Dominant-Current Deep Learning Scheme for Electrical Impedance Tomography

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.

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.

A narrative review of the application of machine learning in venous thromboembolism

OBJECTIVE

To summarize the current research progress of machine learning and venous thromboembolism.

METHODS

The literature on risk factors, diagnosis, prevention and prognosis of machine learning and venous thromboembolism in recent years was reviewed.

RESULTS

Machine learning is the future of biomedical research, personalized medicine, and computer-aided diagnosis, and will significantly promote the development of biomedical research and healthcare. However, many medical professionals are not familiar with it. In this review, we will introduce several commonly used machine learning algorithms in medicine, discuss the application of machine learning in venous thromboembolism, and reveal the challenges and opportunities of machine learning in medicine.

CONCLUSION

The incidence of venous thromboembolism is high, the diagnostic measures are diverse, and it is necessary to classify and treat machine learning, and machine learning as a research tool, it is more necessary to strengthen the special research of venous thromboembolism and machine learning.

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.

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.

DEEP-squared: deep learning powered De-scattering with Excitation Patterning

Limited throughput is a key challenge in in vivo deep tissue imaging using nonlinear optical microscopy. Point scanning multiphoton microscopy, the current gold standard, is slow especially compared to the widefield imaging modalities used for optically cleared or thin specimens. We recently introduced "De-scattering with Excitation Patterning" or "DEEP" as a widefield alternative to point-scanning geometries. Using patterned multiphoton excitation, DEEP encodes spatial information inside tissue before scattering. However, to de-scatter at typical depths, hundreds of such patterned excitations were needed. In this work, we present DEEP2, a deep learning-based model that can de-scatter images from just tens of patterned excitations instead of hundreds. Consequently, we improve DEEP's throughput by almost an order of magnitude. We demonstrate our method in multiple numerical and experimental imaging studies, including in vivo cortical vasculature imaging up to 4 scattering lengths deep in live mice.

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.

Cross modality generative learning framework for anatomical transitive Magnetic Resonance Imaging (MRI) from Electrical Impedance Tomography (EIT) image

This paper presents a cross-modality generative learning framework for transitive magnetic resonance imaging (MRI) from electrical impedance tomography (EIT). The proposed framework is aimed at converting low-resolution EIT images to high-resolution wrist MRI images using a cascaded cycle generative adversarial network (CycleGAN) model. This model comprises three main components: the collection of initial EIT from the medical device, the generation of a high-resolution transitive EIT image from the corresponding MRI image for domain adaptation, and the coalescence of two CycleGAN models for cross-modality generation. The initial EIT image was generated at three different frequencies (70 kHz, 140 kHz, and 200 kHz) using a 16-electrode belt. Wrist T1-weighted images were acquired on a 1.5T MRI. A total of 19 normal volunteers were imaged using both EIT and MRI, which resulted in 713 paired EIT and MRI images. The cascaded CycleGAN, end-to-end CycleGAN, and Pix2Pix models were trained and tested on the same cohort. The proposed method achieved the highest accuracy in bone detection, with 0.97 for the proposed cascaded CycleGAN, 0.68 for end-to-end CycleGAN, and 0.70 for the Pix2Pix model. Visual inspection showed that the proposed method reduced bone-related errors in the MRI-style anatomical reference compared with end-to-end CycleGAN and Pix2Pix. Multifrequency EIT inputs reduced the testing normalized root mean squared error of MRI-style anatomical reference from 67.9% ± 12.7% to 61.4% ± 8.8% compared with that of single-frequency EIT. The mean conductivity values of fat and bone from regularized EIT were 0.0435 ± 0.0379 S/m and 0.0183 ± 0.0154 S/m, respectively, when the anatomical prior was employed. These results demonstrate that the proposed framework is able to generate MRI-style anatomical references from EIT images with a good degree of accuracy.

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.

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.

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.

Deep learning inversion with supervision: A rapid and cascaded imaging technique

Machine learning has been demonstrated to be extremely promising in solving inverse problems, but deep learning algorithms require enormous training samples to obtain reliable results. In this article, we propose a new solution, the deep learning inversion with supervision (DLIS) and applied it for corrosion mapping in guided wave tomography. The inversion results show that when dealing with multiple defects of complex shape on a plate-like structure, DLIS methods can reduce the scale of training set effectively compared with other deep learning algorithms in experiment because a good starting model is provided and the nonlinearity between the global minimum and observed wave field is greatly reduced. In terms of reconstruction accuracy using experimental data, the thickness maps produced by DLIS are reliable with high accuracy. With few modifications, this method can be conveniently extended to 3D cases. These results imply that DLIS is one of the promising methods to be applied in fields with similar physics like non-destructive evaluation (NDE), biomedical imaging and geophysical prospecting.

