Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks

Deep prior embedding method for Electrical Impedance Tomography

This paper presents a novel deep learning-based approach for Electrical Impedance Tomography (EIT) reconstruction that effectively integrates image priors to enhance reconstruction quality. Traditional neural network methods often rely on random initialization, which may not fully exploit available prior information. Our method addresses this by using image priors to guide the initialization of the neural network, allowing for a more informed starting point and better utilization of prior knowledge throughout the reconstruction process. We explore three different strategies for embedding prior information: non-prior embedding, implicit prior embedding, and full prior embedding. Through simulations and experimental studies, we demonstrate that the incorporation of accurate image priors significantly improves the fidelity of the reconstructed conductivity distribution. The method is robust across varying levels of noise in the measurement data, and the quality of the reconstruction is notably higher when the prior closely resembles the true distribution. This work highlights the importance of leveraging prior information in EIT and provides a framework that could be extended to other inverse problems where prior knowledge is available.

Past, present, and future of electrical impedance tomography and myography for medical applications: a scoping review

This scoping review summarizes two emerging electrical impedance technologies: electrical impedance myography (EIM) and electrical impedance tomography (EIT). These methods involve injecting a current into tissue and recording the response at different frequencies to understand tissue properties. The review discusses basic methods and trends, particularly the use of electrodes: EIM uses electrodes for either injection or recording, while EIT uses them for both. Ag/AgCl electrodes are prevalent, and current injection is preferred over voltage injection due to better resistance to electrode wear and impedance changes. Advances in digital processing and integrated circuits have shifted EIM and EIT toward digital acquisition, using voltage-controlled current sources (VCCSs) that support multiple frequencies. The review details powerful processing algorithms and reconstruction tools for EIT and EIM, examining their strengths and weaknesses. It also summarizes commercial devices and clinical applications: EIT is effective for detecting cancerous tissue and monitoring pulmonary issues, while EIM is used for neuromuscular disease detection and monitoring. The role of machine learning and deep learning in advancing diagnosis, treatment planning, and monitoring is highlighted. This review provides a roadmap for researchers on device evolution, algorithms, reconstruction tools, and datasets, offering clinicians and researchers information on commercial devices and clinical studies for effective use and innovative research.

Seeing Through Muddy Water: Laser-Induced Graphene for Portable Tomography Imaging

Due to its outstanding physical and chemical properties, graphene synthesized by laser scribing on polyimide (PI) offers excellent opportunities for photothermal applications, antiviral and antibacterial surfaces, and electrochemical storage and sensing. However, the utilization of such graphene for imaging is yet to be explored. Herein, using chemically durable and electrically conductive laser-induced graphene (LIG) for tomography imaging in aqueous suspensions is proposed. These graphene electrodes are designed as impedance imaging units for four-terminal electrical measurements. Using the real-time portable imaging prototypes, the conductive and dielectric objects can be seen in clear and muddy water with equivalent impedance modeling. This low-cost graphene tomography measurement system offers significant advantages over traditional visual cameras, in which the suspended muddy particles hinder the imaging resolution. This research shows the potential of applying graphene nanomaterials in emerging marine technologies, such as underwater robotics and automatic fisheries.

Multi-Path Fusion in SFCF-Net for Enhanced Multi-Frequency Electrical Impedance Tomography

Multi-frequency electrical impedance tomography (mfEIT) offers a nondestructive imaging technology that reconstructs the distribution of electrical characteristics within a subject based on the impedance spectral differences among biological tissues. However, the technology faces challenges in imaging multi-class lesion targets when the conductivity of background tissues is frequency-dependent. To address these issues, we propose a spatial-frequency cross-fusion network (SFCF-Net) imaging algorithm, built on a multi-path fusion structure. This algorithm uses multi-path structures and hyper-dense connections to capture both spatial and frequency correlations between multi-frequency conductivity images, which achieves differential imaging for lesion targets of multiple categories through cross-fusion of information. According to both simulation and physical experiment results, the proposed SFCF-Net algorithm shows an excellent performance in terms of lesion imaging and category discrimination compared to the weighted frequency-difference, U-Net, and MMV-Net algorithms. The proposed algorithm enhances the ability of mfEIT to simultaneously obtain both structural and spectral information from the tissue being examined and improves the accuracy and reliability of mfEIT, opening new avenues for its application in clinical diagnostics and treatment monitoring.

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.

Image reconstruction of electrostatic tomography based on the improved residual network

The core of electrostatic tomography (EST) is to solve the inverse problem, but the EST independent measurement data are much smaller than the value that needs to be reconstructed, resulting in a more serious inverse problem. This paper presents an improved ResNet-34 network (P-ResNet), which consists of an input layer, a residual feature extraction layer, and an output layer. The number of residual blocks is 3, 4, 4, and 3. After the second convolution in the main path of each residual block, a ReLU activation function is added to enhance the nonlinear expression ability of the network, and the generalization ability of the model is improved by introducing the L2 regularization loss function. A total of 15 930 sets of samples were simulated for the simulation test. After 200 rounds of iteration, the reconstruction results show that the network achieves high accuracy in EST image reconstruction tasks. In addition, the model is tested under different degrees of Gaussian white noise to verify its anti-noise ability. Compared with the traditional algorithms, the image correlation coefficients of this proposed model network are higher. In addition, this paper designs a small sensor to obtain the induced charge values through the principle of electrostatic induction. The reconstructed results obtained from the experimental data are consistent with the simulation results, which verifies the effectiveness and generalization ability of the proposed model.

Layered Fusion Reconstruction Based on Fuzzy Features for Multi-Conductivity Electrical Impedance Tomography

In medical imaging, detecting tissue anomalies is vital for accurate diagnosis and effective treatment. Electrical impedance tomography (EIT) is a non-invasive technique that monitors the changes in electrical conductivity within tissues in real time. However, the current challenge lies in simply and accurately reconstructing multi-conductivity distributions. This paper introduces a layered fusion framework for EIT to enhance imaging in multi-conductivity scenarios. The method begins with pre-imaging and extracts the main object from the fuzzy image to form one layer. Then, the voltage difference in the other layer, where the local anomaly is located, is estimated. Finally, the corresponding conductivity distribution is established, and multiple layers are fused to reconstruct the multi-conductivity distribution. The simulation and experimental results demonstrate that compared to traditional methods, the proposed method significantly improves multi-conductivity separation, precise anomaly localization, and robustness without adding uncertain parameters. Notably, the proposed method has demonstrated exceptional accuracy in local anomaly detection, with positional errors as low as 1% and size errors as low as 33%, which significantly outperforms the traditional method with respective minimum errors of 9% and 228%. This method ensures a balance between the simplicity and accuracy of the algorithm. At the same time, it breaks the constraints of traditional linear methods, struggling to identify multi-conductivity distributions, thereby providing new perspectives for clinical EIT.

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.

