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DE GRUYTER Current Directions in Biomedical Engineering 2020;6(3): 20203010 Rongqing Chen*, and Knut Möller Global Inhomogeneity Index Evaluation of a DCT-based EIT Lung Imaging Abstract: Purpose: To evaluate a novel structural-functional is resulting in improved interpretability for clinicians. DCT-based EIT lung imaging method against the classical The objective of this work is to evaluate the plausibility EIT reconstruction. Method: Taken retrospectively from a of this DCT-based method against the traditional Gauss- former study, EIT data was evaluated using both Newton one step method in clinical settings. In a first step reconstruction methods. For different phases of ventilation, Global Inhomogeneity (GI) index is used for comparison, EIT images are analyzed with respect to the global which indicates the difference of the volume distribution inhomogeneity (GI) index for comparison. Results: A within a ventilation period . significant less variant GI index was observed in the DCT- based method, compared to the index from classical method. 1.1 Classical EIT Reconstruction Conclusion: The DCT-based method generates more accurate lung contour yet decreasing the essential information in the The reconstruction of an EIT image is ill-posed, therefore a image which affects the GI index. These preliminary results regularization is needed to obtain the estimates of the must be consolidated with more patient data in different conductivity distribution [6,7]. The actual conductivity breathing states. distribution can be inhomogeneous, thus, a finite element Keywords: EIT, lung imaging, DCT, GI. model (FEM) is commonly used to discretize the domain into piecewise constant regions. In the following the https://doi.org/10.1515/cdbme-2020-3010 reconstructing process using the one-step Gauss-Newton method for time-difference imaging is introduced. The reconstruction of conductivity can be written as: 2 2 j 1 Introduction x ˆ arg min Jx y Rx (1) 2 j where x represents the reconstructed conductivity change, Electrical Impedance Tomography (EIT) is a feasible non- J is a Jacobian matrix that maps the conductivity change in invasive imaging method with great capability to visualise a FEM element to the measured voltage variation. The the regional ventilation distribution of lungs to assist regularization is defined as R and weighted by to obtain clinician in adjusting proper PEEP levels for patients under a reasonable solution. mechanical ventilation , and further to avoid ventilator With the widely accepted -norm, the distribution is induced lung injury [2,3]. calculated as: However, the spatial resolution of EIT is low, yet 1 T 2 T temporal resolution higher than traditional morphological x ˆ J J λ R J y By (2) imaging methods, such as computed tomography (CT). matrix B is the reconstruction matrix which calculates the Therefore, our team have previous combined imaging impedance distribution variation from the measured modalities of CT and EIT to roughly restrict EIT image to CT boundary voltages. The reconstruction is obtained from a generated anatomy . This DCT-based EIT approach simple matrix multiplication which is so efficient to includes detailed prior information about both the thorax implement real-time EIT imaging. contour and lung shape obtained from the discrete cosine transformation (DCT) of the CT image, which as a side effect 1.2 DCT-based EIT Reconstruction The DCT-based EIT lung imaging algorithm is based on ______ * Corresponding author: Rongqing Chen Institute of Technical prior anatomy information from CT images assessed via the Medicine, Furtwangen University, Jakob-Kienzle-Str. 17, VS- Discrete Cosine Transformation (DCT) method. DCT is a Schwenningen, Germany. e-mail: email@example.com widely implemented method in image processing, e.g. in Knut Möller Institute of Technical Medicine, Furtwangen JPEG image compression . The concept of DCT is to University, Jakob-Kienzle-Str. 17, VS-Schwenningen, Germany. e- represent the image with a sum of cosine functions in varying mail: firstname.lastname@example.org Open Access. © 2020 Rongqing Chen et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License. Rongqing Chen et al., Global Inhomogeneity Index Evaluation of a DCT-based EIT Lung Imaging — 2 frequencies, in x-direction and y-direction respectively. For a 1, pixels within lung P two dimensional image A with M rows and N columns we m,n 0, pixels ouside lung can define the DCT as: Each column k of K is created as follows: M1N1 V A F k T C p, q (7) p ,q p q m,n p , q m0 n0 (3) where T is a map to assign every pixel in C p, q to 2m 1 p 2n 1 q F cos cos element in the FEM model which covers the pixel. The index p ,q 2M 2N j derives from the linear combination of the frequencies p where and q . Upon calculating the matrix K , we can obtain a new , p 0 Jacobian matrix, which further describes the reconstruction as: 1 T 2 T ,1 p M 1 x J J λ R J y B y (8) DCT