Image reconstruction algorithm for electrical impedance tomography using updated sensitivity matrix

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

SAR-CGAN: Improved generative adversarial network for EIT reconstruction of lung diseases

Electrical impedance tomography (EIT) is the process of spatially mapping the conductivity distribution of a domain based on voltage-current relationships observed at the boundary of the domain. Due to its low cost, ease of implementation, and benign nature (i.e. non-ionizing), EIT has received much attention for potential application to damage, strain, and saturation mapping in civil, mechanical, and aerospace venues that employ conductive materials (e.g. nanofiller-modified cements and polymers, carbon fiber composites, etc.). Mathematically, however, EIT is an ill-posed inverse problem predicated on reconstructing the conductivity distribution on a model of the domain. This process is prone to nonconvergence due to factors such as experiment-to-model domain shape discrepancies and electrode misplacement. Time difference imaging is commonly used to overcome this challenge–boundary measurements are collected when the material is in a pristine state and another set of boundary measurements are collected after some conductivity-changing perturbation such that experiment-to-model discrepancies largely subtract out. But this process of time-difference imaging is problematic for several reasons: one, a pristine state is not available for existent or already in-service structures. Two, pristine-state data can be lost over time. And three, the pristine-state data may no longer be applicable if there are significant shape changes, electrodes are reapplied, etc. Thus, it is desirable to have a baseline-free technique for EIT. To that end, we herein present the results of a preliminary investigation on damage detection via frequency-difference imaging (fdEIT). In this approach, we leverage the fact that materials generally exhibit frequency-dependent conductivity such that an EIT image can be formed from the difference between two different frequencies. Experimental measurements of AC conductivity up to 10 MHz were collected from a carbon nanofiber (CNF)-modified glass fiber/epoxy laminate. These measurements were then used in a computational simulation to explore the potential of fdEIT for damage detection and localization. The results of this study suggest that fdEIT may indeed be a viable method of eliminating baseline measurements for EIT thereby providing an important advance towards making EIT a practical inspection modality.

In Electrical Impedance Tomography, conductivity images can be reconstructed using a back-projection algorithm which is very similar to the ones used in other imaging modalities. In this study, the basic assumptions underlying the back-projection algorithm are investigated. Under these assumptions, a sensitivity matrix is derived relating the conductivity variation to the variation in gradients. A new image reconstruction method is suggested based on a minimization procedure which is equivalent to the solution of the sensitivity matrix equation in a generalized sense.

Cross-sectional imaging of an electrical conductivity distribution inside the human body has been an active research goal in impedance imaging. By injecting current into an electrically conducting object through surface electrodes, we induce current density and voltage distributions. Based on the fact that these are determined by the conductivity distribution as well as the geometry of the object and the adopted electrode configuration, electrical impedance tomography (EIT) reconstructs cross-sectional conductivity images using measured current–voltage data on the surface. Unfortunately, there exist inherent technical difficulties in EIT. First, the relationship between the boundary current–voltage data and the internal conductivity distribution bears a nonlinearity and low sensitivity, and hence the inverse problem of recovering the conductivity distribution is ill posed. Second, it is difficult to obtain accurate information on the boundary geometry and electrode positions in practice, and the inverse problem is sensitive to these modeling errors as well as measurement artifacts and noise. These result in EIT images with a poor spatial resolution. In order to produce high-resolution conductivity images, magnetic resonance electrical impedance tomography (MREIT) has been lately developed. Noting that injection current produces a magnetic as well as electric field inside the imaging object, we can measure the induced internal magnetic flux density data using an MRI scanner. Utilization of the internal magnetic flux density is the key idea of MREIT to overcome the technical difficulties in EIT. Following original ideas on MREIT in early 1990s, there has been a rapid progress in its theory, algorithm and experimental techniques. The technique has now advanced to the stage of human experiments. Though it is still a few steps away from routine clinical use, its potential is high as a new impedance imaging modality providing conductivity images with a spatial resolution of a few millimeters or less. This paper reviews MREIT from the basics to the most recent research outcomes. Focusing on measurement techniques and experimental methods rather than mathematical issues, we summarize what has been done and what needs to be done. Suggestions for future research directions, possible applications in biomedicine, biology, chemistry and material science are discussed.

Electrical impedance tomography (EIT) is an emerging technique for medical imaging. According to reconstructed images, the human disease can be identified. Note that the reconstruction of EIT is an ill-posed inverse problem. To solve this problem, various sensitivity-based methods have been proposed. Nevertheless, a sensitivity matrix is affected by a number of factors. Therefore, classification reflected by images is sometimes not very reliable. In this work, a novel method based on a residual neural network is proposed for stroke classification. It is realized by directly processing measured difference data from EIT. After training of the residual neural network, the proposed method is quantitatively evaluated when noise is exerted, shape deviation occurs, and conductivity varies in three different layers. Also, impacts of contact impedance and small-sized inclusion are studied. Furthermore, phantom experiments are conducted. Compared with fully connected neural networks and shallow convolution neural networks, the results demonstrate that the proposed method has a better performance in classification for various cases. This article offers an effective alternative for stroke classification in EIT.

