethodsIn this section, the materials and methods are intro-

duced. After a brief introduction into the EIT measurementprinciple and the dielectric properties of body tissues, somegeneral information on impedance measurements at differentcurrent frequencies are given. Finally, the simulation setupand the evaluation methods are introduced.

2.1. Electrical Impedance Tomography

Electrical impedance tomography (EIT) is a biomed-ical imaging modality. The general idea is to recon-struct impedance changes inside the body from multipleimpedance measurements at the body surface. Current EITsystems use an electrode belt with 16 electrodes, which isplaced around the thorax. For each frame, 208 voltage orimpedance measurements vi are recorded. The impedancechange image ∆Z with respect to a reference measurementvref can then be reconstructed using the so-called GREIT al-gorithm [3]:

∆Z = RM · (vi − vref), (1)

where RM is the reconstruction matrix which maps volt-age difference to an image. RM is calculated from a finite-element model and is constant for one specific model. Typ-

2 J. ORSCHULIK, T. MENDEN, OPTIMIZING THE MEASUREMENT FREQUENCY IN ELETRICAL IMPEDANCE TOMOGRAPHY

Fig. 1. Current path through biological tissue at low and highfrequencies and electrical equivalent circuit (from [7]).

Fig. 2. Conductivity of different tissues between 1 kHz and1 MHz.

ically, the images ∆Z have a dimension of 32 × 32 pixelsand the information is used for ventilation and cardiac mon-itoring.

2.2. Dielectric properties of body tissues

In general, the impedance of biological tissue is fre-quency dependent. Typically, biological tissue is modeledas a suspension of cells in a conductive fluid. While theextra- and intracellular fluids have a mostly resistive behav-ior, the cell membrane acts as an electrical isolator. Thus, thecurrent paths through body tissue vary with the current fre-quency. At low frequencies, the current flows mainly aroundthe cells through the extracellular fluid, whereas at high fre-quencies the current flows through both the extra- and theintracellular fluid as depicted in Fig. 1. This behavior canbe modeled with the equivalent circuit as depicted in Fig. 1,right and is known as the Cole-Model [5]. In 1996, Gabrielet al. performed a characterization of the conductivity ofdifferent biological tissues in the frequency range between10 Hz and 10 GHz [6]. In this paper, the conductivity valuesof deflated and inflated lung tissue, muscle and heart tissuefrom the Gabriel study will be integrated into a model. Fig. 2shows the conductivity of these four tissues in the frequencyrange between 1 kHz and 1 MHz.

2.3. Impedance measurements at different fre-quencies

The change of the current injection frequency has mul-tiple effect on bioimpedance measurements. First of all, themaximal root mean square of the injection current is regu-lated in the standard IEC 60601-1 [8]:

iRMS,max(f) =

100µA f ≤ 1 kHz100µA · f

1 kHz 1 kHz < f < 100 kHz10 mA f ≥ 100 kHz

.

(2)Thus, at an injection frequency of 1 kHz, only 100µARMS are allowed while at higher frequencies above100 kHz, 10 mA RMS are permitted. The second effect onbioimpedance measurements is in the higher framerate thatis possible at higher frequencies. In current systems, an IQ-Demodulation is performed to measure the impedance. Fur-thermore, a fixed number of oscillations, typically 10, is usedfor analog to digital conversion. At higher frequencies, thetime needed for this oscillations is shorter. As 208 voltagemeasurements are performed for each EIT frame, the fram-erate grows linearly with the injection frequency.

2.4. Simulation Setup

The simulation study in this paper was performed inMatlab using the Electrical Impedance Tomography andDiffuse Optical Tomography Reconstruction Software (EI-DORS) [9]. First, a finite element model of the human tho-rax was created as shown in Fig. 3. The shape of this modelis available in EIDORS and has been published in a previousstudy by Grychtol et al. [10]. The model consists of fourmain parts: First, the lungs are modeled as two trimmed el-lipsoids. Second, the heart is modeled as a smaller ellipsoid.Third, the remainder of the FE-model is modeled as muscletissue. Finally, 16 electrodes are placed around the thorax.The conductivites for the different tissues are modeled to befrequency dependent as introduced in Section 2.2. From thismodel, an EIT measurement frame vi can be simulated. Fur-thermore, a reconstruction matrix RM can be calculated. Inthis study, we aim to simulate breathing activity. We do thisby changing the conductivity of the lungs from deflated toinflated lung as provided in the Gabriel database (see Sec-tion 2.2). A total of 76 logarithmic distributed injection fre-quencies between 1 kHz and 1 MHz is simulated. For eachfrequency, the following simulation steps are performed:

1. Calculate the reconstruction matrix RM for the givenFE-model.

2. Set the conductivities for muscle and heart with respectto the frequency as shown in Fig. 2.

3. Set the lung conductivity to deflated.

4. Simulate the reference voltage measurement vref of anEIT frame.

5. Set the lung conductivity to inflated.

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Fig. 3. Finite Element Model of the human thorax.

6. Simulate the voltage vi of an EIT frame.

Based on the simulated voltages, the impedance change im-age can be reconstructed by applying ∆Z = RM · (vi−vref),which displays the impedance change due to the conductiv-ity change of the lungs during breathing activity. A sampleresult is shown in the top left part of Fig. 4.

2.5. Evaluation Criteria

In this paper, we aim to investigate the effect of thecurrent injection frequency on EIT. We do this by analyzingthe effect in two key points of the EIT measurement chain:First, we analyze the raw data vi − vref. As introduced inSection 2.1, the images of the conductivity change are re-constructed from this voltage difference. Thus, we calcu-late the root mean square of this signal at a specific injectionfrequency. This is done both for a constant current ampli-tude of 100µA RMS and for the maximal current amplitudeas introduced in Section 2.3. The second key point is thereconstructed images. First, we analyze the reconstructionquality. This is done using the evaluation chain introducedin Fig. 4: For all frequencies, we extract the lung shape fromthe reconstructed images by performing a binarization of theimages. All pixels that have a value greater then 25% of themaximum value are set to 1 while all other pixels are set tozero. As the biggest conductivity change occurs due to thechanges in lung conductivity, this results in an estimate ofthe lung shape. Then, this image is compared to the truesetup from the underlying model and the wrong pixels arecounted. Second, we analyze the robustness to noise of theimage reconstruction. This is done by adding white gaussiannoise of a given signal-to-noise ratio to the voltage differencevi − vref. The following steps are performed:

1. Calculate white gaussian noise at a given SNR with re-spect to the voltage difference vi − vref. The voltagedifference at 1 kHz is used to determine the signal en-ergy.

2. Add this noise to the voltage difference at all 76 fre-quencies.

3. Reconstruct the noisy EIT image.4. Calculate the signal to noise ratio of the reconstructed

EIT image. Since the reconstruction result without

noise is known, the noise can be easily extracted bysubtracting the real image from the noisy image.

In order to obtain robust results, this process is performed5000 times for each SNR level, which is set between 0 dBand 50 dB. Then, the mean resulting SNR in the images iscalculated for each noise level. Note, that the exact samenoise is added to the voltage difference at all frequencies.Thus, the SNR value is only true for 1 kHz. The step is re-peated for the voltages acquired when applying the maximalallowed current as shown in 2.3.

3. ResultsIn this section, we present the results of the simulation

study. First, we show the influence of the injection frequencyon the raw data. Then, we analyze the effect on the images.

3.1. Raw Data

As mentioned in Section 2.1, the images are recon-structed from the difference of two voltage measurements.Thus, the higher the energy of the difference data, the lowerthe sensitivity additive to noise. Fig. 5(a) shows the rootmean square of the difference data at a given injection fre-quency. Interestingly, the highest VRMS is achieved at f =35 kHz. For higher frequencies, the root mean square of thevoltage difference drops significantly. However, this is onlytrue when keeping the injection current amplitude constantfor all frequencies. When applying the maximal allowed cur-rent amplitude, the result is different as shown in Fig. 5(b).Here, the highest VRMS is achieved at 100 kHz. Thus, withrespect to the raw data, the frequency should be set depend-ing on the amplitude of the injected current. When choosinga current amplitude of 100µA, f = 35 kHz should be cho-sen while at higher currents 100 kHz should be used. Higherfrequencies, however, do not improve the raw signal.