DCT DCT DCT DCT and the reconstruction matrix B maps the voltage variations to the DCT coefficients. , q 0 With the reconstructed x we can now recover the image H , constrained of prior anatomical information derived from the original CT image: ,1 q N 1 ydct xdct The matrix V consists of the DCT coefficients, of ˆ H C p, q x (9) DCT , j which a subset can recover a compressed image of A. m0 n0 M1N1 A V F (4) m,n p q m ,n p ,q m0 n0 1.3 Global Inhomogeneity Index where V is a sparse matrix of the same V size but only having several non-zero elements. The Global Inhomogeneity (GI) was primarily introduced to The dimensionality of the EIT inverse problem can be simplify the intra-individual comparability of EIT images reduced significantly by concentrating on the most important obtained from at different time points. The GI is usually subset of DCT coefficients. The implementation is achieved calculated from a tidal image that derives from subtracting nn by multiplying the Jacobian matrix by a matrix J end-expiration from end-inspiration . The calculation of n DCT K derived from DCT coefficients, which are far less GI requires the median value of a tidal image and the sum of than the number of FEM elements. For this article the same the variation in every pixel, which describes as: number of frequencies (15) in both x-direction and y- DI Median DI xy lung x , ylung direction were chosen, which sums to only 225 DCT GI (10) DI coefficients. xy x , ylung The discussed DCT approach can be expressed as: where the DI denotes the value of impedance variation in M1N1 xy V A D p, q (5) p ,q m ,n m ,n a tidal image, and the DI is the pixel within a detected lung m0 n0 lung area. The lung area detection is calculated using the in which D p, q is the cosine function at frequencies p value which is 20 percent of the mean tidal value, or in the and q . We generate a matrix C p, q to introduce the DCT-based EIT reconstruction algorithm, the anatomical information from the CT image is used for the lung contour. prior anatomy information of the lung contour thus a proper In a clinical setting the GI value is associated with the distribution can be calculated. disease state of a certain patient, which provides clinicians C p, q P D p, q (6) m ,n m,n m, n some indication how to set ventilation therapy . of which P indicates whether the pixel belongs to the m,n lung value. Rongqing Chen et al., Global Inhomogeneity Index Evaluation of a DCT-based EIT Lung Imaging — 3 2 Method 3 Discussion For a preliminary evaluation, EIT data from a former study In this preliminary evaluation between the classical EIT was analyzed retrospectively. The EIT data was recorded by reconstruction and the DCT-based EIT reconstruction, Pulmo Vista 500 (Dräger Medical, Lübeck, Germany). From complex time-difference impedance images were represented this dataset two cycles of ventilation are included into the by an index, the GI. Generally, the GI index varies between evaluation. For each cycle of ventilation, the sequence of the two algorithms, i.e. the GI value seems to depend on the frames was down sampled to a total of 30 frames. Among the reconstruction algorithm, which could be expected. But 30 frames, we selected 6 frames to represent the different unexpectedly, the qualitative results differ. For classical EIT phase of ventilation, where the first frame is the end- reconstruction, the GI value have a tendency to decreases as expiration, and the last frame the end-inspiration. the frame reaching the end-inspiration, while for DCT-based EIT reconstruction, the GI index is more stable, and shows cyclic behaviour. Absolute differences in GI index with respect to the reconstructions can be explained by the different constraints imposed on the images. The Tikhonov prior smoothes images, while the DCT use only less degrees of freedom to reconstruct and a cosine base function. In this study, only the Figure 1: The tidal images generated by different methods. Left: lowest 15 frequencies for x-direction and y-direction, which DCT-based EIT tidal image. Right: Classical EIT tidal image. is in total 225 elements, were used for reconstruction. Compared with the elements of the classical FEM, which For each cycle of ventilation, we implemented both one usually exceeds thousands of degrees of freedom (parameter step Gauss-Newton algorithm for a classical EIT values), the reconstruction process is more stable and less reconstruction, and our DCT-based EIT algorithm for a artefacts are produced as visible, e.g. as in the lung area structural-functional image. For both reconstruction method, estimation in the classical approach. a tidal image is acquired, which are illustrated in Figure 1. For classical EIT construction, we obtained an estimated lung area using a threshold at 20 percent of the mean tidal Table 1: Normalized GI Index Values Calculated from Different Methods variation, while for CT-EIT method, the lung area is derived directly from the CT. Both lung regions are shown in Figure GI for DCT- GI for Ventilation Frames based EIT Classical EIT Cycles Method Method 10 0.9953 1.0000 15 0.9276 0.8430 20 0.9516 0.7541 Figure 2: Lung regions calculated by different 25 0.9857 0.6957 methods. Left: DCT-based EIT generated lung region. Right: Classical EIT generated lung region. 