Electrical Impedance Tomography Reconstruction Research Articles

Landmark registration in CT for lung model approximation in EIT

Abstract For the visualization of pulmonary ventilation with Electrical Impedance Tomography (EIT), most devices rely on generalized reconstruction models. Yet, fixed thorax dimensions, predetermined electrode locations, and standard lung shapes lead to multiple sources of EIT imaging distortion. The following work compares reconstructions of a library model, a practical model based on landmark fitting, and a detailed model based on manual segmentation. CT images of five pigs were segmented into torso surface, electrode positions, and lung borders. Practical models were created with reduced data, registration, and fitting. Detailed models were created by using the complete segmentation data. After EIT reconstruction and tidal image calculation, the overlap of CT lung segmentation and ventilated voxel was calculated. Compared with the results of a standardized model, the practical model reached an average ventilation/segmentation-overlap difference of an additional 12 %, and the detailed model achieved an average difference of 10 %. In conclusion, the shift of reconstructed impedance towards the segmented lung region is similar in both models when compared to the standard model, while the practical model requires a considerably less amount of information.

EIT probe based intraoperative tissue inspection for minimally invasive surgery

Abstract Electrical impedance tomography (EIT) has become an integral component in the repertoire of medical imaging techniques, particularly due to its non-invasive nature and real-time imaging capabilities. Despite its potential, the application of EIT in minimally invasive surgery (MIS) has been hindered by a lack of specialized electrode probes. Existing designs often compromise between invasiveness and spatial sensitivity: probes small enough for MIS often fail to provide detailed imaging, while those offering greater sensitivity are impractically large for use through a surgical trocar. Addressing this challenge, our study presents a breakthrough in EIT probe design. The open electrode probe we have developed features a line of 16 electrodes, thoughtfully arrayed to balance the spatial demands of MIS with the need for precise imaging. Employing an advanced EIT reconstruction algorithm, our probe not only captures images that reflect the electrical characteristics of the tissues but also ensures the homogeneity of the test material is accurately represented. The versatility of our probe is demonstrated by its capacity to generate high-resolution images of subsurface anatomical structures, a feature particularly valuable during MIS where direct visual access is limited. Surgeons can rely on intraoperative EIT imaging to inform their navigation of complex anatomical landscapes, enhancing both the safety and efficacy of their procedures. Through rigorous experimental validation using ex vivo tissue phantoms, we have established the probe’s proficiency. The experiments confirmed the system’s high sensitivity and precision, particularly in the critical tasks of subsurface tissue detection and surgical margin delineation. These capabilities manifest the potential of our probe to revolutionize the field of surgical imaging, providing a previously unattainable level of detail and assurance in MIS procedures.

Discontinuous polynomial approximation in electrical impedance tomography with total variational regularization

In this paper, we present an alternative discrete total variation type functional for image reconstruction in electrical impedance tomography. The modified functional deals with unknown inclusions and values of conductivity. The convergence of the proposed finite element method with uniform refinement is also established: the sequence of discrete solutions contains a subsequence that converges to a solution of the continuous functional. Additionally, we propose an adaptive reconstruction algorithm in which the estimators are based on the discrete state variable, the discrete adjoint variable and the gradient of the discrete functional. A series of numerical examples are provided to illustrate the convergence behavior in diverse scenarios.

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.

Generative-Adversarial-Network-Based Image Reconstruction for the Capacitively Coupled Electrical Impedance Tomography of Stroke.

This study investigated the potential of machine-learning-based stroke image reconstruction in capacitively coupled electrical impedance tomography. The quality of brain images reconstructed using the adversarial neural network (cGAN) was examined. The big data required for supervised network training were generated using a two-dimensional numerical simulation. The phantom of an axial cross-section of the head without and with impact lesions was an average of a three-centimeter-thick layer corresponding to the height of the sensing electrodes. Stroke was modeled using regions with characteristic electrical parameters for tissues with reduced perfusion. The head phantom included skin, skull bone, white matter, gray matter, and cerebrospinal fluid. The coupling capacitance was taken into account in the 16-electrode capacitive sensor model. A dedicated ECTsim toolkit for Matlab was used to solve the forward problem and simulate measurements. A conditional generative adversarial network (cGAN) was trained using a numerically generated dataset containing samples corresponding to healthy patients and patients affected by either hemorrhagic or ischemic stroke. The validation showed that the quality of images obtained using supervised learning and cGAN was promising. It is possible to visually distinguish when the image corresponds to the patient affected by stroke, and changes caused by hemorrhagic stroke are the most visible. The continuation of work towards image reconstruction for measurements of physical phantoms is justified.