3.2. Image data

As introduced in Section 2.5, the evaluation of the im-age data was performed in two steps. The result of the recon-struction quality is shown in Fig. 6. At higher frequencies,the number of wrong pixels decreases. Thus, the frequencyshould be as high as possible. However, the improvement inthe reconstruction is small as the number of wrong pixels isstill in the same range. The noise sensitivity, shows a dif-ferent relation. In Fig. 7(a), the signal to noise ratio in theimages is shown at four different noise levels while keepingthe amplitude of the injection current constant. First of all,the signal to noise ratio in the images is worse than in theraw data. On average, a 6 dB drop in the signal to noise ratiois caused by the image reconstruction. Interestingly, how-ever, the best signal to noise ratio is achieved at the lowestfrequencies. This is especially surprising as the root meansquare of the raw difference data is highest at 35 kHz. How-ever, the reconstruction maps the voltage measurements to

4 J. ORSCHULIK, T. MENDEN, OPTIMIZING THE MEASUREMENT FREQUENCY IN ELETRICAL IMPEDANCE TOMOGRAPHY

Image Lung shape Difference

True

Reconstructed

Fig.4. Evaluation chain. The lung shape is extracted from both the reconstructed image and the true FE-model. Then, the shapesare compared to each other.

(a) Constant current.

(b) Maximal allowed current.

Fig. 5. Root mean square of the measured voltage differencevi − vRef at different injection frequencies. In 5(a), thecurrent was held constant to 100µA RMS while, in 5(b),it set to be the maximum allowed by EN 60601-1 (seeSection 2.3).

Fig. 6. Number of wrong pixels in reconstructed images as in-troduced in Section 2.5.

the image plane, so that parts of the measured signal are am-plified and other parts are attenuated. For the maximal per-mitted current, the result is shown in Fig. 7(b). Here, the bestsignal to noise ratio is achieved for a frequency of 100 kHz.

4. Discussion and ConclusionsIn this paper, we investigated the impact of the current

injection frequency on EIT measurements in a simulationstudy. 76 logarithmically distributed frequencies were sim-ulated and the effect on both the raw measurement data andthe image was evaluated. Unfortunately, the results do notprovide a clear outcome, as different frequencies are bestfor the different evaluation steps. When observing the rawdata, an injection frequency of 35 kHz works best. How-ever, when applying the maximal permitted current with re-spect to the standard IEC 60601-1, an injection frequency of100 kHz should be used. When examining the reconstructedimages, higher frequencies provide a better reconstructionresult. However, the sensitivity for noise is also higher forhigh frequencies. At 100µA, the best signal to noise ra-tio in the images was achieved at low frequencies, while atmaximal current amplitudes, the result was best at 100 kHz.In summary, we recommend a current frequency of 100 kHzwith the highest permitted current amplitude of 10 mA.

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(a) Constant current.

(b) Maximal allowed current.

Fig. 7. Signal to noise ratio in the images at four different noiselevels of the voltage difference at 1 kHz. Note, that theexact same noise was added to the voltage difference atall frequencies.

However, certain limitations apply to this study whichwill be addressed in future work. First, the finite elementmodel only consists of three different tissues. No bones, fator 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. Thenoise model used in this study was purely additive. Never-theless, the results show that the current frequency has animportant role in EIT measurements.

AcknowledgementsResearch described in the paper was supervised by

Prof. Dr.-Ing. Dr. med. Steffen Leonhardt and Dr.-Ing. Mar-ian Walter. Jakob Orschulik gratefully acknowledges finan-cial support provided by the German Research Foundation(DFG), grant no. LE 817/20-1.

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About the Authors

Jakob ORSCHULIK was born inMikolow, Poland and received theB.Sc. and M.Sc. degrees fromRWTH Aachen University, Aachen,Germany in 2011 and 2013, respec-tively. He is currently a researchassociate and Ph.D. student at thePhilips Chair for Medical Informa-tion Technology, Helmholtz-Institutefor Biomedical Engineering at RWTHAachen University. His research in-

terests include bioimpedance spectroscopy and electricalimpedance tomography.

Tobias MENDEN was born January25th, 1990 in Bad Honnef, Ger-many. In June 2016 he received theM.Sc. degree in Electrical Engineer-ing with specialisation on Biomed-ical Engineering from the RWTHAachen University, Germany. Cur-rently he is working as a researchassociate and Ph.D. student at thePhilips Chair for Medical Informa-tion Technology, Helmholtz-Institute

for Biomedical Engineering at RWTH Aachen University.His research interests include electrical impedance tomogra-phy with a focus in the hardware measurement chain.