Evaluation of adjacent and opposite current injection patterns for a wearable chest electrical impedance tomography system

Objective.Wearable electrical impedance tomography (EIT) can be used to monitor regional lung ventilation and perfusion at the bedside. Due to its special system architecture, the amplitude of the injected current is usually limited compared to stationary EIT system. This study aims to evaluate the performance of current injection patterns with various low-amplitude currents in healthy volunteers.Approach.A total of 96 test sets of EIT measurement was recorded in 12 healthy subjects by employing adjacent and opposite current injection patterns with four amplitudes of small current (i.e. 1 mA, 500 uA, 250 uA and 125 uA). The performance of the two injection patterns with various currents was evaluated in terms of signal-to-noise ratio (SNR) of thorax impedance, EIT image metrics and EIT-based clinical parameters.Main results.Compared with adjacent injection, opposite injection had higher SNR (p< 0.01), less inverse artifacts (p< 0.01), and less boundary artifacts (p< 0.01) with the same current amplitude. In addition, opposite injection exhibited more stable EIT-based clinical parameters (p< 0.01) across the current range. For adjacent injection, significant differences were found for three EIT image metrics (p< 0.05) and four EIT-based clinical parameters (p< 0.01) between the group of 125 uA and the other groups.Significance.For better performance of wearable pulmonary EIT, currents greater than 250 uA should be used in opposite injection, 500 uA in adjacent one, to ensure a high level of SNR, a high quality of reconstructed image as well as a high reliability of clinical parameters.

Log-Gaussian gamma processes for training Bayesian neural networks in Raman and CARS spectroscopies

We propose an approach utilizing gamma-distributed random variables, coupled with log-Gaussian modeling, to generate synthetic datasets suitable for training neural networks. This addresses the challenge of limited real observations in various applications. We apply this methodology to both Raman and coherent anti-Stokes Raman scattering (CARS) spectra, using experimental spectra to estimate gamma process parameters. Parameter estimation is performed using Markov chain Monte Carlo methods, yielding a full Bayesian posterior distribution for the model which can be sampled for synthetic data generation. Additionally, we model the additive and multiplicative background functions for Raman and CARS with Gaussian processes. We train two Bayesian neural networks to estimate parameters of the gamma process which can then be used to estimate the underlying Raman spectrum and simultaneously provide uncertainty through the estimation of parameters of a probability distribution. We apply the trained Bayesian neural networks to experimental Raman spectra of phthalocyanine blue, aniline black, naphthol red, and red 264 pigments and also to experimental CARS spectra of adenosine phosphate, fructose, glucose, and sucrose. The results agree with deterministic point estimates for the underlying Raman and CARS spectral signatures.

High-resolution conductivity reconstruction by electrical impedance tomography using structure-aware hybrid-fusion learning

BACKGROUND

Electrical impedance tomography (EIT) has gained considerable attention in the medical field for the diagnosis of lung-related diseases, owing to its non-invasive and real-time characteristics. However, due to the ill-posedness and underdetermined nature of the inverse problem in EIT, suboptimal reconstruction performance and reduced robustness against the measurement noise and modeling errors are common issues.

OBJECTIVES

This study aims to mine the deep feature information from measurement voltages, acquired from the EIT sensor, to reconstruct the high-resolution conductivity distribution and enhance the robustness against the measurement noise and modeling errors using the deep learning method.

METHODS

A novel data-driven method named the structure-aware hybrid-fusion learning (SA-HFL) is proposed. SA-HFL is composed of three main components: a segmentation branch, a conductivity reconstruction branch, and a feature fusion module. These branches work in tandem to extract different feature information from the measurement voltage, which is then fused to reconstruct the conductivity distribution. The unique aspect of this network is its ability to utilize different features extracted from various branches to accomplish reconstruction objectives. To supervise the training of the network, we generated regular-shaped and lung-shaped EIT datasets through numerical calculations.

RESULTS

The simulations and three experiments demonstrate that the proposed SA-HFL exhibits superior performance in qualitative and quantitative analyses, compared with five cutting-edge deep learning networks and the optical image-guided group sparsity (IGGS) method. The evaluation metrics, relative error (RE), mean structural similarity index (MSSIM), and peak signal-to-noise ratio (PSNR), are improved by implementing the SA-HFL method. For the regular-shaped dataset, the values are 0.119 (RE), 0.9882 (MSSIM), and 31.03 (PSNR). For the lung-shaped dataset, the values are 0.257 (RE), 0.9151 (MSSIM), and 18.67 (PSNR). Furthermore, the proposed network can be executed with appropriate parameters and efficient floating-point operations per second (FLOPs), concerning network complexity and inference speed.

CONCLUSIONS

The reconstruction results indicate that fusing feature information from different branches enhances the accuracy of conductivity reconstruction in the EIT inverse problem. Moreover, the study shows that fusing different modalities of information to reconstruct the EIT conductivity distribution may be a future development direction.

Domain independent post-processing with graph U-nets: applications to electrical impedance tomographic imaging⋆

Objective.To extend the highly successful U-Net Convolutional Neural Network architecture, which is limited to rectangular pixel/voxel domains, to a graph-based equivalent that works flexibly on irregular meshes; and demonstrate the effectiveness on electrical impedance tomography (EIT).Approach.By interpreting the irregular mesh as a graph, we develop a graph U-Net with new cluster pooling and unpooling layers that mimic the classic neighborhood based max-pooling important for imaging applications.Mainresults.The proposed graph U-Net is shown to be flexible and effective for improving early iterate total variation (TV) reconstructions from EIT measurements, using as little as the first iteration. The performance is evaluated for simulated data, and on experimental data from three measurement devices with different measurement geometries and instrumentations. We successfully show that such networks can be trained with a simple two-dimensional simulated training set, and generalize to very different domains, including measurements from a three-dimensional device and subsequent 3D reconstructions.Significance.As many inverse problems are solved on irregular (e.g. finite element) meshes, the proposed graph U-Net and pooling layers provide the added flexibility to process directly on the computational mesh. Post-processing an early iterate reconstruction greatly reduces the computational cost which can become prohibitive in higher dimensions with dense meshes. As the graph structure is independent of 'dimension', the flexibility to extend networks trained on 2D domains to 3D domains offers a possibility to further reduce computational cost in training.

