Three-dimensional Electrical Impedance Tomography Research Articles

An optimal transport approach for 3D electrical impedance tomography

Abstract This work solves the three-dimensional inverse boundary value problem with the quadratic Wasserstein distance (W 2), which originates from the optimal transportation (OT) theory. The computation of the W 2 distance on the manifold surface is boiled down to solving the generalized Monge–Ampère equation, whose solution is directly related to the gradient of the W 2 distance. An efficient first-order method based on iteratively solving Poisson’s equation is introduced to solve the fully nonlinear elliptic equation. Combining with the adjoint-state technique, the optimization framework based on the W 2 distance is developed to solve the three-dimensional electrical impedance tomography problem. The proposed method is especially suitable for severely ill-posed and highly nonlinear inverse problems. Numerical experiments demonstrate that our method improves the stability and outperforms the traditional regularization methods.

A novel framework for three-dimensional electrical impedance tomography reconstruction of maize ear via feature reconfiguration and residual networks.

Electrical impedance tomography (EIT) provides an indirect measure of the physiological state and growth of the maize ear by reconstructing the distribution of electrical impedance. However, the two-dimensional (2D) EIT within the electrode plane finds it challenging to comprehensively represent the spatial distribution of conductivity of the intact maize ear, including the husk, kernels, and cob. Therefore, an effective method for 3D conductivity reconstruction is necessary. In practical applications, fluctuations in the contact impedance of the maize ear occur, particularly with the increase in the number of grids and computational workload during the reconstruction of 3D spatial conductivity. These fluctuations may accentuate the ill-conditioning and nonlinearity of the EIT. To address these challenges, we introduce RFNetEIT, a novel computational framework specifically tailored for the absolute imaging of the three-dimensional electrical impedance of maize ear. This strategy transforms the reconstruction of 3D electrical conductivity into a regression process. Initially, a feature map is extracted from measured boundary voltage via a data reconstruction module, thereby enhancing the correlation among different dimensions. Subsequently, a nonlinear mapping model of the 3D spatial distribution of the boundary voltage and conductivity is established, utilizing the residual network. The performance of the proposed framework is assessed through numerical simulation experiments, acrylic model experiments, and maize ear experiments. Our experimental results indicate that our method yields superior reconstruction performance in terms of root-mean-square error (RMSE), correlation coefficient (CC), structural similarity index (SSIM), and inverse problem-solving time (IPST). Furthermore, the reconstruction experiments on maize ears demonstrate that the method can effectively reconstruct the 3D conductivity distribution.

Validation of three-dimensional thoracic electrical impedance tomography of horses during normal and increased tidal volumes

Objective. Data from two-plane electrical impedance tomography (EIT) can be reconstructed into various slices of functional lung images, allowing for more complete visualisation and assessment of lung physiology in health and disease. The aim of this study was to confirm the ability of 3D EIT to visualise normal lung anatomy and physiology at rest and during increased ventilation (represented by rebreathing). Approach. Two-plane EIT data, using two electrode planes 20 cm apart, were collected in 20 standing sedate horses at baseline (resting) conditions, and during rebreathing. EIT data were reconstructed into 3D EIT whereby tidal impedance variation (TIV), ventilated area, and right-left and ventral-dorsal centres of ventilation (CoVRL and CoVVD, respectively) were calculated in cranial, middle and caudal slices of lung, from data collected using the two planes of electrodes. Main results. There was a significant interaction of time and slice for TIV (p < 0.0001) with TIV increasing during rebreathing in both caudal and middle slices. The ratio of right to left ventilated area was higher in the cranial slice, in comparison to the caudal slice (p = 0.0002). There were significant effects of time and slice on CoVVD whereby the cranial slice was more ventrally distributed than the caudal slice (p < 0.0009 for the interaction). Significance. The distribution of ventilation in the three slices corresponds with topographical anatomy of the equine lung. This study confirms that 3D EIT can accurately represent lung anatomy and changes in ventilation distribution during rebreathing in standing sedate horses.

