Electrical Impedance Tomography Image Reconstruction Research Articles

Technical Principles and Clinical Applications of Electrical Impedance Tomography in Pulmonary Monitoring.

Pulmonary monitoring is crucial for the diagnosis and management of respiratory conditions, especially after the epidemic of coronavirus disease. Electrical impedance tomography (EIT) is an alternative non-radioactive tomographic imaging tool for monitoring pulmonary conditions. This review proffers the current EIT technical principles and applications on pulmonary monitoring, which gives a comprehensive summary of EIT applied on the chest and encourages its extensive usage to clinical physicians. The technical principles involving EIT instrumentations and image reconstruction algorithms are explained in detail, and the conditional selection is recommended based on clinical application scenarios. For applications, specifically, the monitoring of ventilation/perfusion (V/Q) is one of the most developed EIT applications. The matching correlation of V/Q could indicate many pulmonary diseases, e.g., the acute respiratory distress syndrome, pneumothorax, pulmonary embolism, and pulmonary edema. Several recently emerging applications like lung transplantation are also briefly introduced as supplementary applications that have potential and are about to be developed in the future. In addition, the limitations, disadvantages, and developing trends of EIT are discussed, indicating that EIT will still be in a long-term development stage before large-scale clinical applications.

Sensitivity-matrix-independent electrical impedance tomography: Damage detection for composite materials

Carbon fiber reinforced polymer (CFRP) is widely utilized due to their superior properties. The structural health monitoring (SHM) for composite materials is crucial to prevent catastrophic failures. Electrical impedance tomography (EIT), which allows for the visualization of the conductivity distribution through the measurement of electrical parameters on the boundary, presents a potential solution for SHM. Existing studies applying EIT to CFRP concentrate on traditional linearization methods that rely on sensitivity matrix, which ignore challenges posed by non-uniform sensitivity. This paper introduces an EIT image reconstruction method that is independent of the sensitivity matrix, offering a novel way for rapid damage detection and real-time SHM. Furthermore, the domain shape transformation is achieved by conformal mapping. Simulations and experiments indicate that the sensitivity-matrix-independent EIT can avoid issues such as blurring in the central region and artifacts near the boundary caused by non-uniform distribution of the sensitivity in the CFRP damage detection.

Electrical impedance tomography image reconstruction for lung monitoring based on ensemble learning algorithms1

AbstractElectrical impedance tomography (EIT) is a promising non‐invasive imaging technique that visualizes the electrical conductivity of an anatomic structure to form based on measured boundary voltages. However, the EIT inverse problem for the image reconstruction is nonlinear and highly ill‐posed. Therefore, in this work, a simulated dataset that mimics the human thorax was generated with boundary voltages based on given conductivity distributions. To overcome the challenges of image reconstruction, an ensemble learning method was proposed. The ensemble method combines several convolutional neural network models, which are the simple Convolutional Neural Network (CNN) model, AlexNet, AlexNet with residual block, and the modified AlexNet model. The ensemble models’ weights selection was based on average technique giving the best coefficient of determination (R2 score). The reconstruction quality is quantitatively evaluated by calculating the root mean square error (RMSE), the coefficient of determination (R2 score), and the image correlation coefficient (ICC). The proposed method's best performance is an RMSE of 0.09404, an R2 score of 0.926186, and an ICC of 0.95783 using an ensemble model. The proposed method is promising as it can construct valuable images for clinical EIT applications and measurements compared to previous studies.

TSS-ConvNet for electrical impedance tomography image reconstruction

Objective. The objective of this study was to propose a novel data-driven method for solving ill-posed inverse problems, particularly in certain conditions such as time-difference electrical impedance tomography for detecting the location and size of bubbles inside a pipe. Approach. We introduced a new layer architecture composed of three paths: spatial, spectral, and truncated spectral paths. The spatial path processes information locally, whereas the spectral and truncated spectral paths provide the network with a global receptive field. This unique architecture helps eliminate the ill-posedness and nonlinearity inherent in the inverse problem. The three paths were designed to be interconnected, allowing for an exchange of information on different receptive fields with varied learning abilities. Our network has a bottleneck architecture that enables it to recover signal information from noisy redundant measurements. We named our proposed model truncated spatial-spectral convolutional neural network (TSS-ConvNet). Main results. Our model demonstrated superior accuracy with relatively high resolution on both simulation and experimental data. This indicates that our approach offers significant potential for addressing ill-posed inverse problems in complex conditions effectively and accurately. Significance. The TSS-ConvNet overcomes the receptive field limitation found in most existing models that only utilize local information in Euclidean space. We trained the network on a large dataset covering various configurations with random parameters to ensure generalization over the training samples.