Comparing machine learning algorithms for non-invasive detection and classification of failure in piezoresistive bone cement via electrical impedance tomography

At an estimated cost of $8 billion annually in the United States, revision surgeries to total joint replacements represent a substantial financial burden to the health care system and a tremendous mental and physical burden on patients and their caretakers. Fixation failures, such as implant loosening, wear, and mechanical instability of the poly(methyl methacrylate) (PMMA) cement, which bonds the implant to the bone, are the main causes of long-term implant failure. Early and accurate diagnosis of cement failure is critical for developing novel therapeutic strategies and reducing the high risk of a misjudged revision. Unfortunately, prevailing imaging modalities, notably plain radiographs, struggle to detect the precursors of implant failure and are often interpreted incorrectly. Our prior work has shown that the modification of PMMA bone cement with low concentrations of conductive fillers makes it piezoresistive and therefore self-sensing. When combined with a conductivity imaging modality such as electrical impedance tomography (EIT), it is possible to monitor load transfer across the PMMA using cost-effective, physiologically benign, non-contact, and real-time electrical measurements. Despite the ability of EIT for monitoring load transfer across self-sensing PMMA bone cement, it is unable to accurately characterize failure mechanisms. Overcoming this challenge is critical to the success of this technology in practice. Therefore, we herein expand upon our previous results by integrating machine learning techniques with EIT for cement condition characterization with the goal of establishing the feasibility of even off-the-shelf machine learning algorithms to address this important problem. We survey a wide variety of different machine learning algorithms for application to this problem, including neural networks on voltage readings of an EIT phantom for tracking the spatial position of a sample, specifying defect orientation within a sample, and classifying defect types, including cracks and delaminations. In addition, we explore the utilization of principal component analysis (PCA) for pre-treating impedance signals in each of these problems. Within the tested algorithms, our results show clear advantages of neural networks, support vector machines, and K-nearest neighbor algorithms for interpreting EIT signals. We also show that PCA is an effective addition to machine learning. These preliminary results demonstrate that the combination of smart materials, EIT, and machine learning may be a powerful instrumentation tool for diagnosing the origin and evolution of mechanical failure in joint replacements.

A cascaded convolutional neural networks for stroke detection imaging

In recent years, electrical impedance tomography has widely been used in stroke detection. To improve the prediction accuracy and anti-noise ability of the system, the inverse problem of electrical impedance tomography needs to be solved, for which cascade convolutional neural networks are used. The proposed network is divided into two parts so that the advantages can be compounded when parts of a network are cascaded together. To get high-resolution imaging, an optimized network based on encoding and decoding is designed in the first part. The second part is composed of a residual module, which is used to extract the characteristics of voltage information and ensure that no information is lost. The anti-noise performance of the network is better than other networks. In physical experiments, it is also proved that the algorithm can roughly restore the location of the object in the field.

MMV-Net: A Multiple Measurement Vector Network for Multifrequency Electrical Impedance Tomography

Multifrequency electrical impedance tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods suffer from low spatial resolution, unconstrained frequency correlation, and high computational cost. Deep learning has been extensively applied in solving the EIT inverse problem in biomedical and industrial process imaging. However, most existing learning-based approaches deal with the single-frequency setup, which is inefficient and ineffective when extended to the multifrequency setup. This article presents a multiple measurement vector (MMV) model-based learning algorithm named MMV-Net to solve the mfEIT image reconstruction problem. MMV-Net considers the correlations between mfEIT images and unfolds the update steps of the Alternating Direction Method of Multipliers for the MMV problem (MMV-ADMM). The nonlinear shrinkage operator associated with the weighted l2,1 regularization term of MMV-ADMM is generalized in MMV-Net with a cascade of a Spatial Self-Attention module and a Convolutional Long Short-Term Memory (ConvLSTM) module to better capture intrafrequency and interfrequency dependencies. The proposed MMV-Net was validated on our Edinburgh mfEIT Dataset and a series of comprehensive experiments. The results show superior image quality, convergence performance, noise robustness, and computational efficiency against the conventional MMV-ADMM and the state-of-the-art deep learning methods.

Electrical Impedance Tomography of Industrial Two-Phase Flow Based on Radial Basis Function Neural Network Optimized by the Artificial Bee Colony Algorithm

In electrical impedance tomography (EIT) detection of industrial two-phase flows, the Gauss-Newton algorithm is often used for imaging. In complex cases with multiple bubbles, this method has poor imaging accuracy. To address this issue, a new algorithm called the artificial bee colony-optimized radial basis function neural network (ABC-RBFNN) is applied to industrial two-phase flow EIT for the first time. This algorithm aims to enhance the accuracy of image reconstruction in electrical impedance tomography (EIT) technology. The EIDORS-v3.10 software platform is utilized to generate electrode data for a 16-electrode EIT system with varying numbers of bubbles. This generated data is then employed as training data to effectively train the ABC-RBFNN model. The reconstructed electrical impedance image produced from this process is evaluated using the image correlation coefficient (ICC) and root mean square error (RMSE) criteria. Tests conducted on both noisy and noiseless test set data demonstrate that the ABC-RBFNN algorithm achieves a higher ICC value and a lower RMSE value compared to the Gauss-Newton algorithm and the radial basis function neural network (RBFNN) algorithm. These results validate that the ABC-RBFNN algorithm exhibits superior noise immunity. Tests conducted on bubble models of various sizes and quantities, as well as circular bubble models, demonstrate the ABC-RBFNN algorithm's capability to accurately determine the size and shape of bubbles. This outcome confirms the algorithm's generalization ability. Moreover, when experimental data collected from a 16-electrode EIT experimental device is employed as test data, the ABC-RBFNN algorithm consistently and accurately identifies the size and position of the target. This achievement establishes a solid foundation for the practical application of the algorithm.

Dual-Modal Image Reconstruction for Electrical Impedance Tomography With Overlapping Group Lasso and Laplacian Regularization

OBJECTIVE

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.

METHODS

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.

RESULTS

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.

CONCLUSION

This work proves the effectiveness of OGLL in improving EIT image quality.

SIGNIFICANCE

This study demonstrates that EIT has the potential to be adopted in quantitative tissue analysis by using such dual-modal imaging approaches.

Shape analysis of training data for neural networks in Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) is a cost-effective and fast way to visualize dielectric properties of the human body, through the injection of alternating currents and measurement of the resulting potential on the bodies surface. However, this comes at the cost of low resolution as EIT is a non-linear ill-posed inverse problem. Recently Deep Learning methods have gained the interest in this field, as they provide a way to mimic non-linear functions. Most of the approaches focus on the structure of the Artificial Neural Networks (ANNs), while only glancing over the used training data. However, the structure of the training data is of great importance, as it needs to be simulated. In this work, we analyze the effect of basic shapes to be included as targets in the training data set. We compared inclusions of ellipsoids, cubes and octahedra as training data for ANNs in terms of reconstruction quality. For that, we used the well-established GREIT figures of merit on laboratory tank measurements. We found that ellipsoids resulted in the best reconstruction quality of EIT images. This shows that the choice of simulation data has an impact on the ANN reconstruction quality.Clinical relevance- This work helps to improve time independent EIT reconstruction, which in turn allows for extraction of time independent features of e.g., the lung.

