Comparing D-bar and common regularization-based methods for electrical impedance tomography

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.

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.

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.

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.

Robust imaging using electrical impedance tomography: review of current tools

Electrical impedance tomography (EIT) is a medical imaging technique with many advantages and great potential for development in the coming years. Currently, some limitations of EIT are related to the ill-posed nature of the problem. These limitations are translated on a practical level by a lack of genericity of the developed tools. In this paper, the main robust data acquisition and processing tools for EIT proposed in the scientific literature are presented. Their relevance and potential to improve the robustness of EIT are analysed, in order to conclude on the feasibility of a robust EIT tool capable of providing resistivity or difference of resistivity mapping in a wide range of applications. In particular, it is shown that certain measurement acquisition tools and algorithms, such as faulty electrode detection algorithm or particular electrode designs, can ensure the quality of the acquisition in many circumstances. Many algorithms, aiming at processing acquired data, are also described and allow to overcome certain difficulties such as an error in the knowledge of the position of the boundaries or the poor conditioning of the inverse problem. They have a strong potential to faithfully reconstruct a quality image in the presence of disturbances such as noise or boundary modelling error.

A Point-Matching Method of Moment with Sparse Bayesian Learning Applied and Evaluated in Dynamic Lung Electrical Impedance Tomography

Dynamic lung imaging is a major application of Electrical Impedance Tomography (EIT) due to EIT's exceptional temporal resolution, low cost and absence of radiation. EIT however lacks in spatial resolution and the image reconstruction is very sensitive to mismatches between the actual object's and the reconstruction domain's geometries, as well as to the signal noise. The non-linear nature of the reconstruction problem may also be a concern, since the lungs' significant conductivity changes due to inhalation and exhalation. In this paper, a recently introduced method of moment is combined with a sparse Bayesian learning approach to address the non-linearity issue, provide robustness to the reconstruction problem and reduce image artefacts. To evaluate the proposed methodology, we construct three CT-based time-variant 3D thoracic structures including the basic thoracic tissues and considering 5 different breath states from end-expiration to end-inspiration. The Graz consensus reconstruction algorithm for EIT (GREIT), the correlation coefficient (CC), the root mean square error (RMSE) and the full-reference (FR) metrics are applied for the image quality assessment. Qualitative and quantitative comparison with traditional and more advanced reconstruction techniques reveals that the proposed method shows improved performance in the majority of cases and metrics. Finally, the approach is applied to single-breath online in-vivo data to qualitatively verify its applicability.

3D ELECTRICAL IMPEDANCE TOMOGRAPHY RECONSTRUCTIONS FROM SIMULATED ELECTRODE DATA USING DIRECT INVERSION texp AND CALDERÓN METHODS

The first numerical implementation of a t ^exp method in 3D using simulated electrode data is presented. Results are compared to Calderón's method as well as more common TV and smoothness regularization-based methods. The t ^exp method for EIT is based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. In 2D, t ^exp methods have shown great promise for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D t ^exp and Calderón methods are demonstrated to provide comparable quality to their 2D counterparts, and hold promise for real-time reconstructions due to their fast, non-optimized, computational cost.

Electrical Impedance Tomography - Recent Applications and Developments

Electrical impedance tomography (EIT) is a low-cost noninvasive imaging method. The main purpose of this paper is to highlight the main aspects of the EIT method and to review the recent advances and developments. The advances in instrumentation and in the different image reconstruction methods and systems are demonstrated in this review. The main applications of the EIT are presented and a special attention made to the papers published during the last years (from 2015 until 2020). The advantages and limitations of EIT are also presented. In conclusion, EIT is a promising imaging approach with a strong potential that has a large margin of progression before reaching the maturity phase.

The D-bar method for electrical impedance tomography-demystified

Electrical impedance tomography (EIT) is an imaging modality where a patient or object is probed using harmless electric currents. The currents are fed through electrodes placed on the surface of the target, and the data consists of voltages measured at the electrodes resulting from a linearly independent set of current injection patterns. EIT aims to recover the internal distribution of electrical conductivity inside the target. The inverse problem underlying the EIT image formation task is nonlinear and severely ill-posed, and hence sensitive to modeling errors and measurement noise. Therefore, the inversion process needs to be regularized. However, traditional variational regularization methods, based on optimization, often suffer from local minima because of nonlinearity. This is what makes regularized direct (non-iterative) methods attractive for EIT. The most developed direct EIT algorithm is the D-bar method, based on Complex Geometric Optics solutions and a nonlinear Fourier transform. Variants and recent developments of D-bar methods are reviewed, and their practical numerical implementation is explained.

Electrical Impedance Tomography-Based Abdominal Subcutaneous Fat Estimation Method Using Deep Learning

This paper proposes a deep learning method based on electrical impedance tomography (EIT) to estimate the thickness of abdominal subcutaneous fat. EIT for evaluating the thickness of abdominal subcutaneous fat is an absolute imaging problem that aims at reconstructing conductivity distributions from current-to-voltage data. Existing reconstruction methods based on EIT have difficulty handling the inherent drawbacks of strong nonlinearity and severe ill-posedness of EIT; hence, absolute imaging may not be possible using linearized methods. To handle nonlinearity and ill-posedness, we propose a deep learning method that finds useful solutions within a restricted admissible set by accounting for prior information regarding abdominal anatomy. We determined that a specially designed training dataset used during the deep learning process significantly reduces ill-posedness in the absolute EIT problem. In the preprocessing stage, we normalize current-voltage data to alleviate the effects of electrodeposition and body geometry by exploiting knowledge regarding electrode positions and body geometry. The performance of the proposed method is demonstrated through numerical simulations and phantom experiments using a 10 channel EIT system and a human-like domain.

A novel time-difference electrical impedance tomography algorithm using multi-frequency information

BACKGROUND

Electrical impedance tomography (EIT) is a noninvasive, radiation-free, and low-cost imaging modality for monitoring the conductivity distribution inside a patient. Nowadays, time-difference EIT (tdEIT) is used extensively as it has fast imaging speed and can reflect the dynamic changes of diseases, which make it attractive for a number of medical applications. Moreover, modeling errors are compensated to some extent by subtraction of voltage measurements collected before and after the change. However, tissue conductivity varies with frequency and tdEIT does not efficiently exploit multi-frequency information as it only uses measurements associated with a single frequency.

METHODS

This paper proposes a tdEIT algorithm that imposes spectral constraints on the framework of the linear least squares problem. Simulation and phantom experiments are conducted to compare the proposed spectral constraints algorithm (SC) with the damped least squares algorithm (DLS), which is a stable tdEIT algorithm used in clinical practice. The condition number and rank of the matrices needing inverses are analyzed, and image quality is evaluated using four indexes. The possibility of multi-tissue imaging and the influence of spectral errors are also explored.

RESULTS

Significant performance improvement is achieved by combining multi-frequency and time-difference information. The simulation results show that, in one-step iteration, both algorithms have the same condition number and rank, but SC effectively reduces image noise by 20.25% compared to DLS. In addition, deformation error and position error are reduced by 8.37% and 7.86%, respectively. In two-step iteration, the rank of SC is greatly increased, which suggests that more information is employed in image reconstruction. Image noise is further reduced by an average of 32.58%, and deformation error and position error are also reduced by 20.20% and 31.36%, respectively. The phantom results also indicate that SC has stronger noise suppression and target identification abilities, and this advantage is more obvious with iteration. The results of multi-tissue imaging show that SC has the unique advantage of automatically extracting a single tissue to image.

CONCLUSIONS

SC enables tdEIT to utilize multi-frequency information in cases where the spectral constraints are known and then provides higher quality images for applications.