This research has been aimed to carry out a study of peculiarities that arise in a numerical simulation of the electrical impedance tomography (EIT) problem. Static EIT image reconstruction is sensitive to a measurement noise and approximation error. A special consideration has been given to reducing of the approximation error, which originates from numerical implementation drawbacks. This paper presents in detail two numerical approaches for solving EIT forward problem. The finite volume method (FVM) on unstructured triangular mesh is introduced. In order to compare this approach, the finite element (FEM) based forward solver was implemented, which has gained the most popularity among researchers. The calculated potential distribution with the assumed initial conductivity distribution has been compared to the analytical solution of a test Neumann boundary problem and to the results of problem simulation by means of ANSYS FLUENT commercial software. Two approaches to linearized EIT image reconstruction are discussed. Reconstruction of the conductivity distribution is an ill-posed problem, typically requiring a large amount of computation and resolved by minimization techniques. The objective function to be minimized is constructed of measured voltage and calculated boundary voltage on the electrodes. A classical modified Newton type iterative method and the stochastic differential evolution method are employed. A software package has been developed for the problem under investigation. Numerical tests were conducted on simulated data. The obtained results could be helpful to researches tackling the hardware and software issues for medical applications of EIT.

In this paper, we consider imaging of moving fluids with electrical impedance tomography (EIT). In EIT, the conductivity distribution is reconstructed on the basis of electrical boundary measurements. In the case of time-varying targets—such as moving fluids in process industry—it is advantageous to formulate the reconstruction problem as a state-estimation problem, because the state-estimation approach allows incorporation of target evolution models in the reconstruction. The reconstruction algorithms consist of recursions in which the state predictions given by the evolution model are updated with the information provided by measurements. When monitoring single-phase flow, the evolution of the substance concentration can be described with the convection–diffusion model. The convection–diffusion model includes the fluid velocity field. In our previous studies, we have assumed that the velocity field is known. In this paper, we extend the approach to cases of unknown velocity fields. The velocity field is reconstructed simultaneously with the conductivity distribution by using an extended Kalman filter. The numerical results indicate that estimating the velocity field from EIT measurements is possible—at least to some extent.

In this study, a reconstruction algorithm for a 16-electrode interleaved-drive electrical impedance tomography (EIT) system is developed, based on inversion of an analytically calculated sensitivity matrix. The sensitivity matrix is calculated using Geselowitz's lead-sensitivity theorem. Eight interleaved electrodes out of 16 (equally spaced) electrodes are designated as current injection electrodes and the remaining eight electrodes are designated as measurement electrodes. The sensitivity matrix is singular, therefore singular value decomposition (SVD) of the sensitivity matrix, followed by pseudoinversion - with and without truncation - is used to reconstruct images. The algorithm is a single-pass algorithm. Data from a saline filled tank and in vivo data during respiration and the cardiac cycle, acquired by using a Sheffield multifrequency system, are used to reconstruct images. The effect of different truncation levels on the reconstructed images is investigated.

Electrical impedance tomography (EIT) uses electrical measurements at electrodes placed around the thorax to image changes in the conductivity distribution within the thorax. This technique is well suited to studying pulmonary function because the movement of air, blood, and extravascular fluid induces significant conductivity changes within the thorax. We conducted three experimental protocols in a total of 19 dogs to assess the accuracy with which EIT can quantify changes in the volumes of both gas and fluid in the lungs. In the first protocol, lung volume increments from 50 to 1,000 ml were applied with a large syringe. EIT measured these volume changes with an average error of 27 +/- 6 ml. In the second protocol, EIT measurements were made at end expiration and end inspiration during regular ventilation with tidal volume ranging from 100 to 1,000 ml. The average error in the EIT estimates of tidal volume was 90 +/- 43 ml. In the third protocol, lung liquid volume was measured by instilling 5% albumin solution into a lung lobe in increments ranging from 10 to 100 ml. EIT measured these volume changes with an average error of 10 +/- 10 ml and was also able to detect into which lobe the fluid had been instilled. These results indicate that EIT can noninvasively measure changes in the volumes of both gas and fluid in the lungs with clinically useful accuracy.