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.

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.

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.

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.

Supervised Descent Learning for Thoracic Electrical Impedance Tomography

OBJECTIVE

The absolute image reconstruction problem of electrical impedance tomography (EIT) is ill-posed. Traditional methods usually solve a nonlinear least squares problem with some kind of regularization. These methods suffer from low accuracy, poor anti-noise performance, and long computation time. Besides, the integration of a priori information is not very flexible. This work tries to solve EIT inverse problem using a machine learning algorithm for the application of thorax imaging.

METHODS

We developed the supervised descent learning EIT (SDL-EIT) inversion algorithm based on the idea of supervised descent method (SDM). The algorithm approximates the mapping from measured data to the conductivity image by a series of descent directions learned from training samples. We designed a training data set in which the thorax contour, and some general structure of lungs, and heart are embedded. The algorithm is implemented in both two-, and three-dimensional cases, and is evaluated using synthetic, and measured thoracic data. Results, and conclusion: For synthetic data, SDL-EIT shows better accuracy, and anti-noise performance compared with traditional Gauss-Newton inversion (GNI) method. For measured data, the result of SDL-EIT is reasonable compared with computed tomography (CT) scan image.

SIGNIFICANCE

Using SDL-EIT, prior information can be easily integrated through the specifically designed training data set, and the image reconstruction process can be accelerated. The algorithm is effective in inverting measured thoracic data. It is a potential algorithm for human thorax imaging.

Neural network-based supervised descent method for 2D electrical impedance tomography

OBJECTIVE

In this work, we study the application of the neural network-based supervised descent method (NN-SDM) for 2D electrical impedance tomography.

APPROACH

The NN-SDM contains two stages: offline training and online prediction. In the offline stage, neural networks are iteratively applied to learn a sequence of descent directions for minimizing the objective function, where the training data set is generated in advance according to prior information or historical data. In the online stage, the trained neural networks are directly used to predict the descent directions.

MAIN RESULTS

Numerical and experimental results are reported to assess the efficiency and accuracy of the NN-SDM for both model-based and pixel-based inversions. In addition, the performance of the NN-SDM is compared with the linear SDM (LSDM), an end-to-end neural network (E2E-NN) and the Gauss-Newton (GN) method. The results demonstrate that the NN-SDM achieves faster convergence than the LSDM and GN method, and achieves a stronger generalization ability than the E2E-NN.

SIGNIFICANCE

The NN-SDM combines the strong non-linear fitting ability of the neural network and good generalization capability of the supervised descent method (SDM), which also provides good flexibility to incorporate prior information and accelerates the convergence of iteration.

B-Spline Level Set Method for Shape Reconstruction in Electrical Impedance Tomography

A B-spline level set (BLS) based method is proposed for shape reconstruction in electrical impedance tomography (EIT). We assume that the conductivity distribution to be reconstructed is piecewise constant, transforming the image reconstruction problem into a shape reconstruction problem. The shape/interface of inclusions is implicitly represented by a level set function (LSF), which is modeled as a continuous parametric function expressed using B-spline functions. Starting from modeling the conductivity distribution with the B-spline based LSF, we show that the shape modeling allows us to compute the solution by restricting the minimization problem to the space spanned by the B-splines. As a consequence, the solution to the minimization problem is obtained in terms of the B-spline coefficients. We illustrate the behavior of this method using simulated as well as water tank data. In addition, robustness studies considering varying initial guesses, differing numbers of control points, and modeling errors caused by inhomogeneity are performed. Both simulation and experimental results show that the BLS-based approach offers clear improvements in preserving the sharp features of the inclusions in comparison to the recently published parametric level set method.