Voltage-based separation of respiration and cardiac activity by harmonic analysis in electrical impedance tomography

This study aims to improve the accuracy of Electrical Impedance Tomography (EIT) measurements for monitoring ventilation and cardiac signal in medical imaging by proposing a new signal separation approach that does not require contrast agents. Conventionally, contrast agents like high-conductive saline solutions are used for signal separation in EIT measurements. This study uses a harmonic analysis on EIT raw voltage data to separate the ventilation- and cardiac-related signals (early separation). It evaluates its efficacy with a simulation model at low (1%) and high (10%) superimposed additive noise levels against the already published harmonic analysis at pixel level after EIT image reconstruction (late separation). The findings indicate that the voltage-based harmonic analysis approach, i.e., early separation, provides reliable signal separation, especially under high noise conditions, compared to the late separation. This method enables the possibility of incorporating independent cardiac-specific or ventilation-specific prior knowledge into the image reconstruction process, potentially improving the resulting images.

EIT-MP: A 2-D Electrical Impedance Tomography Image Reconstruction Method Based on Mixed Precision Asymmetrical Neural Network for Hardware-Software Co-Optimization Platform

EIT-MP: A 2-D Electrical Impedance Tomography Image Reconstruction Method Based on Mixed Precision Asymmetrical Neural Network for Hardware-Software Co-Optimization Platform

Damage detection of CFRP laminates based on Adamax-INN model for EIT

Carbon fiber reinforced polymer (CFRP) is electrically conductive, making it possible to detect structural damage of CFRP laminates with electrical impedance tomography (EIT). However, the inverse problem of EIT is severely non-linear, ill-posed, and underdetermined, thus limiting the resolution and accuracy of images reconstructed with EIT. This paper solves the inverse problem of EIT based on invertible neural networks (INN) and optimizes INN with Adamax gradient descent algorithm. Simulation and experimental results demonstrated that, compared with traditional EIT image reconstruction algorithms and radial basis function (RBF) neural network algorithm, the Adamax-INN model largely reduced the artifacts in reconstructed images, improved the damage recognition accuracy and edge clarity, and displayed good noise immunity.

Image Reconstruction Using Supervised Learning in Wearable Electrical Impedance Tomography of the Thorax.

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.

Dual-modal Image Reconstruction for Electrical Impedance Tomography with Overlapping Group Lasso and Laplacian Regularization.

Electrical Impedance Tomography (EIT) is a promising biomedical imaging modality, yet EIT image reconstruction remains an open challenge due to its severe ill-posedness. High-quality EIT image reconstruction algorithms are desired. This paper reports a segmentation-free dual-modal EIT image reconstruction algorithm that uses Overlapping Group Lasso and Laplacian (OGLL) regularization. An overlapping group lasso penalty is constructed based on conductivity change properties and encodes the imaging targets' structural information obtained from an auxiliary imaging modality that provides structural images of the sensing region. We introduce Laplacian regularization to alleviate the artifacts caused by group overlapping. The performance of OGLL is evaluated and compared with single-modal and dual-modal image reconstruction algorithms using simulation and real-world data. Quantitative metrics and visualized images confirm the superiority of the proposed method in terms of structure preservation, background artifact (BA) suppression, and conductivity contrast differentiation. This work proves the effectiveness of OGLL in improving EIT image quality. This study demonstrates that EIT has the potential to be adopted in quantitative tissue analysis by using such dual-modal imaging approaches.

Influence of a Structural Prior Mask on EIT Image Reconstruction.

Electrical Impedance Tomography (EIT) is a low-cost imaging method with promising results in visualizing ventilation distribution within the lungs. However, in clinical settings, the interpretability of EIT images is often limited by blurred anatomical alignment and reconstruction artifacts. Integrating structural priors into the EIT reconstruction process can enhance the interpretability of EIT images. In this contribution, we introduced a patient-specific structural prior mask into the EIT reconstruction process. Such prior mask ensures that only conductivity changes within the lung regions are reconstructed. With the aim to investigate the influence of the structural prior mask on the EIT images, we conducted numerical simulations in terms of four different ventilation status. EIT images were reconstructed with Gauss-Newton algorithm and discrete cosine transform-based EIT algorithm. We carried out quantitative analysis including the reconstruction error and figures of merit for the evaluation. The results show that the morphological structures of the lungs introduced by the prior mask are preserved in the EIT images, and the reconstruction artefacts are also limited. In conclusion, the incorporation of the structural prior mask enhances the interpretability of EIT images in clinical settings.Clinical relevance-The correct interpretation of an EIT image is crucial for a clinical diagnosis. This research demonstrates that a structural prior mask might have the potential to improve the interpretability of an EIT image, which facilitates the clinicians with a better understanding of EIT results.

