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Small pneumothorax. From top left: The true conductivity distribution, reconstruction of γ abs with no prior, γ diff with no prior, γ abs pr with the spatial prior, γ diff pr with the spatial prior, a difference image in which the data for the example of healthy heart and lungs in Figure 2 with no pathology is chosen for γ ref . The L2 norms of the differences between those reconstructions and the ground truth are 0.3038, 0.3137, 0.3013 and 0.3112 in order.
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Bedside imaging of ventilation and perfusion is a leading application of 2-D medical electrical impedance tomography (EIT), in which dynamic cross-sectional images of the torso are created by numerically solving the inverse problem of computing the conductivity from voltage measurements arising on electrodes due to currents applied on electrodes on...
Citations
... EIT is a technology that utilizes the surface potential change exhibited by the area being tested [3], along with an appropriate imaging algorithm, to obtain an image of the impedance change in that area. Conductivity distribution changes are associated with pathological changes and physiological activities such as tumors, hemorrhage, ischemia, inflammation, etc. ...
The issue of Electrical Impedance Tomography (EIT) is a well-known inverse problem that presents challenging characteristics. In order to address the difficulties associated with ill-conditioned inverses, regularization methods are typically employed. One commonly used approach is total variation (TV) regularization, which has shown effectiveness in EIT. In order to meet the requirements of real-time tracking, it is essential to acquire fast and reliable algorithms for image reconstruction. Therefore, we present a modified second-order generalized regularization algorithm that enables more-accurate reconstruction of organ boundaries and internal structures, to reduce EIT artifacts, and to overcome the inability of the conventional Tikhonov regularization method in solving the step effect of the medium boundary. The proposed algorithm uses the improved alternating direction method of multipliers (ADMM) to tackle this optimization issue and adopts the second-order generalized total variation (SOGTV) function with strong boundary-preserving features as the regularization generalization function. The experiments are based on simulation data and the physical model of the circular water tank that we developed. The results showed that SOGTV regularization can improve image realism compared with some classic regularization.
... Conceptually, the proposed deep Calderón method can be viewed as a way of incorporating spatial / anatomical priori information into the EIT imaging algorithms [14,19,49]. This idea has been explored recently for Calderón's method in [44,45]. In the works [44,45], the approximate location of each organ and their approximate constant conductivity are assumed to be known, since such information can be attained from other imaging modalities, e.g., CT-scans or ultrasound Images are credited to [21,44]. ...
... This idea has been explored recently for Calderón's method in [44,45]. In the works [44,45], the approximate location of each organ and their approximate constant conductivity are assumed to be known, since such information can be attained from other imaging modalities, e.g., CT-scans or ultrasound Images are credited to [21,44]. ...
... Conceptually, the proposed deep Calderón method can be viewed as a way of incorporating spatial / anatomical a priori information into the EIT imaging algorithms [13,18,48]. This idea has been explored recently for Calderón's method in [43,44]. In the works [43,44], the approximate location of each organ and their approximate constant conductivity are assumed to be known, since such information can be attained from other imaging modalities, e.g., CT-scans or ultrasound imaging, and then the prior information is incorporated to the scattering transformation which allows reconstructions with higher-resolution. ...
... This idea has been explored recently for Calderón's method in [43,44]. In the works [43,44], the approximate location of each organ and their approximate constant conductivity are assumed to be known, since such information can be attained from other imaging modalities, e.g., CT-scans or ultrasound imaging, and then the prior information is incorporated to the scattering transformation which allows reconstructions with higher-resolution. Note that the method proposed in this work can be viewed as a new way of utilizing the spatial a priori information to Calderón's method. ...