A Second-Order Generalized Total Variation with Improved Alternating Direction Method of Multipliers Algorithm for Electrical Impedance Tomography Reconstruction

The issue of Electrical Impedance Tomography (EIT) is a well-known inverse problem that presents challenging characteristics. In order to address the difficulties associated with ill-conditioned inverses, regularization methods are typically employed. One commonly used approach is total variation (TV) regularization, which has shown effectiveness in EIT. In order to meet the requirements of real-time tracking, it is essential to acquire fast and reliable algorithms for image reconstruction. Therefore, we present a modified second-order generalized regularization algorithm that enables more-accurate reconstruction of organ boundaries and internal structures, to reduce EIT artifacts, and to overcome the inability of the conventional Tikhonov regularization method in solving the step effect of the medium boundary. The proposed algorithm uses the improved alternating direction method of multipliers (ADMM) to tackle this optimization issue and adopts the second-order generalized total variation (SOGTV) function with strong boundary-preserving features as the regularization generalization function. The experiments are based on simulation data and the physical model of the circular water tank that we developed. The results showed that SOGTV regularization can improve image realism compared with some classic regularization.

Enhancing Electrical Impedance Tomography Reconstruction Using Learned Half-Quadratic Splitting Networks with Anderson Acceleration

Enhancing Electrical Impedance Tomography Reconstruction Using Learned Half-Quadratic Splitting Networks with Anderson Acceleration

Regularized full waveform inversion for low frequency ultrasound tomography with a structural similarity EIT prior

In previous work by Rueter et al., low frequency (10–750 kHz) ultrasound was shown to penetrate the lung, motivating its use as a nonionizing tomographic technique for pulmonary monitoring. Here, we present a method for regularized full waveform inversion for low-frequency tomographic ultrasound data. A novel structural similarity index metric (SSIM)-based regularization term is introduced that compares the structural correlation of the current sound speed iterate to a prior reconstruction computed by electrical impedance tomography (EIT). Full waveform reconstructions of sound speeds from numerically simulated low frequency ultrasound data with 0.1% additive Gaussian noise are computed, and the results are compared using Tikhonov regularization, total variation regularization, and both terms combined with the SSIM-EIT regularization term. The EIT reconstruction was computed from simulated voltage data on the same phantom using one step of a Newton-Raphson method with a high-pass Gaussian filter as a regularizer. Reconstructions including the SSIM-EIT regularization term converged fastest, and an adaptive regularization parameter provided the most accurate reconstructions. The method is then iterated by computing an EIT reconstruction using the USCT result as a prior, and a subsequent USCT reconstruction is computed using the SSIM-EIT regularization term with the updated EIT reconstruction.

Post-processing electrical impedance tomography reconstructions with incomplete data using convolutional neural networks

Post-processing electrical impedance tomography reconstructions with incomplete data using convolutional neural networks

Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT) Inverse Problem

This paper aims to determine whether regularization improves image reconstruction in electrical impedance tomography (EIT) using a radial basis network. The primary purpose is to investigate the effect of regularization to estimate the network parameters of the radial basis function network to solve the inverse problem in EIT. Our approach to studying the efficacy of the radial basis network with regularization is to compare the performance among several different regularizations, mainly Tikhonov, Lasso, and Elastic Net regularization. We vary the network parameters, including the fixed and variable widths for the Gaussian used for the network. We also perform a robustness study for comparison of the different regularizations used. Our results include (1) determining the optimal number of radial basis functions in the network to avoid overfitting; (2) comparison of fixed versus variable Gaussian width with or without regularization; (3) comparison of image reconstruction with or without regularization, in particular, no regularization, Tikhonov, Lasso, and Elastic Net; (4) comparison of both mean square and mean absolute error and the corresponding variance; and (5) comparison of robustness, in particular, the performance of the different methods concerning noise level. We conclude that by looking at the R2 score, one can determine the optimal number of radial basis functions. The fixed-width radial basis function network with regularization results in improved performance. The fixed-width Gaussian with Tikhonov regularization performs very well. The regularization helps reconstruct the images outside of the training data set. The regularization may cause the quality of the reconstruction to deteriorate; however, the stability is much improved. In terms of robustness, the RBF with Lasso and Elastic Net seem very robust compared to Tikhonov.