Effective Electrical Impedance Tomography Based on Enhanced Encoder-Decoder Using Atrous Spatial Pyramid Pooling Module

Electrical impedance tomography (EIT) is a noninvasive and radiation-free imaging method. As a "soft-field" imaging technique, in EIT, the target signal in the center of the measured field is frequently swamped by the target signal at the edge, which restricts its further application. To alleviate this problem, this study presents an enhanced encoder-decoder (EED) method with an atrous spatial pyramid pooling (ASPP) module. The proposed method enhances the ability to detect central weak targets by constructing an ASPP module that integrates multiscale information in the encoder. The multilevel semantic features are fused in the decoder to improve the boundary reconstruction accuracy of the center target. The average absolute error of the imaging results by the EED method reduced by 82.0%, 83.6%, and 36.5% in simulation experiments and 83.0%, 83.2%, and 36.1% in physical experiments compared with the errors of the damped least-squares algorithm, Kalman filtering method, and U-Net-based imaging method, respectively. The average structural similarity improved by 37.3%, 42.9%, and 3.6%, and 39.2%, 45.2%, and 3.8% in the simulation and physical experiments, respectively. The proposed method provides a practical and reliable means of extending the application of EIT by solving the problem of weak central target reconstruction under the effect of strong edge targets in EIT.

Effect of a Patient-Specific Structural Prior Mask on Electrical Impedance Tomography Image Reconstructions

Electrical Impedance Tomography (EIT) is a low-cost imaging method which reconstructs two-dimensional cross-sectional images, visualising the impedance change within the thorax. However, the reconstruction of an EIT image is an ill-posed inverse problem. In addition, blurring, anatomical alignment, and reconstruction artefacts can hinder the interpretation of EIT images. In this contribution, we introduce a patient-specific structural prior mask into the EIT reconstruction process, with the aim of improving image interpretability. Such a prior mask ensures that only conductivity changes within the lung regions are reconstructed. To evaluate the influence of the introduced structural prior mask, we conducted numerical simulations with two scopes in terms of their different ventilation statuses and varying atelectasis scales. Quantitative analysis, including the reconstruction error and figures of merit, was applied in the evaluation procedure. The results show that the morphological structures of the lungs introduced by the mask are preserved in the EIT reconstructions and the reconstruction artefacts are decreased, reducing the reconstruction error by 25.9% and 17.7%, respectively, in the two EIT algorithms included in this contribution. The use of the structural prior mask conclusively improves the interpretability of the EIT images, which could facilitate better diagnosis and decision-making in clinical settings.

Robust electrical impedance tomography for biological application: A mini review

Electrical impedance tomography (EIT) has been used by researchers across several areas because of its low-cost and no-radiation properties. Researchers use complex conductivity in bioimpedance experiments to evaluate changes in various indicators within the image target. The diverse volumes and edges of biological tissues and the large impedance range impose dedicated demands on hardware design. The EIT hardware with a high signal-to-noise ratio (SNR), fast scanning and suitable for the impedance range of the image target is a fundamental foundation that EIT research needs to be equipped with. Understanding the characteristics of this technique and state-of-the-art design will accelerate the development of the robust system and provide a guidance for the superior performance of next-generation EIT. This review explores the hardware strategies for EIT proposed in the literature.

The Synergy between Deep Learning and Organs-on-Chips for High-Throughput Drug Screening: A Review

Organs-on-chips (OoCs) are miniature microfluidic systems that have arguably become a class of advanced in vitro models. Deep learning, as an emerging topic in machine learning, has the ability to extract a hidden statistical relationship from the input data. Recently, these two areas have become integrated to achieve synergy for accelerating drug screening. This review provides a brief description of the basic concepts of deep learning used in OoCs and exemplifies the successful use cases for different types of OoCs. These microfluidic chips are of potential to be assembled as highly potent human-on-chips with complex physiological or pathological functions. Finally, we discuss the future supply with perspectives and potential challenges in terms of combining OoCs and deep learning for image processing and automation designs.

Implicit Solutions of the Electrical Impedance Tomography Inverse Problem in the Continuous Domain with Deep Neural Networks

Electrical impedance tomography (EIT) is a non-invasive imaging modality used for estimating the conductivity of an object Ω from boundary electrode measurements. In recent years, researchers achieved substantial progress in analytical and numerical methods for the EIT inverse problem. Despite the success, numerical instability is still a major hurdle due to many factors, including the discretization error of the problem. Furthermore, most algorithms with good performance are relatively time consuming and do not allow real-time applications. In our approach, the goal is to separate the unknown conductivity into two regions, namely the region of homogeneous background conductivity and the region of non-homogeneous conductivity. Therefore, we pose and solve the problem of shape reconstruction using machine learning. We propose a novel and simple jet intriguing neural network architecture capable of solving the EIT inverse problem. It addresses previous difficulties, including instability, and is easily adaptable to other ill-posed coefficient inverse problems. That is, the proposed model estimates the probability for a point of whether the conductivity belongs to the background region or to the non-homogeneous region on the continuous space Rd&cap;Ω with d∈{2,3}. The proposed model does not make assumptions about the forward model and allows for solving the inverse problem in real time. The proposed machine learning approach for shape reconstruction is also used to improve gradient-based methods for estimating the unknown conductivity. In this paper, we propose a piece-wise constant reconstruction method that is novel in the inverse problem setting but inspired by recent approaches from the 3D vision community. We also extend this method into a novel constrained reconstruction method. We present extensive numerical experiments to show the performance of the architecture and compare the proposed method with previous analytic algorithms, mainly the monotonicity-based shape reconstruction algorithm and iteratively regularized Gauss-Newton method.

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.

Regularization Solver Guided FISTA for Electrical Impedance Tomography

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.

Structural priors represented by discrete cosine transform improve EIT functional imaging

Structural prior information can improve electrical impedance tomography (EIT) reconstruction. In this contribution, we introduce a discrete cosine transformation-based (DCT-based) EIT reconstruction algorithm to demonstrate a way to incorporate the structural prior with the EIT reconstruction process. Structural prior information is obtained from other available imaging methods, e.g., thorax-CT. The DCT-based approach creates a functional EIT image of regional lung ventilation while preserving the introduced structural information. This leads to an easier interpretation in clinical settings while maintaining the advantages of EIT in terms of bedside monitoring during mechanical ventilation. Structural priors introduced in the DCT-based approach are of two categories in terms of different levels of information included: a contour prior only differentiates lung and non-lung region, while a detail prior includes information, such as atelectasis, within the lung area. To demonstrate the increased interpretability of the EIT image through structural prior in the DCT-based approach, the DCT-based reconstructions were compared with reconstructions from a widely applied one-step Gauss-Newton solver with background prior and from the advanced GREIT algorithm. The comparisons were conducted both on simulation data and retrospective patient data. In the simulation, we used two sets of forward models to simulate different lung conditions. A contour prior and a detail prior were derived from simulation ground truth. With these two structural priors, the reconstructions from the DCT-based approach were compared with the reconstructions from both the one-step Gauss-Newton solver and the GREIT. The difference between the reconstructions and the simulation ground truth is calculated by the ℓ2-norm image difference. In retrospective patient data analysis, datasets from six lung disease patients were included. For each patient, a detail prior was derived from the patient's CT, respectively. The detail prior was used for the reconstructions using the DCT-based approach, which was compared with the reconstructions from the GREIT. The reconstructions from the DCT-based approach are more comprehensive and interpretable in terms of preserving the structure specified by the priors, both in simulation and retrospective patient data analysis. In simulation analysis, the ℓ2-norm image difference of the DCT-based approach with a contour prior decreased on average by 34% from GREIT and 49% from the Gauss-Newton solver with background prior; for reconstructions of the DCT-based approach with detail prior, on average the ℓ2-norm image difference is 53% less than GREIT and 63% less than the reconstruction with background prior. In retrospective patient data analysis, the reconstructions from both the DCT-based approach and GREIT can indicate the current patient status, but the DCT-based approach yields more interpretable results. However, it is worth noting that the preserved structure in the DCT-based approach is derived from another imaging method, not from the EIT measurement. If the structural prior is outdated or wrong, the result might be misleadingly interpreted, which induces false clinical conclusions. Further research in terms of evaluating the validity of the structural prior and detecting the outdated prior is necessary.