Electrical impedance tomography (EIT) is a noninvasive medical imaging modality utilizing the current-density/voltage data measured on the surface of the subject. Calder\'on's method is a relatively recent EIT imaging algorithm that is non-iterative, fast, and capable of reconstructing complex-valued electric impedances. However, due to the regularization via low-pass filtering and linearization, the reconstructed images suffer from severe blurring and underestimation of the exact conductivity values. In this work, we develop an enhanced version of Calder\'on's method, using convolution neural networks (i.e., U-net) via a postprocessing step. Specifically, we learn a U-net to postprocess the EIT images generated by Calder\'on's method so as to have better resolutions and more accurate estimates of conductivity values. We simulate chest configurations with which we generate the current-density/voltage boundary measurements and the corresponding reconstructed images by Calder\'on's method. With the paired training data, we learn the neural network and evaluate its performance on real tank measurement data. The experimental results indicate that the proposed approach indeed provides a fast and direct (complex-valued) impedance tomography imaging technique, and substantially improves the capability of the standard Calder\'on's method.
... With the advantages of being non-damaging, noninvasive, non-radiation, low-cost, a simple operation and providing rich functional information, electrical impedance tomography has been researched deeply in the biomedical and industrial fields [3]. In biomedical applications, EIT has been used for lung imaging, which is based on the principle of assessing recoverable alveolar collapse and overdistension by images obtained during end-expiratory positive pressure titration [4,5]. In addition, EIT has also been used to varying degrees in brain function, brain activity and tumor localization studies [6][7][8]. ...
Electrical impedance tomography (EIT) is non-destructive monitoring technology that can visualize the conductivity distribution in the observed area. The inverse problem for imaging is characterized by a serious nonlinear and ill-posed nature, which leads to the low spatial resolution of the reconstructions. The iterative algorithm is an effective method to deal with the imaging inverse problem. However, the existing iterative imaging methods have some drawbacks, such as random and subjective initial parameter setting, very time consuming in vast iterations and shape blurring with less high-order information, etc. To solve these problems, this paper proposes a novel fast convergent iteration method for solving the inverse problem and designs an initial guess method based on an adaptive regularization parameter adjustment. This method is named the Regularization Solver Guided Fast Iterative Shrinkage Threshold Algorithm (RS-FISTA). The iterative solution process under the L1-norm regular constraint is derived in the LASSO problem. Meanwhile, the Nesterov accelerator is introduced to accelerate the gradient optimization race in the ISTA method. In order to make the initial guess contain more prior information and be independent of subjective factors such as human experience, a new adaptive regularization weight coefficient selection method is introduced into the initial conjecture of the FISTA iteration as it contains more accurate prior information of the conductivity distribution. The RS-FISTA method is compared with the methods of Landweber, CG, NOSER, Newton—Raphson, ISTA and FISTA, six different distributions with their optimal parameters. The SSIM, RMSE and PSNR of RS-FISTA methods are 0.7253, 3.44 and 37.55, respectively. In the performance test of convergence, the evaluation metrics of this method are relatively stable at 30 iterations. This shows that the proposed method not only has better visualization, but also has fast convergence. It is verified that the RS-FISTA algorithm is the better algorithm for EIT reconstruction from both simulation and physical experiments.
... Electrical impedance tomography is a non-invasive imaging method [1], which applies current or voltage excitation to electrodes at the boundary of an observation domain and uses the obtained electrical response signals to reconstruct the electrical conductivity distribution in the domain. Due to its low cost, portable equipment, high time resolution and lack of radiation, EIT has received extensive attention in biomedical imaging [2], and it has great potential application prospects and application value in the continuous monitoring of the functions of the human heart [3,4], lungs [5][6][7], brain [8,9], breast [10][11][12], abdomen [13,14] and other major organs. ...
Electrical impedance tomography (EIT) is a non-invasive detection technology that uses the electrical response value at the boundary of an observation field to image the conductivity changes in an area. When EIT is applied to the thoracic cavity of the human body, the conductivity change caused by the heartbeat will be concentrated in a sub-region of the thoracic cavity, that is, the heart region. In order to improve the spatial resolution of the target region, two sensor optimization methods based on conformal mapping theory were proposed in this study. The effectiveness of the proposed method was verified by simulation and phantom experiment. The qualitative analysis and quantitative index evaluation of the reconstructed image showed that the optimized model could achieve higher imaging accuracy of the heart region compared with the standard sensor. The reconstruction results could effectively reflect the periodic diastolic and systolic movements of the heart and had a better ability to recognize the position of the heart in the thoracic cavity.