A noise-controlling method by hybrid current-stimulation and voltage-measurement for electrical impedance tomography (HCSVM-EIT)

Image reconstruction in electrical impedance tomography (EIT) is a typical ill-posed inverse problem, from which the stability of conductivity reconstruction affects the reliability of physiological parameters evaluation. In order to improve the stability, the effect of boundary voltage noise on conductivity reconstruction should be controlled. A noise-controlling method based on hybrid current-stimulation and voltage-measurement for EIT (HCSVM-EIT) is proposed for stable conductivity reconstruction. In HCSVM-EIT, the boundary voltage is measured by one current-stimulation and voltage-measurement pattern (high-SNR pattern) with a higher signal-to-noise ratio (SNR); the sensitivity matrix is calculated by another current-stimulation and voltage-measurement pattern (low-cond pattern) with a lower condition number; the boundary voltage is then transformed from the high-SNR pattern into the low-cond pattern by multiplying by an optimized transformation matrix for image reconstruction. The stability of conductivity reconstruction is improved by combining the advantages of the high-SNR pattern for boundary voltage measurement and the low-cond pattern for sensitivity matrix calculation. The simulation results show that the HCSVM-EIT increases the correlation coefficient (CC) of conductivity reconstruction. The experiment results show that the CC of conductivity reconstruction of the human lower limb is increased from 0.3424 to 0.5580 by 62.97% compared to the quasi-adjacent pattern, and from 0.4942 to 0.5580 by 12.91% compared to the adjacent pattern. In conclusion, the stable conductivity reconstruction with higher CC in HCSVM-EIT improves the reliability of physiological parameters evaluation for disease detection.

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

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

Improved Electrical Impedance Tomography Reconstruction via a Bayesian Approach With an Anatomical Statistical Shape Model.

electrical impedance tomography (EIT) is a promising technique for rapid and continuous bedside monitoring of lung function. Accurate and reliable EIT reconstruction of ventilation requires patient-specific shape information. However, this shape information is often not available and current EIT reconstruction methods typically have limited spatial fidelity. This study sought to develop a statistical shape model (SSM) of the torso and lungs and evaluate whether patient-specific predictions of torso and lung shape could enhance EIT reconstructions in a Bayesian framework. torso and lung finite element surface meshes were fitted to computed tomography data from 81 participants, and a SSM was generated using principal component analysis and regression analyses. Predicted shapes were implemented in a Bayesian EIT framework and were quantitatively compared to generic reconstruction methods. Five principal shape modes explained 38% of the cohort variance in lung and torso geometry, and regression analysis yielded nine total anthropometrics and pulmonary function metrics that significantly predicted these shape modes. Incorporation of SSM-derived structural information enhanced the accuracy and reliability of the EIT reconstruction as compared to generic reconstructions, demonstrated by reduced relative error, total variation, and Mahalanobis distance. As compared to deterministic approaches, Bayesian EIT afforded more reliable quantitative and visual interpretation of the reconstructed ventilation distribution. However, no conclusive improvement of reconstruction performance using patient specific structural information was observed as compared to the mean shape of the SSM. The presented Bayesian framework builds towards a more accurate and reliable method for ventilation monitoring via EIT.

Dual-modal Image Reconstruction for Electrical Impedance Tomography with Overlapping Group Lasso and Laplacian Regularization.

Electrical Impedance Tomography (EIT) is a promising biomedical imaging modality, yet EIT image reconstruction remains an open challenge due to its severe ill-posedness. High-quality EIT image reconstruction algorithms are desired. This paper reports a segmentation-free dual-modal EIT image reconstruction algorithm that uses Overlapping Group Lasso and Laplacian (OGLL) regularization. An overlapping group lasso penalty is constructed based on conductivity change properties and encodes the imaging targets' structural information obtained from an auxiliary imaging modality that provides structural images of the sensing region. We introduce Laplacian regularization to alleviate the artifacts caused by group overlapping. The performance of OGLL is evaluated and compared with single-modal and dual-modal image reconstruction algorithms using simulation and real-world data. Quantitative metrics and visualized images confirm the superiority of the proposed method in terms of structure preservation, background artifact (BA) suppression, and conductivity contrast differentiation. This work proves the effectiveness of OGLL in improving EIT image quality. This study demonstrates that EIT has the potential to be adopted in quantitative tissue analysis by using such dual-modal imaging approaches.

DeepEIT: Deep Image Prior Enabled Electrical Impedance Tomography.

Neural networks (NNs) have been widely applied in tomographic imaging through data-driven training and image processing. One of the main challenges in using NNs in real medical imaging is the requirement of massive amounts of training data - which are not always available in clinical practice. In this article, we demonstrate that, on the contrary, one can directly execute image reconstruction using NNs without training data. The key idea is to bring in the recently introduced deep image prior (DIP) and merge it with electrical impedance tomography (EIT) reconstruction. DIP provides a novel approach to the regularization of EIT reconstruction problems by compelling the recovered image to be synthesized from a given NN architecture. Then, by relying on the NN's built-in back-propagation and the finite element solver, the conductivity distribution is optimized. Quantitative results based on simulation and experimental data show that the proposed method is an effective unsupervised approach capable of outperforming state-of-the-art alternatives.