Using Novel Multi-Frequency Analysis Methods to Retrieve Material and Temperature Information in Tactile Sensing Areas

This article presents a novel artificial skin technology based on the Electric Impedance Tomography (EIT) that employs multi-frequency currents for detecting the material and the temperature of objects in contact with piezoresistive sheets. To date, few artificial skins in the literature are capable of detecting an object's material, e.g., wood, skin, leather, or plastic. EIT-based artificial skins have been employed mostly to detect the position of the contact but not its characteristics. Thanks to multi-frequency currents, our EIT-based artificial skin is capable of characterising the spectral profile of objects in contact and identifying an object's material at ambient temperature. Moreover, our model is capable of detecting several levels of temperature (from -10 up to 60 °C) and can also maintain a certain accuracy for material identification. In addition to the known capabilities of EIT-based artificial skins concerning detecting pressure and location of objects, as well as being low cost, these two novel modalities demonstrate the potential of EIT-based artificial skins to achieve global tactile sensing.

Case-Specific Focal Sensor Design for Cardiac Electrical Impedance Tomography

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.

Study and comparison of different Machine Learning-based approaches to solve the inverse problem in Electrical Impedance Tomographies

Electrical Impedance Tomography (EIT) is a non-invasive technique used to obtain the electrical internal conductivity distribution from the interior of bodies. This is a promising method from the manufacturing viewpoint, since it could be used to estimate different physical inner body properties during the production of goods. Nevertheless, this technique requires dealing with an inverse problem that makes its usage in real-time processes challenging. Recently, Machine Learning techniques have been proposed to solve the inverse problem accurately. However, the majority of prior research is focused on qualitative results, and they typically lack a systematic methodology to determine the optimal hyperparameters appropriately. This work presents a systematic comparison of six popular Machine Learning algorithms: Artificial Neural Network, Random Forest, K-Nearest Neighbors, Elastic Net, Ada Boost, and Gradient Boosting. Particularly, the last two algorithms were based on decision tree learners. Furthermore, we studied the relationship between model performance and different EIT configurations. Specifically, we analyzed whether the measurement pattern and the number of used electrodes could increase the model performance. Experiments revealed that tree-based models present high performance, even better than Neural Networks, the most widely-used Machine Learning model to deal with EIT. Experiments also showed a model performance improvement when the EIT configuration was optimized. Most favorable metrics were attained using the tree-based Gradient Boosting model with a combination of both adjacent and mono measurement patterns as well as with 32 electrodes deployed during the tomographic process. With this particular setting, we achieved an accuracy of 99.14% detecting internal artifacts and a Root Mean Square Error of 4.75 predicting internal conductivity distributions.

Optimal Implementation Parameters of a Nonlinear Electrical Impedance Tomography Method Using the Complete Electrode Model

This study discusses a nonlinear electrical impedance tomography (EIT) technique under different analysis conditions to propose its optimal implementation parameters. The forward problem for calculating electric potential is defined by the complete electrode model. The inverse problem for reconstructing the target electrical conductivity profile is presented based on a partial-differential-equation-constrained optimization approach. The electrical conductivity profile is iteratively updated by solving the Karush-Kuhn-Tucker optimality conditions and using the conjugate gradient method with an inexact line search. Various analysis conditions such as regularization scheme, number of electrodes, current input patterns, and electrode arrangement were set differently, and the corresponding results were compared. It was found from this study that the proposed EIT method yielded appropriate inversion results with various parameter settings, and the optimal implementation parameters of the EIT method are presented. This study is expected to expand the utility and applicability of EIT for the non-destructive evaluation of structures.

Improved resolution of D-bar images of ventilation using a Schur complement property and an anatomical atlas

BACKGROUND

Electrical impedance tomography (EIT) is a nonionizing imaging technique for real-time imaging of ventilation of patients with respiratory distress. Cross-sectional dynamic images are formed by reconstructing the conductivity distribution from measured voltage data arising from applied alternating currents on electrodes placed circumferentially around the chest. Since the conductivity of lung tissue depends on air content, blood flow, and the presence of pathology, the dynamic images provide regional information about ventilation, pulsatile perfusion, and abnormalities. However, due to the ill-posedness of the inverse conductivity problem, EIT images have a coarse spatial resolution. One method of improving the resolution is to include prior information in the reconstruction.

PURPOSE

In this work, we propose a technique in which a statistical prior built from an anatomical atlas is used to postprocess EIT reconstructions of human chest data. The effectiveness of the method is demonstrated on data from two patients with cystic fibrosis.

METHODS

A direct reconstruction algorithm known as the D-bar method was used to compute a two-dimensional reconstruction of the conductivity distribution in the plane of the electrodes. Reconstructions using one step in an iterative (regularized) Newton's method were also computed for comparison. An anatomical atlas consisting of 1589 synthetic EIT images computed from X-ray computed tomography (CT) scans of 74 adult male subjects was computed for use as a statistical prior. The resolution of the D-bar images was then improved by maximizing the conditional probability density function of an image that is consistent with the a priori information and the statistical model. A new method to evaluate the accuracy of the EIT images using CT scans of the imaged patient as ground truth is presented. The novel approach is tested on data from two patients with cystic fibrosis.

RESULTS AND CONCLUSIONS

The D-bar images resulted in better structural similarity index measures (SSIM) and multiscale (MS) SSIM measures for both subjects using the mask or amplitude evaluation approach than the one-step (regularized) Newton's method. Further improvement was achieved using the Schur complement (SC) approach, with MS-SSIM values of 0.718 and 0.682 using SC evaluated with the mask and amplitude approach, respectively, for Patient 1, and MS-SSIM values of 0.726 and 0.692 using SC evaluated with the mask and amplitude approach, respectively, for Patient 2. The results from applying an anatomical atlas and statistical prior to EIT data from two patients with cystic fibrosis suggest that the spatial resolution of the EIT image can be improved to reveal pathology that may be difficult to discern in the original EIT image. The novel metric of evaluation is consistent with the appearance of improved spatial resolution and provides a new way to evaluate the accuracy of EIT reconstructions when a CT scan is available.