Design of Three-Dimensional Electrical Impedance Tomography System for Rock Samples

Research on the electrical properties of rocks and ores plays a crucial role in the development of geophysical electromagnetism methods. However, currently available instruments suffer from high power consumption, a limited number of electrodes, inaccurate measurements, poor portability, and a limited ability to measure the electrical parameters of rocks and ores. To address these issues, this paper presents a three-dimensional electrical impedance tomography system for rock samples with high-density microelectrodes based on an Android system and STM32 microcontroller. The system features high observation accuracy, dense electrode arrays (with 384 current and potential electrodes), flexible electrode selection, user-friendly human–computer interaction, good stability, and real-time performance. Powered by a single power bank, the entire instrument can be controlled and monitored wirelessly via Bluetooth and Wi-Fi technology using an Android smartphone. Additionally, the system not only enables accurate measurement of electrical parameters, but also facilitates the generation of three-dimensional impedance imaging of specimens via inversion algorithms after data export, allowing for a comprehensive understanding of the electrical properties of rocks and ores. This system holds great potential for future research in this field.

Non-invasive imaging of neural activity with magnetic detection electrical impedance tomography (MDEIT): a modelling study

Objectives. (1) Develop a computational pipeline for three-dimensional fast neural magnetic detection electrical impedance tomography (MDEIT), (2) determine whether constant current or constant voltage is preferable for MDEIT, (3) perform reconstructions of simulated neural activity in a human head model with realistic noise and compare MDEIT to EIT and (4) perform a two-dimensional study in a saline tank for MDEIT with optically pumped magnetometers (OPMs) and compare reconstruction algorithms. Approach. Forward modelling and image reconstruction were performed with a realistic model of a human head in three dimensions and at three noise levels for four perturbations representing neural activity. Images were compared using the error in the position and size of the reconstructed perturbations. Two-dimensional MDEIT was performed in a saline tank with a resistive perturbation and one OPM. Six reconstruction algorithms were compared using the error in the position and size of the reconstructed perturbations. Main results. A computational pipeline was developed in COMSOL Multiphysics, reducing the Jacobian calculation time from months to days. MDEIT reconstructed images with a lower reconstruction error than EIT with a mean difference of 7.0%, 5.5% and 11% for three noise cases representing current noise, reduced current source noise and reduced current source and magnetometer noise. A rank analysis concluded that the MDEIT Jacobian was less rank-deficient than the EIT Jacobian. Reconstructions of a phantom in a saline tank had a best reconstruction error of 13%, achieved using 0th-order Tikhonov regularisation with simulated noise-based correction. Significance. This study demonstrated that three-dimensional MDEIT for neural imaging is feasible and that MDEIT reconstructed superior images to EIT, which can be explained by the lesser rank deficiency of the MDEIT Jacobian. Reconstructions of a perturbation in a saline tank demonstrated a proof of principle for two-dimensional MDEIT with OPMs and identified the best reconstruction algorithm.

Three-dimensional electrical impedance tomography (EIT) to study regional ventilation/perfusion (V/Q̇) ratios in anesthetized pigs.

This study aimed to develop a 3D method for assessing ventilation/perfusion (V/Q̇) ratios in a pig model of hemodynamic perturbations using electrical impedance tomography (EIT). In order to evaluate the physiological coherence of changes in EIT-derived V/Q̇ ratios, global EIT-derived V/Q̇ mismatches were compared with global gold-standards. The study found regional heterogeneity in the distribution of V/Q̇ ratios in both the ventrodorsal and craniocaudal directions. Although global EIT-derived indices of V/Q̇ mismatch consistently underestimated both low and high V/Q̇ mismatch compared to global gold standards, the direction of the change was similar. We made the software available at no cost for other researchers to use. Future studies should compare regional V/Q̇ ratios determined by our method against other regional, high-resolution methods.

Technique for estimating the time spent on measuring and computing process in three-dimensional electrical impedance tomography

The work is devoted to the problems of estimating time delays that arise in studies using the method of three-dimensional electrical impedance tomography. The block diagram of the hardware-software complex of three-dimensional electrical impedance tomography is considered. A general algorithm for visualizing the internal structures of the object under study by the method of three-dimensional electrical impedance tomography is described, and it is shown which parts of it affect the occurrence of time delays. Methods for minimizing the time delays that occur during research are described, which will reduce the time for obtaining research results and increase the frequency of their output.

Methodology for assessing the energy consumption of three-dimensional electrical impedance tomography technical means

The paper deals with the issues of energy consumption of complexes of three-dimensional electrical impedance tomography. The designs of stationary complexes and wearable devices are considered. Their block diagrams are developed and considered. The main elements of the considered versions are described, their contribution to the total energy consumption of EIT devices is estimated. Consumers of electrical energy critical for one or another performance are indicated.

