Impedance imaging with first-order TV regularization

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

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

The Research Progress of Electrical Impedance Tomography for Lung Monitoring

Medical imaging can intuitively show people the internal structure, morphological information, and organ functions of the organism, which is one of the most important inspection methods in clinical medical diagnosis. Currently used medical imaging methods can only be applied to some diagnostic occasions after qualitative lesions have been generated, and the general imaging technology is usually accompanied by radiation and other conditions. However, electrical impedance tomography has the advantages of being noninvasive and non-radiative. EIT (Electrical Impedance Tomography) is also widely used in the early diagnosis and treatment of some diseases because of these advantages. At present, EIT is relatively mature and more and more image reconstruction algorithms are used to improve imaging resolution. Hardware technology is also developing rapidly, and the accuracy of data collection and processing is continuously improving. In terms of clinical application, EIT has also been used for pathological treatment of lungs, the brain, and the bladder. In the future, EIT has a good application prospect in the medical field, which can meet the needs of real-time, long-term monitoring and early diagnosis. Aiming at the application of EIT in the treatment of lung pathology, this article reviews the research progress of EIT, image reconstruction algorithms, hardware system design, and clinical applications used in the treatment of lung diseases. Through the research and introduction of several core components of EIT technology, it clarifies the characteristics of EIT system complexity and its solutions, provides research ideas for subsequent research, and once again verifies the broad development prospects of EIT technology in the future.

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

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

A Statistical Shape-Constrained Reconstruction Framework for Electrical Impedance Tomography

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

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.

Multifrequency electrical impedance tomography with total variation regularization

Multifrequency electrical impedance tomography (MFEIT) reconstructs the distribution of conductivity by exploiting the dependence of tissue conductivity on frequency. MFEIT can be performed on a single instance of data, making it promising for applications such as stroke and cancer imaging, where it is not possible to obtain a 'baseline' measurement of healthy tissue. A nonlinear MFEIT algorithm able to reconstruct the volume fraction distribution of tissue rather than conductivities has been developed previously. For each volume, the fraction of a certain tissue should be either 1 or 0; this implies that the sharp changes of the fractions, representing the boundaries of tissue, contain all the relevant information. However, these boundaries are blurred by traditional regularization methods using [Formula: see text] norm. The total variation (TV) regularization can overcome this problem, but it is difficult to solve due to its non-differentiability. Because the fraction must be between 0 and 1, this imposes a constraint on the MFEIT method based on the fraction model. Therefore, a constrained optimization method capable of dealing with non-differentiable problems is required. Based on the primal and dual interior point method, we propose a new constrained TV regularized method to solve the fraction reconstruction problem. The noise performance of the new MFEIT method is analysed using simulations on a 2D cylindrical mesh. Convergence performance is also analysed through experiments using a cylindrical tank. Finally, simulations on an anatomically realistic head-shaped mesh are demonstrated. The proposed MFEIT method with TV regularization shows higher spatial resolution, particularly at the edges of the perturbation, and stronger noise robustness, and its image noise and shape error are 20% to 30% lower than the traditional fraction method.

Comparison of total variation algorithms for electrical impedance tomography

The applications of total variation (TV) algorithms for electrical impedance tomography (EIT) have been investigated. The use of the TV regularisation technique helps to preserve discontinuities in reconstruction, such as the boundaries of perturbations and sharp changes in conductivity, which are unintentionally smoothed by traditional l2 norm regularisation. However, the non-differentiability of TV regularisation has led to the use of different algorithms. Recent advances in TV algorithms such as the primal dual interior point method (PDIPM), the linearised alternating direction method of multipliers (LADMM) and the spilt Bregman (SB) method have all been demonstrated successful EIT applications, but no direct comparison of the techniques has been made. Their noise performance, spatial resolution and convergence rate applied to time difference EIT were studied in simulations on 2D cylindrical meshes with different noise levels, 2D cylindrical tank and 3D anatomically head-shaped phantoms containing vegetable material with complex conductivity. LADMM had the fastest calculation speed but worst resolution due to the exclusion of the second-derivative; PDIPM reconstructed the sharpest change in conductivity but with lower contrast than SB; SB had a faster convergence rate than PDIPM and the lowest image errors.