Signal-to-noise ratio variance impact on the image reconstruction of electrical resistance tomography in solutions with high background conductivity

Electrical Resistance Tomography (ERT) has the potentialities of non-intrusive techniques and high temporal resolution which are essential characteristics for multiphase flow measurements. However, high background conductivities, such as saline water in oil extraction, impose a limitation in ERT image reconstruction. Focusing on the operational limits of an ERT tomography system operating in different conductivity backgrounds from 0.010 to 4.584 S/m, the impact on the image reconstruction was assessed via signal-to-noise variance. The signal-to-noise ratio (SNR) variance had a strong correlation (p-value = 5.40 × 10^-15) with the image reconstruction quality at the threshold of 30 dB, reaching a correlation value of r = -0.92 in the range of 0.010-0.246 S/m. Regarding the position error of the phantom, p-value = 1.30 × 10^-5 and r = -0.66 were attained. The global results revealed that the correlation of the mean of the SNR (p-value = 5 × 10^-4 and r = 0.55) was kept unaltered through the whole conductivity range, showing that such a statistical index can induce bias in establishing the operational limits of the hardware.

A Model-Based Iterative Learning Approach for Diffuse Optical Tomography

Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse problem, due to the non-linear light propagation in tissues and limited boundary measurements. The ill-posedness means that the image reconstruction is sensitive to measurement and modelling errors. The Bayesian approach for the inverse problem of DOT offers the possibility of incorporating prior information about the unknowns, rendering the problem less ill-posed. It also allows marginalisation of modelling errors utilising the so-called Bayesian approximation error method. A more recent trend in image reconstruction techniques is the use of deep learning, which has shown promising results in various applications from image processing to tomographic reconstructions. In this work, we study the non-linear DOT inverse problem of estimating the (absolute) absorption and scattering coefficients utilising a 'model-based' learning approach, essentially intertwining learned components with the model equations of DOT. The proposed approach was validated with 2D simulations and 3D experimental data. We demonstrated improved absorption and scattering estimates for targets with a mix of smooth and sharp image features, implying that the proposed approach could learn image features that are difficult to model using standard Gaussian priors. Furthermore, it was shown that the approach can be utilised in compensating for modelling errors due to coarse discretisation enabling computationally efficient solutions. Overall, the approach provided improved computation times compared to a standard Gauss-Newton iteration.

Majorization–Minimization Total Variation Solution Methods for Electrical Impedance Tomography

Inverse problems arise in many areas of science and engineering, such as geophysics, biology, and medical imaging. One of the main imaging modalities that have seen a huge increase in recent years is the noninvasive, nonionizing, and radiation-free imaging technique of electrical impedance tomography (EIT). Other advantages of such a technique are the low cost and ubiquitousness. An imaging technique is used to recover the internal conductivity of a body using measurements from electrodes from the body’s surface. The standard procedure is to obtain measurements by placing electrodes in the body and measuring conductivity inside the object. A current with low frequency is applied on the electrodes below a threshold, rendering the technique harmless for the body, especially when applied to living organisms. As with many inverse problems, EIT suffers from ill-posedness, i.e., the reconstruction of internal conductivity is a severely ill-posed inverse problem and typically yields a poor-quality solution. Moreover, the desired solution has step changes in the electrical properties that are typically challenging to be reconstructed by traditional smoothing regularization methods. To counter this difficulty, one solves a regularized problem that is better conditioned than the original problem by imposing constraints on the regularization term. The main contribution of this work is to develop a general ℓp regularized method with total variation to solve the nonlinear EIT problem through a iteratively reweighted majorization–minimization strategy combined with the Gauss–Newton approach. The main idea is to majorize the linearized EIT problem at each iteration and minimize through a quadratic tangent majorant. Simulated numerical examples from complete electrode model illustrate the effectiveness of our approach.

Impedance-Optical Dual-Modal Cell Culture Imaging With Learning-Based Information Fusion

While Electrical Impedance Tomography (EIT) has found many biomedicine applications, better image quality is needed to provide quantitative analysis for tissue engineering and regenerative medicine. This paper reports an impedance-optical dual-modal imaging framework that primarily targets at high-quality 3D cell culture imaging and can be extended to other tissue engineering applications. The framework comprises three components, i.e., an impedance-optical dual-modal sensor, the guidance image processing algorithm, and a deep learning model named multi-scale feature cross fusion network (MSFCF-Net) for information fusion. The MSFCF-Net has two inputs, i.e., the EIT measurement and a binary mask image generated by the guidance image processing algorithm, whose input is an RGB microscopic image. The network then effectively fuses the information from the two different imaging modalities and generates the final conductivity image. We assess the performance of the proposed dual-modal framework by numerical simulation and MCF-7 cell imaging experiments. The results show that the proposed method could improve the image quality notably, indicating that impedance-optical joint imaging has the potential to reveal the structural and functional information of tissue-level targets simultaneously.

Adaptively Regularized Bases-Expansion Subspace Optimization Methods for Electrical Impedance Tomography

OBJECTIVE

In this work, to deal with the difficulties in choosing regularization weighting parameters and low spatial resolution problems in difference electrical impedance tomography (EIT), we propose two adaptively regularized bases-expansion subspace optimization methods (AR-BE-SOMs).

METHODS

Firstly, an adaptive L1-norm based total variation (TV) regularization is introduced under the framework of BE-SOM. Secondly, besides the additive regularization, an adaptive weighted L2-norm multiplicative regularization is further proposed. The regularized objective functions are optimized by conjugate gradient method, where the unknowns in both methods are update alternatively between induced contrast current (ICC) and conductivity domain.

CONCLUSION

Both numerical and experimental tests are conducted to validate the proposed methods, where AR-BE-SOMs show better edge-preserving, anti-noise performance, lower relative errors, and higher structure similarity indexes than BE-SOM.

SIGNIFICANCE

Unlike the common regularization techniques in EIT, the proposed regularization factors can be obtained adaptively during the optimization process. More importantly, ARBE-SOMs perform well in reconstructions of some challenging geometry with sharp corners such as the heart and lung phantoms, deformation phantoms, triangles and even rectangles. It is expected that the proposed AR-BE-SOMs will find their applications for high-quality lung health monitoring and other clinical applications.

A Rotational Invariant Neural Network for Electrical Impedance Tomography Imaging without Reference Voltage: RF-REIM-NET

Background: Electrical Impedance Tomography (EIT) is a radiation-free technique for image reconstruction. However, as the inverse problem of EIT is non-linear and ill-posed, the reconstruction of sharp conductivity images poses a major problem. With the emergence of artificial neural networks (ANN), their application in EIT has recently gained interest. Methodology: We propose an ANN that can solve the inverse problem without the presence of a reference voltage. At the end of the ANN, we reused the dense layers multiple times, considering that the EIT exhibits rotational symmetries in a circular domain. To avoid bias in training data, the conductivity range used in the simulations was greater than expected in measurements. We also propose a new method that creates new data samples from existing training data. Results: We show that our ANN is more robust with respect to noise compared with the analytical Gauss–Newton approach. The reconstruction results for EIT phantom tank measurements are also clearer, as ringing artefacts are less pronounced. To evaluate the performance of the ANN under real-world conditions, we perform reconstructions on an experimental pig study with computed tomography for comparison. Conclusions: Our proposed ANN can reconstruct EIT images without the need of a reference voltage.