Neural networks for classification of strokes in electrical impedance tomography on a 3D head model

&lt;abstract&gt;&lt;p&gt;We consider the problem of the detection of brain hemorrhages from three-dimensional (3D) electrical impedance tomography (EIT) measurements. This is a condition requiring urgent treatment for which EIT might provide a portable and quick diagnosis. We employ two neural network architectures - a fully connected and a convolutional one - for the classification of hemorrhagic and ischemic strokes. The networks are trained on a dataset with $ 40\, 000 $ samples of synthetic electrode measurements generated with the complete electrode model on realistic heads with a 3-layer structure. We consider changes in head anatomy and layers, electrode position, measurement noise and conductivity values. We then test the networks on several datasets of unseen EIT data, with more complex stroke modeling (different shapes and volumes), higher levels of noise and different amounts of electrode misplacement. On most test datasets we achieve $ \geq 90\% $ average accuracy with fully connected neural networks, while the convolutional ones display an average accuracy $ \geq 80\% $. Despite the use of simple neural network architectures, the results obtained are very promising and motivate the applications of EIT-based classification methods on real phantoms and ultimately on human patients.&lt;/p&gt;&lt;/abstract&gt;

Diagnostic accuracy and prognostic value of three-dimensional electrical impedance tomography imaging in patients with breast cancer.

Three-dimensional electrical impedance tomography (3D EIT) is a novel, non-invasive, radiation-free imaging technology for breast cancer screening. This study aimed to identify characteristics and classification of 3D EIT breast cancer imaging that could provide diagnostic accuracy and prognostic value for breast cancer patients. A total of 645 suspicious breast lesions [Breast Imaging Reporting and Data System (BI-RADS) III, IV, V] identified by mammography or ultrasound were examined with 3D EIT (MEIK, SIM-Technika, Yaroslavl, Russia). Breast tissue conductivity was quantified using MEIK 5.6 software. Diagnostic performance of visually interpreted 3D EIT was assessed using histology (surgical excision or vacuum core biopsy) and clinical follow-up. Kaplan-Meier analysis was used to calculate progression-free survival (PFS) and overall survival (OS) rates. Hazard ratio (HR) with a 95% confidence interval (95% CI) for various clinicopathological variables were determined using univariate and multivariate Cox regression models. Breast cancer was confirmed in 272 of 645 patients by histopathology and other diagnostic imaging modalities. Among the confirmed cases, 218 patients had positive 3D EIT findings. The sensitivity, specificity, accuracy, positive likelihood, and negative likelihood ratios of 3D EIT were 80.1%, 75.1%, 77.2%, 70.1%, and 83.8%. There were no significant differences in the diagnostic accuracy, sensitivity, or specificity between 3D EIT and mammography, ultrasound, or combined mammography and ultrasound. 3D EIT breast cancer images were classified into 3 different types, including Ia [non-complicated breast cancer (NCBC), 62 cases], Ib [complicated breast cancer (CBC), 131 cases], and Ic [edematous-infiltrative breast cancer (EIBC), 25 cases], which were associated with tumor size (P<0.001), TNM stage (P<0.001), and lymph node metastasis (P=0.012). At 5-year follow-up, multivariate analysis demonstrated that breast cancer 3D EIT imaging classification was an independent predictor for decreased OS (HR: 2.399, 95% CI: 1.035, 5.564, P=0.041) and PFS (HR: 2.836, 95% CI: 1.555, 5.172, P=0.012) in patients with breast cancer. 3D EIT breast cancer images were classified into 3 types based on different image characteristics. 3D EIT appeared to be useful in clinical diagnostic performance and prognostic evaluation in patients with breast cancer.

Three-Dimensional Electrical Impedance Tomography With Multiplicative Regularization.

The multiplicative regularization scheme is applied to three-dimensional electrical impedance tomography (EIT) image reconstruction problem to alleviate its ill-posedness. A cost functional is constructed by multiplying the data misfit functional with the regularization functional. The regularization functional is based on a weighted L2-norm with the edge-preserving characteristic. Gauss-Newton method is used to minimize the cost functional. A method based on the discrete exterior calculus (DEC) theory is introduced to formulate the discrete gradient and divergence operators related to the regularization on unstructured meshes. Both numerical and experimental results show good reconstruction accuracy and anti-noise performance of the algorithm. The reconstruction results using human thoracic data show promising applications in thorax imaging. The multiplicative regularization can be applied to EIT image reconstruction with promising applications in thorax imaging. In the multiplicative regularization scheme, there is no need to set an artificial regularization parameter in the cost functional. This helps to reduce the workload related to choosing a regularization parameter which may require expertise and many numerical experiments. The DEC-based method provides a systematic and rigorous way to formulate operators on unstructured meshes. This may help EIT image reconstructions using regularizations imposing structural or spatial constraints.