Image reconstruction method for electrical impedance tomography based on RBF and attention mechanism

Electrical impedance tomography (EIT) is an imaging technology for estimating the conductivity change for the measured field of the human body. However, because EIT image reconstruction is severely ill-posed and nonlinear inverse problem, the reconstructed image based on traditional algorithm is lower accurate with obscure boundaries and lots of artifacts. In order to improve the accuracy of reconstructed image, an EIT image reconstruction method based on RBF and attention mechanism is proposed in this paper. The proposed RCU-Net network architecture consists of two sub-networks: RBF and CBAM-UNet. The RBF neural network accomplishes the nonlinear mapping between the boundary voltages and conductivity distribution values. The CBAM-UNet combining attention mechanism CBAM with U-Net makes further processing for the resulting images to obtain more sharp and explicit images. RCU-Net was trained and tested on the simulated dataset created by EIDORS platform. The experiment reveals that the proposed method outperforms the traditional methods in distinguishing multi-target, generalization ability and anti-interference, and it has improved the reconstructed image quality which has an average reduction of 55.09% and 26.23% on RE (Relative Error) and an increase of 14.19% and 3.08% on CC (Correlation Coefficient) respectively compared with RBF-EIT and RBF-UNet methods. In addition, the experimental data from KIT4 system can be applied to the trained network. This successful transition also demonstrates the proposed method can reconstruct more explicit images with high fidelity.

An MSA-Net Algorithm for Direct Estimation of Gas Holdup Based on Electrical Impedance Tomography System

Electrical impedance tomography (EIT) is a nondestructive testing technique, which has great potential to be used for the detection of the cross-sectional gas-holdup ratio (CGR) of gas–liquid two-phase flow. Due to the nonlinear and ill-posed characteristics of the EIT image reconstruction, the accuracy of image-based CGR estimation methods is poor. To improve the detection accuracy, a learning-based direct CGR estimation method is proposed in this study, which applies a novel multiscale attention network (MSA-Net) to directly estimate the CGR from the voltage measurements. Multiscale feature extraction and residual structure are introduced into MSA-Net to fully extract the features, and attention unit (AU) is also used to capture high-frequency features. As a result, accurate and robust CGR estimation can be realized by MSA-Net. ResNet18 and single-scale attention network (SSA-Net) are selected for comparison. The simulation results indicate that the relative error (RE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\text {CG}}{)}$ </tex-math></inline-formula> of CGR estimated by the learning-based direct CGR estimation method is far lower than that of the image-based CGR estimation methods. Compared with ResNet18 and SSA-Net, the RECG of the CGR estimated by MSA-Net is lower, and the range is 0.07%–0.36%. Moreover, MSA-Net shows good noise robustness simultaneously. The experiment is also set to test MSA-Net. The range of RECG is 0.1%–1.12%, which further verifies the practicability of the proposed learning-based direct CGR estimation method.

Reconstruction of conductivity distribution variation with Tikhonov and wavelet frame combined method for electrical impedance tomography

Electrical impedance tomography (EIT) is receiving considerable research interest in a variety of applications. With this technique, it is possible to reconstruct conductivity distribution inside the detected region. Note that reconstruction of conductivity distribution is an ill-posed inverse problem. To deal with this problem, Tikhonov regularization method has been preferred. However, this method suffers from poor reconstruction quality. In this work, a novel approach which combines Tikhonov regularization method with wavelet frame is proposed for image reconstruction of EIT. The proposed method is superior to the popular Tikhonov regularization method in enforcing sparse of the solution and enhancing sharp feature. Simulation work has been conducted to validate the performance of the proposed method. Compared with Landweber method, total variation (TV) regularization method, and Tikhonov regularization method, reconstructions of six different models show that images reconstructed by the proposed method have better quality and are more robust to noise. In addition, image reconstruction is also performed based on phantom experimental data. The results further demonstrate that the proposed method outperforms other three methods since the inclusion has been more accurately reconstructed, and there are almost no artifacts in the reconstructed images.