Damage detection of carbon fiber reinforced polymer composite materials based on one-dimensional multi-scale residual convolution neural network

Carbon fiber reinforced polymers (CFRPs) have been widely applied in the aerospace industry, and the health conditions of CFRPs largely affect aerospace safety. Due to the limitations of traditional detection methods, electrical impedance tomography (EIT) has been gradually applied in the damage detection of CFRP composite materials. Aiming at the problems of poor imaging quality and low identification rate in the traditional EIT reconstruction algorithm, an EIT algorithm based on the one-dimensional multi-scale residual convolution neural network (1D-MSK-ResNet) is proposed in this paper. A "voltage vector-conductivity media distribution" dataset is first established, and the training results of the testing dataset are used to verify and evaluate the algorithm. Simulation and experimental results indicated that the 1D-MSK-ResNet EIT algorithm could enhance the ability of damage identification and significantly improve the imaging quality.

Advances in electrical impedance tomography-based brain imaging

Novel advances in the field of brain imaging have enabled the unprecedented clinical application of various imaging modalities to facilitate disease diagnosis and treatment. Electrical impedance tomography (EIT) is a functional imaging technique that measures the transfer impedances between electrodes on the body surface to estimate the spatial distribution of electrical properties of tissues. EIT offers many advantages over other neuroimaging technologies, which has led to its potential clinical use. This qualitative review provides an overview of the basic principles, algorithms, and system composition of EIT. Recent advances in the field of EIT are discussed in the context of epilepsy, stroke, brain injuries and edema, and other brain diseases. Further, we summarize factors limiting the development of brain EIT and highlight prospects for the field. In epilepsy imaging, there have been advances in EIT imaging depth, from cortical to subcortical regions. In stroke research, a bedside EIT stroke monitoring system has been developed for clinical practice, and data support the role of EIT in multi-modal imaging for diagnosing stroke. Additionally, EIT has been applied to monitor the changes in brain water content associated with cerebral edema, enabling the early identification of brain edema and the evaluation of mannitol dehydration. However, anatomically realistic geometry, inhomogeneity, cranium completeness, anisotropy and skull type, etc., must be considered to improve the accuracy of EIT modeling. Thus, the further establishment of EIT as a mature and routine diagnostic technique will necessitate the accumulation of more supporting evidence.

Structural engineering from an inverse problems perspective

The field of structural engineering is vast, spanning areas from the design of new infrastructure to the assessment of existing infrastructure. From the onset, traditional entry-level university courses teach students to analyse structural responses given data including external forces, geometry, member sizes, restraint, etc.-characterizing a forward problem (structural causalities → structural response). Shortly thereafter, junior engineers are introduced to structural design where they aim to, for example, select an appropriate structural form for members based on design criteria, which is the inverse of what they previously learned. Similar inverse realizations also hold true in structural health monitoring and a number of structural engineering sub-fields (response → structural causalities). In this light, we aim to demonstrate that many structural engineering sub-fields may be fundamentally or partially viewed as inverse problems and thus benefit via the rich and established methodologies from the inverse problems community. To this end, we conclude that the future of inverse problems in structural engineering is inexorably linked to engineering education and machine learning developments.

Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method typical for nonlinear inverse problems, interpolation and embeddings are needed. To overcome this, we present a flexible framework to extend model-based learning directly to nonuniform meshes, by interpreting the mesh as a graph and formulating our network architectures using graph convolutional neural networks. This gives rise to the proposed iterative Graph Convolutional Newton-type Method (GCNM), which includes the forward model in the solution of the inverse problem, while all updates are directly computed by the network on the problem specific mesh. We present results for Electrical Impedance Tomography, a severely ill-posed nonlinear inverse problem that is frequently solved via optimization-based methods, where the forward problem is solved by finite element methods. Results for absolute EIT imaging are compared to standard iterative methods as well as a graph residual network. We show that the GCNM has good generalizability to different domain shapes and meshes, out of distribution data as well as experimental data, from purely simulated training data and without transfer training.

Electrical impedance tomography for non-invasive identification of fatty liver infiltrate in overweight individuals

Non-alcoholic fatty liver disease (NAFLD) is one of the most common causes of cardiometabolic diseases in overweight individuals. While liver biopsy is the current gold standard to diagnose NAFLD and magnetic resonance imaging (MRI) is a non-invasive alternative still under clinical trials, the former is invasive and the latter costly. We demonstrate electrical impedance tomography (EIT) as a portable method for detecting fatty infiltrate. We enrolled 19 overweight subjects to undergo liver MRI scans, followed by EIT measurements. The MRI images provided the a priori knowledge of the liver boundary conditions for EIT reconstruction, and the multi-echo MRI data quantified liver proton-density fat fraction (PDFF%) to validate fat infiltrate. Using the EIT electrode belts, we circumferentially injected pairwise current to the upper abdomen, followed by acquiring the resulting surface-voltage to reconstruct the liver conductivity. Pearson's correlation analyses compared EIT conductivity or MRI PDFF with body mass index, age, waist circumference, height, and weight variables. We reveal that the correlation between liver EIT conductivity or MRI PDFF with demographics is statistically insignificant, whereas liver EIT conductivity is inversely correlated with MRI PDFF (R = -0.69, p = 0.003, n = 16). As a pilot study, EIT conductivity provides a portable method for operator-independent and cost-effective detection of hepatic steatosis.

Toward More Robust Hand Gesture Recognition on EIT Data

Striving for more robust and natural control of multi-fingered hand prostheses, we are studying electrical impedance tomography (EIT) as a method to monitor residual muscle activations. Previous work has shown promising results for hand gesture recognition, but also lacks generalization across multiple sessions and users. Thus, the present paper aims for a detailed analysis of an existing EIT dataset acquired with a 16-electrode wrist band as a prerequisite for further improvements of machine learning results on this type of signal. The performed t-SNE analysis confirms a much stronger inter-session and inter-user variance compared to the expected in-class variance. Additionally, we observe a strong drift of signals within a session. To handle these challenging problems, we propose new machine learning architectures based on deep learning, which allow to separate undesired from desired variation and thus significantly improve the classification accuracy. With these new architectures we increased cross-session classification accuracy on 12 gestures from 19.55 to 30.45%. Based on a fundamental data analysis we developed three calibration methods and thus were able to further increase cross-session classification accuracy to 39.01, 55.37, and 56.34%, respectively.

An efficient Point-Matching Method-of-Moments for 2D and 3D Electrical Impedance Tomography Using Radial Basis functions

AbstractObjective: The inverse problem of computing conductivity distributions in 2D and 3D objects interrogated by low frequency electrical signals, which is called Electrical Impedance Tomography (EIT), is treated using a Method-of-Moment technique.