Impedance-based cellular assays for regenerative medicine.

Therapies based on regenerative techniques have the potential to radically improve healthcare in the coming years. As a result, there is an emerging need for non-destructive and label-free technologies to assess the quality of engineered tissues and cell-based products prior to their use in the clinic. In parallel, the emerging regenerative medicine industry that aims to produce stem cells and their progeny on a large scale will benefit from moving away from existing destructive biochemical assays towards data-driven automation and control at the industrial scale. Impedance-based cellular assays (IBCA) have emerged as an alternative approach to study stem-cell properties and cumulative studies, reviewed here, have shown their potential to monitor stem-cell renewal, differentiation and maturation. They offer a novel method to non-destructively assess and quality-control stem-cell cultures. In addition, when combined with in vitro disease models they provide complementary insights as label-free phenotypic assays. IBCA provide quantitative and very sensitive results that can easily be automated and up-scaled in multi-well format. When facing the emerging challenge of real-time monitoring of three-dimensional cell culture dielectric spectroscopy and electrical impedance tomography represent viable alternatives to two-dimensional impedance sensing.This article is part of the theme issue 'Designer human tissue: coming to a lab near you'.

Optimal distance of multi-plane sensor in three-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) is a visual imaging technique for obtaining the conductivity and permittivity distributions in the domain of interest. As an advanced technique, EIT has the potential to be a valuable tool for continuously bedside monitoring of pulmonary function. The EIT applications in any three-dimensional (3 D) field are very limited to the 3 D effects, i.e. the distribution of electric field spreads far beyond the electrode plane. The 3 D effects can result in measurement errors and image distortion. An important way to overcome the 3 D effect is to use the multiple groups of sensors. The aim of this paper is to find the best space resolution of EIT image over various electrode planes and select an optimal plane spacing in a 3 D EIT sensor, and provide guidance for 3 D EIT electrodes placement in monitoring lung function. In simulation and experiment, several typical conductivity distribution models, such as one rod (central, midway and edge), two rods and three rods, are set at different plane spacings between the two electrode planes. A Tikhonov regularization algorithm is utilized for reconstructing the images; the relative error and the correlation coefficient are utilized for evaluating the image quality. Based on numerical simulation and experimental results, the image performance at different spacing conditions is evaluated. The results demonstrate that there exists an optimal plane spacing between the two electrode planes for 3 D EIT sensor. And then the selection of the optimal plane spacing between the electrode planes is suggested for the electrodes placement of multi-plane EIT sensor.

Three-Dimensional Electrical Impedance Tomography to Monitor Unsaturated Moisture Ingress in Cement-Based Materials

The development of tools to monitor unsaturated moisture flow in cement-based material is of great importance, as most degradation processes in cement-based materials take place in the presence of moisture. In this paper, the feasibility of electrical impedance tomography (EIT) to monitor three-dimensional (3D) moisture flow in mortar containing fine aggregates is investigated. In the experiments, EIT measurements are taken during moisture ingress in mortar, using electrodes attached on the outer surface of specimens. For EIT, the so-called difference imaging scheme is adopted to reconstruct the change of the 3D electrical conductivity distribution within a specimen caused by the ingress of water into mortar. To study the ability of EIT to detect differences in the rate of ingress, the experiment is performed using plain water and with water containing a viscosity-modifying agent yielding a slower flow rate. To corroborate EIT, X-ray computed tomography (CT) and simulations of unsaturated moisture flow are carried out. While X-ray CT shows contrast with respect to background only in highly saturated regions, EIT shows the conductivity change also in the regions of low degree of saturation. The results of EIT compare well with simulations of unsaturated moisture flow. Moreover, the EIT reconstructions show a clear difference between the cases of water without and with the viscosity-modifying agent and demonstrate the ability of EIT to distinguish between different flow rates.

Finite Element Approximation and Numerical Analysis of Three-dimensional Electrical Impedance Tomography

Electrical impedance tomography is solved by solving an inverse problem of elliptic equation, and a new numerical method or a new technique is argued to consider finite element (such as normal element and mixed element) in this paper on three dimensional region. Introducing different perturbations to boundary restrictions and using different spacial steps, the authors obtain numerical solutions and give comparison with exact solutions. Numerical data show that numerical solution can approximate exact solution well as spacial step taken small and the approximation of Neumann boundary condition is more stable than that of Dirichlet case.&lt;br /&gt;For Newton iterations on finite element method, a large-scaled system of massive linear equations is solved in each iteration, thus the computation is quite expensive. So two techniques are argued in the first half of this paper. Firstly, the invariance property of quasi-element stiffness matrix is used in the iterations and a type of special current model is introduced. Then the minimum number of direct problems solved is considered. Later a local conservative numerical approximation, low order mixed element (block-centered method) is presented in the latter part and the positive semi-definiteness and the existence of its solution are proved. Computational formula of error functional Jacobi matrix is derived and the least direct problems in each iteration are solved by using the symmetry of algorithm and a special current basis. This method has been applied successfully in actual numerical simulation of three-dimensional electrical impedance tomography.