Image Reconstruction for Electrical Impedance Tomography (EIT) With Improved Wasserstein Generative Adversarial Network (WGAN)

The image reconstruction of electrical impedance tomography (EIT) is highly ill-posed and nonlinear. Because of the poor nonlinear fitting ability of analytical algorithms, reconstructed images of these algorithms are blurry and lack detailed features. Although high-quality EIT images can be obtained by applying deep-learning networks to image reconstruction, the interpretability and generalization ability of the network are difficult to guarantee. A deep-learning structure, namely conditional Wasserstein generative adversarial network with attention mechanism (CWGAN-AM), is proposed for EIT image reconstruction. CWGAN-AM consists of an imaging module, a generator, and a discriminator. The initial conductivity image obtained by the imaging module is added to both the generator and the discriminator as a constraint to improve the stability of reconstruction. The enhanced residual blocks (ERBs), the structure of residual in residual (RIR), and the attention unit are used in the generator to further improve the reconstruction accuracy for the inclusion boundary. The imaging results indicate that CWGAN-AM can accurately recover the irregular boundaries of inclusions, and effective reconstruction can be accomplished for the new conductivity distribution (inclusions with size/shape variations) and noisy samples.

Enhanced Multi-Scale Feature Cross-Fusion Network for Impedance–Optical Dual-Modal Imaging

The intrinsic issue of low spatial resolution of electrical impedance tomography (EIT) is a long-standing challenge that hinders the capability of performing quantitative analysis based on EIT image. Our recent work demonstrates an impedance–optical dual-modal imaging framework and a deep learning model named multi-scale feature cross-fusion network (MSFCF-Net) to realize information fusion and high-quality EIT image reconstruction. However, this framework’s performance is limited by the accuracy of the mask image obtained from an auxiliary imaging modality. This article further proposes a two-stage deep neural network, which is the enhanced version of MSFCF-Net (named En-MSFCF-Net), to automatically improve the mask image and conduct information fusion and image reconstruction. Compared with MSFCF-Net, En-MSFCF-Net demonstrates the superior ability to correct the inaccurate mask image, leading to a more accurate conductivity estimation. Furthermore, En-MSFCF-Net also maintains the best shape preservation and conductivity prediction accuracy among given learning-based and model-based algorithms. Both the qualitative and quantitative results indicate that En-MSFCF-Net could make dual-modal imaging more robust in real-world situations.

Electrical Impedance Tomography Image Reconstruction With Attention-Based Deep Convolutional Neural Network

Electrical impedance tomography (EIT) is a promising functional and structural imaging method in process tomography. However, due to the ’soft-field’ nature and the high dependence on the prior information, it often suffers serious artifacts in quantitative analysis. Most recently, EIT image quality has improved significantly because of the state-of-the-art deep learning-based models in the aspect of solving the inverse problem, especially fully convolutional networks (FCN) and V-Net variants. Despite their success, these deep convolutional networks (CNNs) have two limitations: (1) The long-range information transition is frequently lost and the reverse gradient often disappears in deep CNNs; (2) Some novel skip connections, such as residual and dense connections, often occupy substantial computational resources. To overcome these two limitations, we propose V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> A-Net, a new neural architecture based on redesigned feature transited connections by the terms of (1) A pre-reconstructor based on the iterative Newton-Raphson method, which maps the nonlinear function between the measurements and the initial images, (2) Dual cascaded V-Net are combined, which play the role of an encoder and a decoder, respectively, (3) A new parallel attention mechanism via channel attention and coordinate attention to learn the conductivity distributions and boundary-shaped feature separately, and (4) the light-weight skip connections reduce the computational resources (or accelerate the inference speed) of EIT imaging. The V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> A-Net is evaluated by using the multi-phase flow industrial applications, and the results demonstrate that (1) V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> A-Net has better performance in shape reconstruction with sharp ’corner’, (2) V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> A-Net could reconstruct the model accurately where it has some low-contrast conductivity distributions, (3) V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> A-Net enhances the quality of interfaces with the stratified flow, and (4) the pruned V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> A-Net achieves significant speedup compared with the VDD-Net or V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DNet. The analyses show that the average relative error is 0.05, the average correlation coefficient is 0.92, the average structural similarity is 0.92 on the testing datasets. In addition, the average relative cover ratio is 0.97 and the average relative contrast ratio is 0.98 on the testing datasets.

An EIT image reconstruction method based on DenseNet with multi-scale convolution.