METHODS

A Point-Matching-Method-of-Moment technique is used to formulate a global integral equation solver. Radial Basis Functions are adopted to express the conductivity distribution. Single-step quadratic-norm (L2) and iterative total variation (L1) regularization techniques are exploited to solve the inverse problem.

RESULTS

Simulation and experimental tests on a circular reconstruction domain show satisfactory performance in deriving conductivity distribution, achieving a Correlation Coefficient (CC) up to 0:863 for 70 dB voltage SNR and 0:842 for 40 dB voltage SNR. The proposed methodology with L2-norm regularization provided better results than traditional iterative Gauss-Newtons approach, whereas with L1-norm regularization it showed promising performance. Moreover, 3D reconstructions on a cylindrical cavity demonstrated superior results near the electrodes planes compared to those of the conventional linearized approach. Finally, application to EIT medical data for dynamic lung imaging successfully revealed the breath-cycle conductivity changes.

CONCLUSION

The results show that the proposed method can be effective for both 2D and 3D EIT and applicable to many applications.

SIGNIFICANCE

Strong conductivity variations are successfully tackled with a very good Correlation Coefficient. In contrast to conventional EIT solutions based on weak-form and linearization on small conductivity changes, the proposed method requires only one step to converge with L2-norm regularization. The proposed method with L1-norm regularization also achieves good reconstruction quality with a low number of iterations.

Evaluation of Thoracic Equivalent Multiport Circuits Using an Electrical Impedance Tomography Hardware Simulation Interface

Electrical impedance tomography is a low-cost, safe, and high temporal resolution medical imaging modality which finds extensive application in real-time thoracic impedance imaging. Thoracic impedance changes can reveal important information about the physiological condition of patients’ lungs. In this way, electrical impedance tomography can be a valuable tool for monitoring patients. However, this technique is very sensitive to measurement noise or possible minor signal errors, coming from either the hardware, the electrodes, or even particular biological signals. Thus, the design of a good performance electrical impedance tomography hardware setup which properly interacts with the tissue examined is both an essential and a challenging concept. In this paper, we adopt an extensive simulation approach, which combines the system’s analogue and digital hardware, along with equivalent circuits of 3D finite element models that represent thoracic cavities. Each thoracic finite element model is created in MATLAB based on existing CT images, while the tissues’ conductivity and permittivity values for a selected frequency are acquired from a database using Python. The model is transferred to a multiport RLC network, embedded in the system’s hardware which is simulated at LT SPICE. The voltage output data are transferred to MATLAB where the electrical impedance tomography signal sampling and digital processing is also simulated. Finally, image reconstructions are performed in MATLAB, using the EIDORS library tool and considering the signal noise levels and different electrode and signal sampling configurations (ADC bits, sampling frequency, number of taps).

Inferring Respiratory and Circulatory Parameters from Electrical Impedance Tomography With Deep Recurrent Models

Electrical impedance tomography (EIT) is a noninvasive imaging modality that allows a continuous assessment of changes in regional bioimpedance of different organs. One of its most common biomedical applications is monitoring regional ventilation distribution in critically ill patients treated in intensive care units. In this work, we put forward a proof-of-principle study that demonstrates how one can reconstruct synchronously measured respiratory or circulatory parameters from the EIT image sequence using a deep learning model trained in an end-to-end fashion. For this purpose, we devise an architecture with a convolutional feature extractor whose output is processed by a recurrent neural network. We demonstrate that one can accurately infer absolute volume, absolute flow, normalized airway pressure and within certain limitations even the normalized arterial blood pressure from the EIT signal alone, in a way that generalizes to unseen patients without prior calibration. As an outlook with direct clinical relevance, we furthermore demonstrate the feasibility of reconstructing the absolute transpulmonary pressure from a combination of EIT and absolute airway pressure, as a way to potentially replace the invasive measurement of esophageal pressure. With these results, we hope to stimulate further studies building on the framework put forward in this work.

Magnetic-resonance-based measurement of electromagnetic fields and conductivity in vivo using single current administration-A machine learning approach

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) is a newly developed technique that combines MR-based measurements of magnetic flux density with diffusion tensor MRI (DT-MRI) data to reconstruct electrical conductivity tensor distributions. DT-MREIT techniques normally require injection of two independent current patterns for unique reconstruction of conductivity characteristics. In this paper, we demonstrate an algorithm that can be used to reconstruct the position dependent scale factor relating conductivity and diffusion tensors, using flux density data measured from only one current injection. We demonstrate how these images can also be used to reconstruct electric field and current density distributions. Reconstructions were performed using a mimetic algorithm and simulations of magnetic flux density from complementary electrode montages, combined with a small-scale machine learning approach. In a biological tissue phantom, we found that the method reduced relative errors between single-current and two-current DT-MREIT results to around 10%. For in vivo human experimental data the error was about 15%. These results suggest that incorporation of machine learning may make it easier to recover electrical conductivity tensors and electric field images during neuromodulation therapy without the need for multiple current administrations.

Fusing electrical and elasticity imaging

Electrical and elasticity imaging are promising modalities for a suite of different applications, including medical tomography, non-destructive testing and structural health monitoring. These emerging modalities are capable of providing remote, non-invasive and low-cost opportunities. Unfortunately, both modalities are severely ill-posed nonlinear inverse problems, susceptive to noise and modelling errors. Nevertheless, the ability to incorporate complimentary datasets obtained simultaneously offers mutually beneficial information. By fusing electrical and elastic modalities as a joint problem, we are afforded the possibility to stabilize the inversion process via the utilization of auxiliary information from both modalities as well as joint structural operators. In this study, we will discuss a possible approach to combine electrical and elasticity imaging in a joint reconstruction problem giving rise to novel multi-modality applications for use in both medical and structural engineering. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Reconstruction of conductivity distribution with electrical impedance tomography based on hybrid regularization method

Purpose: Physiological or pathological variation would cause a change of conductivity. Electrical impedance tomography (EIT) is favorable in reconstructing conductivity distribution inside the detected area. However, the reconstruction is an ill-posed inverse problem and the spatial resolution of the reconstructed image is relatively poor. Approach: To deal with the problem, a regularization method is commonly applied. Traditional regularization methods have their own disadvantages. In this work, we develop an innovative hybrid regularization method to determine the conductivity distribution from the boundary measurement. To address the unwanted artifact observed in the total variation (TV) method, the proposed approach incorporates the TV method with the non-convex sparse penalty term-based wavelet transform. In the reconstruction, the sensitivity matrix is also normalized to increase the sensitivity of the measurement to the variation of the conductivity. The objective function is minimized with the split augmented Lagrangian shrinkage algorithm. Results: The feasibility of the proposed method is evaluated by numerical simulation and phantom experiment. The results verify that the reconstruction with the proposed method is more advantageous, as obvious improvement is observed in the reconstructed image. Conclusions: With the proposed method, the artifact can be effectively suppressed and the reconstructed image of conductivity distribution is improved. It has great potential in medical imaging, which would be helpful for the accurate diagnosis of disease.