Induced-Current Learning Method for Nonlinear Reconstructions in Electrical Impedance Tomography

Electrical impedance tomography (EIT) is an attractive technique that aims to reconstruct the unknown electrical property in a domain from the surface electrical measurements. In this work, the induced-current learning method (ICLM) is proposed to solve nonlinear electrical impedance tomography (EIT) problems. Specifically, the cascaded end-to-end convolutional neural network (CEE-CNN) architecture is designed to implement the ICLM. The CEE-CNN greatly decreases the nonlinearities in EIT problems by designing a combined objective function and introducing multiple labels. A noticeable characteristic of the proposed CNN scheme is that the input parameters are chosen as both induced contrast current (ICC) and the updated electrical field from a spectral analysis and the output is chosen as ICC, which is fundamentally different from prevailing CNN schemes. Further, several skip connections are introduced to focus on learning only the unknown part of ICC. ICLM is verified with both numerical and experimental tests on typical EIT problems, and it is found that ICLM is able to solve typical EIT problems in less than 1 second with high image qualities. More importantly, it is also highly robust to measurement noises and modeling errors, such as inaccurate boundary data.

A Moving Morphable Components Based Shape Reconstruction Framework for Electrical Impedance Tomography

This paper presents a new computational framework in electrical impedance tomography (EIT) for shape reconstruction based on the concept of moving morphable components (MMC). In the proposed framework, the shape reconstruction problem is solved in an explicit and geometrical way. Compared with the traditional pixel or shape-based solution framework, the proposed framework can incorporate more geometry and prior information into shape and topology optimization directly and therefore render the solution process more flexibility. It also has the afford potential to substantially reduce the computational burden associated with shape and topology optimization. The effectiveness of the proposed approach is tested with noisy synthetic data and experimental data, which demonstrates the most popular biomedical application of EIT: lung imaging. In addition, robustness studies of the proposed approach considering modeling errors caused by non-homogeneous background, varying initial guesses, differing numbers of candidate shape components, and differing exponent in the shape and topology description function are performed. The simulation and experimental results show that the proposed approach is tolerant to modeling errors and is fairly robust to these parameter choices, offering significant improvements in image quality in comparison to the conventional absolute reconstructions using smoothness prior regularization and total variation regularization.

A Statistical Shape-Constrained Reconstruction Framework for Electrical Impedance Tomography

A statistical shape-constrained reconstruction (SSCR) framework is presented to incorporate the statistical prior information of human lung shapes for lung electrical impedance tomography. The prior information is extracted from 8000 chest-computed tomography scans across 800 patients. The reconstruction framework is implemented with two approaches-a one-step SSCR and an iterative SSCR in lung imaging. The one-step SSCR provides fast and high accurate reconstructions of healthy lungs, whereas the iterative SSCR allows to simultaneously estimate the pre-injured lung and the injury lung part. The approaches are evaluated with the simulated examples of thorax imaging and also with the experimental data from a laboratory setting, with difference imaging considered in both the approaches. It is demonstrated that the accuracy of lung shape reconstruction is significantly improved. In addition, the proposed approaches are proved to be robust against measurement noise, modeling error caused by inaccurately known domain boundary, and the selection of the regularization parameters.

Multi-Objective Optimization for Personalized Prediction of Venous Thromboembolism in Ovarian Cancer Patients

Thrombotic events are one of the leading causes of mortality and morbidity related to cancer, with ovarian cancer having one of the highest incidence rates. The need to prevent these events through the prescription of adequate schemes of antithrombotic prophylaxis has motivated the development of models that aid the identification of patients at higher risk of thrombotic events with lethal consequences. However, antithrombotic prophylaxis increases the risk of bleeding and this risk depends on the class and intensity of the chosen antithrombotic prophylactic scheme, the clinical and personal condition of the patient and the disease characteristics. Moreover, the datasets used to obtain current models are imbalanced, i.e., they incorporate more patients who did not suffer thrombotic events than patients who experienced them what can lead to wrong predictions, especially for the clinically relevant patient group at high risk of thrombosis. Herein, predictive models based on machine learning were developed utilizing 121 high-grade serous ovarian carcinoma patients, considering the clinical variables of the patients and those typical of the disease. To properly manage the data imbalance, cost-sensitive classification together with multi-objective optimization was performed considering different combinations of metrics. In this way, five Pareto fronts and a series of optimal models with different false positive and false negative rates were obtained. With this novel approach to the development of clinical predictive models, personalized models can be developed, helping the clinician to achieve a better balance between the risk of bleeding and the risk of thrombosis.