30 1.0000 0.6859 10 1.0000 1.0000 For each breathing cycle the 5 selected frames, which 15 0.8872 0.9132 represent the different phase of a ventilation cycle, we calculated the median and sum of the variation within the 2 20 0.8521 0.8213 lung area, and further calculated the GI value for every frame 25 0.8856 0.7149 for both methods. We further normalized the GI value of 30 0.9142 0.6792 each method for every cycle with the largest GI value in that group. The GI value is listed in Table 1 for comparison. The DCT method must be further investigated to gain insight into the potential of structural-functional image reconstruction. By fusing CT morphological information naturally to the EIT image, clinicians will be given a better Rongqing Chen et al., Global Inhomogeneity Index Evaluation of a DCT-based EIT Lung Imaging — 4 intuition how to interpret dynamics during ventilation. Research funding: This research was partly supported by the However, as GI index is considered to provide important German Federal Ministry of Education and Research information associated with inhomogeneous tidal volume (MOVE, Grant 13FH628IX6) and H2020 MCSA Rise distribution in the lung, a standard GI index must be (#872488— DCPM). Conflict of interest: Authors state no generated. Thus, more reconstruction methods and other conflict of interest. Informed consent: Informed consent has ventilation indices will be included in further steps of this been obtained from all individuals included in this study. evaluation. Ethical approval: The research related to human use complies One of the limitation of this study is that only two with all the relevant national regulations, institutional ventilation cycles from one patient are analysed, which policies and was performed in accordance with the tenets of results may not generalize. However, the comparison the Helsinki Declaration, and has been approved by the between different frames already provide an indication that authors' institutional review board or equivalent committee. considerable differences can be found in further investigations including multiple patients with diverse References pathological states. The DCT-based EIT reconstruction generates images are much easier interpretable for clinicians  Zhao, Z., Steinmann, D., Frerichs, I., Guttmann, J., & Möller, as the anatomically lung contour is clearly illustrated, and the K. (2010). PEEP titration guided by ventilation homogeneity: distribution of air is better allocated to defined lung areas a feasibility study using electrical impedance tomography. Critical Care, 14 (1), R8. compared with the classical EIT reconstruction.  Frerichs, I. (2000). Electrical impedance tomography (EIT) in applications related to lung and ventilation: a review of experimental and clinical activities. Physiological measurement, 21(2), R1. 4 Conclusion  Hinz, J., Neumann, P., Dudykevych, T., Andersson, LG, Wrigge, H., Burchardi, H., & Hedenstierna, G. (2003). The DCT-based EIT lung imaging method is feasible to Regional ventilation by electrical impedance tomography: a comparison with ventilation scintigraphy in pigs. Chest, 124 reduce the artefacts outside the lung region, and to (1), 314-322. reconstruct a more clinician-friendly image during ventilation  Schullcke, B., Gong, B., Krueger-Ziolek, S., Soleimani, M., for the patient. The GI index evaluation indicates that the Mueller-Lisse, U., & Moeller, K. (2016). Structural-functional reconstruction process has influence on the distribution of lung imaging using a combined CT-EIT and a Discrete regional gas allocation. Therefore, we will further investigate Cosine Transformation reconstruction method. Scientific reports, 6, 25951. the influence of different reconstruction methods to clinically  Zhao, Z., Möller, K., Steinmann, D., Frerichs, I., & Guttmann, relevant indices. J. (2009). Evaluation of an electrical impedance tomography- based global inhomogeneity index for pulmonary ventilation distribution. Intensive care medicine, 35(11), 1900.  Soleimani, M. (2008). Computational aspects of low frequency electrical and electromagnetic tomography: A Acknowledgement review study. Int. J. Numer. Anal. Model , 5 (3), 407-440. We appreciate Mr. Benjamin Schullcke’s help in form of his  Vauhkonen, M., Kaipio, JP, Somersalo, E., & Karjalainen, PA previous implementation of the DCT-based EIT lung imaging (1997). Electrical impedance tomography with basis constraints. Inverse problems, 13 (2), 523. algorithm. Author Statement
Current Directions in Biomedical Engineering – de Gruyter
Published: Sep 1, 2020
Keywords: EIT; lung imaging; DCT; GI
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