Traditional lung electrical impedance imaging devices require the placement of measurement electrodes around the chest, which is inconvenient for clinical application in patients in a supine position. To address this issue, this study proposes a Virtual Electrode-based Level Set combined with GREIT algorithm (VESL-GREIT) for pulmonary impedance tomography. It utilizes measurement data from electrodes placed on only one side of the chest and generates full-electrode measurement data using a deep learning network. The improved GREIT algorithm is then employed for image reconstruction. Acting as a "gray box," VESL-GREIT not only takes advantage of prior information about the lungs but also enhances the robustness and generalizability of the algorithm. Simulation experiments demonstrate that with a measurement signal-to-noise ratio (SNR) above 20 dB, the imaging relative error (RE) and structure correlation coefficient (CC) change slowly, indicating high robustness of the algorithm. Physical model experiments show that compared to traditional dynamic electrical impedance imaging algorithms, the proposed algorithm achieves a relative error of 0.167 and a structure correlation coefficient of 0.886, enabling more accurate characterization of lung ventilation status. This research contributes to promoting the clinical application and dissemination of lung electrical impedance imaging monitoring methods and provides a new approach for open dynamic electrical impedance imaging.
Electrical impedance tomography (EIT) is a non-invasive, cost-effective and structurally simple technology that enables applications in many fields by measuring changes in electrical parameters. However, the nonlinearity and ill-posedness of the EIT image reconstruction process hinder the complete recovery of the electrical parameters of the field from the measured data, making it still challenging. A Calderón’s method-guided deep neural network (CGDNN) which consists of Calderón’s method as a preliminary imaging module and deep neural network as an image segmentation module is proposed in this paper. The preliminary imaging module of CGDNN avoids the computation of sensitivity matrix and provides a fast and stable nonlinear mapping from measurement data to reconstruction images to facilitate image-to-image mapping by deep neural networks. The preliminary imaging module and the image segmentation module are connected by multi-channel to avoid the manual selection of optimal pre-image. In order to obtain more accurate reconstruction results, a network structure of multi-level U-Net with dense skip connections is applied. Simulation data and experimental data are used to evaluate the feasibility and effectiveness of CGDNN. The results show that CGDNN can obtain high-quality electrical properties distribution images quickly and accurately compared with traditional methods and deep learning image reconstruction methods.
Electrical impedance tomography (EIT) is a non-invasive technique for visualizing the internal structure of a human body. Capacitively coupled electrical impedance tomography (CCEIT) is a new contactless EIT technique that can potentially be used as a wearable device. Recent studies have shown that a machine learning-based approach is very promising for EIT image reconstruction. Most of the studies concern models containing up to 22 electrodes and focus on using different artificial neural network models, from simple shallow networks to complex convolutional networks. However, the use of convolutional networks in image reconstruction with a higher number of electrodes requires further investigation. In this work, two different architectures of artificial networks were used for CCEIT image reconstruction: a fully connected deep neural network and a conditional generative adversarial network (cGAN). The training dataset was generated by the numerical simulation of a thorax phantom with healthy and illness-affected lungs. Three kinds of illnesses, pneumothorax, pleural effusion, and hydropneumothorax, were modeled using the electrical properties of the tissues. The thorax phantom included the heart, aorta, spine, and lungs. The sensor with 32 area electrodes was used in the numerical model. The ECTsim custom-designed toolbox for Matlab was used to solve the forward problem and measurement simulation. Two artificial neural networks were trained with supervision for image reconstruction. Reconstruction quality was compared between those networks and one-step algebraic reconstruction methods such as linear back projection and pseudoinverse with Tikhonov regularization. This evaluation was based on pixel-to-pixel metrics such as root-mean-square error, structural similarity index, 2D correlation coefficient, and peak signal-to-noise ratio. Additionally, the diagnostic value measured by the ROC AUC metric was used to assess the image quality. The results showed that obtaining information about regional lung function (regions affected by pneumothorax or pleural effusion) is possible using image reconstruction based on supervised learning and deep neural networks in EIT. The results obtained using cGAN are strongly better than those obtained using a fully connected network, especially in the case of noisy measurement data. However, diagnostic value estimation showed that even algebraic methods allow us to obtain satisfactory results.