Electrical impedance tomography (EIT) is an imaging technique that non-invasively acquires the electrical conductivity distribution within a field. The ill-posed and nonlinear nature of the image reconstruction process results in lower quality of the obtained images. To solve this problem, an EIT image reconstruction method based on DenseNet with multi-scale convolution named MS-DenseNet is proposed. In the proposed method, three different multi-scale convolutional dense blocks are incorporated to replace the conventional dense blocks; they are placed in parallel to improve the generalization ability of the network. The connection layer between dense blocks adopts a hybrid pooling structure, which reduces the loss of information in the traditional pooling process. A learning rate setting achieves reduction in two stages and optimizes the fitting ability of the network. The input of the constructed network is the boundary voltage data, and the output is the conductivity distribution of the imaging area. The network was trained and tested on a simulated dataset, and it was further tested using actual measurement data. The images reconstructed via this method were evaluated by employing root mean square error, structural similarity index measure, mean absolute error and image correlation coefficient in comparison with conventional DenseNet and Gauss-Newton. The results show that the method improves the artifact and edge blur problems, achieves higher values on the image metrics and improves the EIT image quality.

Advances of deep learning in electrical impedance tomography image reconstruction.

Electrical impedance tomography (EIT) has been widely used in biomedical research because of its advantages of real-time imaging and nature of being non-invasive and radiation-free. Additionally, it can reconstruct the distribution or changes in electrical properties in the sensing area. Recently, with the significant advancements in the use of deep learning in intelligent medical imaging, EIT image reconstruction based on deep learning has received considerable attention. This study introduces the basic principles of EIT and summarizes the application progress of deep learning in EIT image reconstruction with regards to three aspects: a single network reconstruction, deep learning combined with traditional algorithm reconstruction, and multiple network hybrid reconstruction. In future, optimizing the datasets may be the main challenge in applying deep learning for EIT image reconstruction. Adopting a better network structure, focusing on the joint reconstruction of EIT and traditional algorithms, and using multimodal deep learning-based EIT may be the solution to existing problems. In general, deep learning offers a fresh approach for improving the performance of EIT image reconstruction and could be the foundation for building an intelligent integrated EIT diagnostic system in the future.

The influence of reference electrode in electrical impedance tomography

BackgroundSome electrical impedance tomography (EIT) devices equip reference electrodes. In practice, it is not uncommon to observe high contact impedance for the reference electrode. The influence of bad contact reference electrode on data quality is unknown. The study aimed to investigate the influence of reference electrode on EIT image reconstruction. MethodsThirty lung healthy volunteers were prospectively examined with EIT. The subjects were spontaneously breathing in supine position. Three scenarios were constructed: 1. Normal measurement; 2. Reference electrode disconnected without recalibration; 3. Reference electrode disconnected, and the measurement restarted after recalibration of the system. EIT-based parameters measuring spatial and temporal ventilation distributions were calculated and compared. A so-call deviation score was calculated to assess the differences in EIT parameters between scenarios 2 and 1, between 3 and 1. ResultsThe absolute differences for all parameters were significantly higher than zero (p < 0.01 for all parameters and scenarios). Deviation score for scenario 2 was 4.5 ± 3.5. Four subjects had a deviation score of 0 in scenario 2 and five subjects had a score of 1. The deviation in scenario 3 was higher (6.1 ± 3.1). No subjects had a score of 0 and only two subjects had a score of 1. ConclusionsFor EIT systems that equips with reference electrode, it is important to ensure the proper contact and functionality of the reference electrode. The EIT data quality would remain unchanged in only a small portion of subjects.

Convolutional neural network method for damage detection of CFRP in electrical impedance tomography

Damage detection is vitally important for carbon fiber reinforced polymer (CFRP) laminates. When CFRP laminates are damaged, its impedance property is changed. Based on the electrical properties of CFRP laminates, the changed conductivity distribution can be reconstructed with the electrical impedance tomography (EIT) method. The detection method is attractive due to its simple equipment, low cost, and easy operation. However, image reconstruction of EIT faces a serious ill-conditioned nonlinear inverse problem. In order to solve this problem, a feature fusion convolutional neural network based on the dense connection (FF-D) method is applied in EIT to establish the mapping relationship between voltage measurement and conductivity distribution in this paper. The optimization can extract and utilize features to a greater degree and improve reconstruction accuracy and robustness. For the purpose of simulating the electrical properties of CFRP better, the conductivity values measured by an impedance analyzer are used as the data set. The correlation coefficient (CC) and root mean square error (RMSE) are used as indicators to evaluate the quality of image reconstruction. The simulation and experimental results suggest that the FF-D method can reconstruct images better than typical algorithms based on deep learning and conventional algorithms of EIT.