Towards intraoperative surgical margin assessment: Validation of an electrical impedance-based probe with ex vivo bovine tissue.

Radical prostatectomy (RP) is a common surgical therapy to treat prostate cancer. The procedure has a high positive surgical margin (PSM) rate ranging from 4-48%. Patients with PSMs have a higher rate of cancer recurrence and often undergo noxious adjuvant therapy. Intraoperative surgical margin assessment (SMA) with an electrical impedance-based probe can potentially identify PSMs in real-time. This would enable surgeons to make data-based decisions in the operating room to improve patient outcomes. This paper focuses on characterizing an impedance sensing SMA probe with specialized electrodes to improve speed and bandwidth while maintaining accuracy. 3D electrical impedance tomography (EIT) reconstructions were generated from ex vivo bovine tissue to characterize probe imaging and to determine an optimal applied pressure range (15 Pa to 38 Pa). Classification accuracy of adipose and muscle tissue was evaluated by comparing the experimental data set to simulated data based on a ground truth binary map of the tissue. Experimental AUCs ≥0.83 were maintained up to 50 kHz. The developed impedance sensing probe successfully classified between muscle and adipose tissue in an ex vivo bovine model. Future work includes improving performance of the SMA probe with custom hardware and collecting data from ex vivo and in vivo prostatic tissues.Clinical Relevance-This technology is expected to reduce the rate of PSMs in RP and decrease the use of post-surgical adjuvant therapies. It is also anticipated that intraoperative impedance measurements will increase efficacy of nerve sparing procedures and reduce complications such as incontinence and erectile dysfunction.

Influence of a Structural Prior Mask on EIT Image Reconstruction.

Electrical Impedance Tomography (EIT) is a low-cost imaging method with promising results in visualizing ventilation distribution within the lungs. However, in clinical settings, the interpretability of EIT images is often limited by blurred anatomical alignment and reconstruction artifacts. Integrating structural priors into the EIT reconstruction process can enhance the interpretability of EIT images. In this contribution, we introduced a patient-specific structural prior mask into the EIT reconstruction process. Such prior mask ensures that only conductivity changes within the lung regions are reconstructed. With the aim to investigate the influence of the structural prior mask on the EIT images, we conducted numerical simulations in terms of four different ventilation status. EIT images were reconstructed with Gauss-Newton algorithm and discrete cosine transform-based EIT algorithm. We carried out quantitative analysis including the reconstruction error and figures of merit for the evaluation. The results show that the morphological structures of the lungs introduced by the prior mask are preserved in the EIT images, and the reconstruction artefacts are also limited. In conclusion, the incorporation of the structural prior mask enhances the interpretability of EIT images in clinical settings.Clinical relevance-The correct interpretation of an EIT image is crucial for a clinical diagnosis. This research demonstrates that a structural prior mask might have the potential to improve the interpretability of an EIT image, which facilitates the clinicians with a better understanding of EIT results.

A fully connected neural Network-based voltage compensation method for accurate reconstruction in brain electrical impedance tomography

Acute cerebral ischemia is commonly accompanied by cerebral edema. With brain electrical impedance tomography (EIT), it is possible to monitor conductivity variation during dehydration treatment of the cerebral edema. However, the scalp is also dehydrated when dehydrating brain tissue which exerts a large impact on boundary measurement. Consequently, reconstruction quality of cerebral edema is seriously affected. To reduce the influence of scalp dehydration, a voltage data compensation method based on a fully connected neural network (FCNN) is proposed in this work. With this method, the voltage measured when brain tissue and scalp are simultaneously dehydrated can be compensated. To evaluate the performance of the proposed method, reconstruction of simulated cerebral ischemia in a three-layer head model is conducted. Images reconstructed with the compensated voltage data are compared with the results when there is no compensation. Besides, quantitative comparison is performed. The results indicate that it is almost impossible to identify the simulated cerebral ischemia without voltage compensation. In contrast, cerebral ischemia can be much more accurately reconstructed when the measured voltage is compensated with the proposed method.

Deep learning correction for image reconstruction in electrical impedance tomography using UNet model

Deep learning correction for image reconstruction in electrical impedance tomography using UNet model

Structural priors represented by discrete cosine transform improve EIT functional imaging.

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