In electrical impedance tomography (EIT), a forward solver capable of predicting the voltages on electrodes for a given conductivity distribution is essential for reconstruction. The EIT forward solver is normally based on the conventional finite element method (FEM). One of the major problems of three-dimensional (3-D) EIT is its high demand in computing power and memory since high precision is required for obtaining a small secondary field which is typical for a small anomaly. This accuracy requirement is also set by the level of noise in the real data; although currently the noise level is still an issue, future EIT systems should significantly reduce the noise level to be capable of detecting very small anomalies. To accurately simulate the forward solution with the FEM, a mesh with large number of nodes and elements is usually needed. To overcome this problem, we proposed the spectral element method (SEM) for EIT forward problem. With the introduction of SEM, a smaller number of nodes and hence less computational time and memory are needed to achieve the same or better accuracy in the forward solution than the FEM. Numerical results demonstrate the efficiency of the SEM in 3-D EIT simulation.

<div class="section abstract"><div class="htmlview paragraph">For 2D surface temperature monitoring applications, a variant of Electrical Impedance Tomography (EIT) was evaluated computationally in this study. Literature examples of poor sensor performance in the center of the 2D domains away from the side electrodes motivated these efforts which seek to overcome some of the previously noted shortcomings. In particular, the use of ‘sensing skins’ with novel tailored baseline conductivities was examined using the EIDORS package for EIT. It was found that the best approach for detecting a temperature hot spot depends on several factors such as the current injection (stimulation) patterns, the measurement patterns, and the reconstruction algorithms. For well-performing combinations of these factors, customized baseline conductivities were assessed and compared to the baseline uniform conductivity.</div><div class="htmlview paragraph">It was discovered that for some EIT applications, a tailored distribution needs to be smooth and that sudden changes in the conductivity gradients should be avoided to prevent the introduction of artifacts in the reconstructed conductivity field. Still, the benefits in terms of improved EIT performance were small for conditions for which the EIT measurements had been ‘optimized’ for the uniform baseline case. Within the limited scope of this study, only two specific cases showed benefits from customized distributions. For one case, a smooth tailored distribution with increased baseline conductivity in the center provided a better separation of two centrally located hot spots. For another case, a smooth tailored distribution with reduced conductivity in the center provided better estimates of the magnitudes of two hot spots near the center of the sensing skin.</div><div class="htmlview paragraph">Overall, the results at hand suggest that improved 2D surface temperature measurement are best served by continued development of measurements and reconstruction algorithms rather than the use of sensing skins with tailored baseline conductivity distributions.</div></div>

Electrical resistance tomography (ERT) is an imaging technique of conductivity distribution. The image reconstruction algorithm based on the empty field sensitivity matrix is widely used because it provides an approximate solution to the complex ERT inverse problems. However, due to the soft field effect, the sensitivity matrix changes with the media distribution, leading to significant errors in image reconstruction. To address this issue, an error-constrained deep learning scheme for bubble flow, namely cross fusion residual attention network (CFRA-Net) is designed to update the sensitivity matrix during gas–liquid–solid fluidized bed operation. CFRA-Net employs a multi-head self-attention mechanism to enhance bubble features in boundary measurements, a multilevel cross fusion (CF) module to fuse empty field strength and boundary measurement information, and a novel serial-channel residual spatial attention block to boost the feature extraction capability of the model. A weighted loss function is designed to give more weight to the gas phase distribution region. Additionally, this paper establishes a dataset for gas–liquid–solid three-phase flow, considering background field conductivity variations. Validation and reliability of the proposed method are assessed through ablation, comparison, and noise experiments. The experimental results demonstrate that CFRA-Net achieves rapid updates of the sensitivity matrix, high imaging accuracy, and robust noise immunity.

Electrical Impedance Tomography (EIT) is non-invasive method to reconstruct the conductivity distribution of the testing domain. Due to its advantages of low-cost, fast and non-radiation, EIT has unique application in biological tissue imaging. However, EIT techniques suffers from low spatial resolution, the size and position of object biological tissue couldn’t be identified clearly from the reconstruction results, limiting its application on malignant lesion detection. Based on the analysis of electrical field in human abdomen, a series of numerical simulations are conducted to improve the performance of EIT in abdomen lesion detection. A novel approach of EIT reconstruction method combining ultrasound reflection information are proposed and presented in detail to provide accurate reconstruction. Both simulation and experiment results demonstrated the benefits of proposed method where the lesion size and position are well reconstructed with preferable accuracy and higher image purity.

Electrical Impedance Tomography (EIT) is an emerging method for monitoring damages in carbon fiber reinforced polymer CFRP composites. This paper presents a method of detecting the shape and position for the damages of anisotropic CFRP laminates based on EIT with embedded electrodes. According to the boundary values of voltage change collected from the electrodes, the conductivity distribution map of the material is reconstructed to assess the damage condition. In order to improve the quality of reconstructed images, a new modified residual norm steepest descent (MRNSD) algorithm is applied to reconstruct the conductivity distribution. Moreover, the EIT test system is built for experimental verification. The experimental results verify both the feasibility and effectiveness of the proposed method.