A numerical method for solving a three-dimensional electrical impedance tomography problem in the case of the data given on part of the boundary

A three-dimensional electrical impedance tomography problem in the case of an object with a piecewise constant electrical conductivity is considered. The task is to determine the unknown boundary separating regions of an object with different conductivity values, which are assumed to be known. The initial data for determining the inhomogeneity boundary represents electrical measurements taken on part of the object’s boundary. A numerical method for solving the problem is proposed and the numerical results are presented.

A fast time-difference inverse solver for 3D EIT with application to lung imaging.

A class of sparse optimization techniques that require solely matrix-vector products, rather than an explicit access to the forward matrix and its transpose, has been paid much attention in the recent decade for dealing with large-scale inverse problems. This study tailors application of the so-called Gradient Projection for Sparse Reconstruction (GPSR) to large-scale time-difference three-dimensional electrical impedance tomography (3D EIT). 3D EIT typically suffers from the need for a large number of voxels to cover the whole domain, so its application to real-time imaging, for example monitoring of lung function, remains scarce since the large number of degrees of freedom of the problem extremely increases storage space and reconstruction time. This study shows the great potential of the GPSR for large-size time-difference 3D EIT. Further studies are needed to improve its accuracy for imaging small-size anomalies.

Compressed sampling for boundary measurements in three-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) utilizes electrodes on a medium's surface to produce measured data from which the conductivity distribution inside the medium is estimated. For the cases that relocation of electrodes is impractical or no a priori assumptions can be made to optimize the electrodes placement, a large number of electrodes may be needed to cover all possible imaging volume. This may occur in dynamically varying conductivity distribution in 3D EIT. Three-dimensional EIT then requires inverting very large linear systems to calculate the conductivity field, which causes significant problems regarding storage space and reconstruction time in addition to that data acquisition for a large number of electrodes will reduce the achievable frame rate, which is considered as major advantage of EIT imaging. This study proposes an idea to reduce the reconstruction complexity based on the well-known compressed sampling theory. By applying the so-called model-based CoSaMP algorithm to large size data collected by a 256 channel system, the size of forward operator and data acquisition time is reduced to those of a 32 channel system, while accuracy of reconstruction is significantly improved. The results demonstrate great capability of compressed sampling for overriding the challenges arising in 3D EIT.

Iterative method for solving a three-dimensional electrical impedance tomography problem in the case of piecewise constant conductivity and one measurement on the boundary

The problem of electrical impedance tomography in a bounded three-dimensional domain with a piecewise constant electrical conductivity is considered. The boundary of the inhomogeneity is assumed to be unknown. The inverse problem is to determine the surface that is the boundary of the inhomogeneity from given measurements of the potential and its normal derivative on the outer boundary of the domain. An iterative method for solving the inverse problem is proposed, and numerical results are presented.

Recovering conductivity at the boundary in three-dimensional electrical impedance tomography

The aim of electrical impedance tomography (EIT) is to reconstruct the conductivity values inside a conductive object from electric measurements performed at the boundary of the object. EIT has applications in medical imaging, nondestructive testing, geological remote sensing and subsurface monitoring. Recovering the conductivity and its normal derivative at the boundary is a preliminary step in many EIT algorithms; Nakamura and Tanuma introduced formulae for recovering them approximately from localized voltage-to-current measurements in [Recent Development in Theories & Numerics, International Conference on Inverse Problems 2003]. The present study extends that work both theoretically and computationally. As a theoretical contribution, reconstruction formulas are proved in a more general setting. On the computational side, numerical implementation of the reconstruction formulae is presented in three-dimensional cylindrical geometry. These experiments, based on simulated noisy EIT data, suggest that the conductivity at the boundary can be recovered with reasonable accuracy using practically realizable measurements. Further, the normal derivative of the conductivity can also be recovered in a similar fashion if measurements from a homogeneous conductor (dummy load) are available for use in a calibration step.