A Parametric Level Set-Based Approach to Difference Imaging in Electrical Impedance Tomography

Implicit Solutions of the Electrical Impedance Tomography Inverse Problem in the Continuous Domain with Deep Neural Networks

Electrical impedance tomography (EIT) is a non-invasive imaging modality used for estimating the conductivity of an object Ω from boundary electrode measurements. In recent years, researchers achieved substantial progress in analytical and numerical methods for the EIT inverse problem. Despite the success, numerical instability is still a major hurdle due to many factors, including the discretization error of the problem. Furthermore, most algorithms with good performance are relatively time consuming and do not allow real-time applications. In our approach, the goal is to separate the unknown conductivity into two regions, namely the region of homogeneous background conductivity and the region of non-homogeneous conductivity. Therefore, we pose and solve the problem of shape reconstruction using machine learning. We propose a novel and simple jet intriguing neural network architecture capable of solving the EIT inverse problem. It addresses previous difficulties, including instability, and is easily adaptable to other ill-posed coefficient inverse problems. That is, the proposed model estimates the probability for a point of whether the conductivity belongs to the background region or to the non-homogeneous region on the continuous space Rd∩Ω with d∈{2,3}. The proposed model does not make assumptions about the forward model and allows for solving the inverse problem in real time. The proposed machine learning approach for shape reconstruction is also used to improve gradient-based methods for estimating the unknown conductivity. In this paper, we propose a piece-wise constant reconstruction method that is novel in the inverse problem setting but inspired by recent approaches from the 3D vision community. We also extend this method into a novel constrained reconstruction method. We present extensive numerical experiments to show the performance of the architecture and compare the proposed method with previous analytic algorithms, mainly the monotonicity-based shape reconstruction algorithm and iteratively regularized Gauss-Newton method.

Deep feature-domain matching for cardiac-related component separation from a chest electrical impedance tomography image series: proof-of-concept study

Objectives.The cardiac-related component in chest electrical impedance tomography (EIT) measurement is of potential value to pulmonary perfusion monitoring and cardiac function measurement. In a spontaneous breathing case, cardiac-related signals experience serious interference from ventilation-related signals. Traditional cardiac-related signal-separation methods are usually based on certain features of signals. To further improve the separation accuracy, more comprehensive features of the signals should be exploited.Approach.We propose an unsupervised deep-learning method called deep feature-domain matching (DFDM), which exploits the feature-domain similarity of the desired signals and the breath-holding signals. This method is characterized by two sub-steps. In the first step, a novel Siamese network is designed and trained to learn common features of breath-holding signals; in the second step, the Siamese network is used as a feature-matching constraint between the separated signals and the breath-holding signals.Main results.The method is first tested using synthetic data, and the results show satisfactory separation accuracy. The method is then tested using the data of three patients with pulmonary embolism, and the consistency between the separated images and the radionuclide perfusion scanning images is checked qualitatively.Significance.The method uses a lightweight convolutional neural network for fast network training and inference. It is a potential method for dynamic cardiac-related signal separation in clinical settings.

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.

Removing Clinical Motion Artifacts During Ventilation Monitoring With Electrical Impedance Tomography: Introduction of Methodology and Validation With Simulation and Patient Data

Objective

Electrical impedance tomography (EIT) is a bedside tool for lung ventilation and perfusion assessment. However, the ability for long-term monitoring diminished due to interferences from clinical interventions and motion artifacts. The purpose of this study is to investigate the feasibility of the discrete wavelet transform (DWT) to detect and remove the common types of motion artifacts in thoracic EIT.

Methods

Baseline drifting, step-like and spike-like interferences were simulated to mimic three common types of motion artifacts. The discrete wavelet decomposition was employed to characterize those motion artifacts in different frequency levels with different wavelet coefficients, and those motion artifacts were then attenuated by suppressing the relevant wavelet coefficients. Further validation was conducted in two patients when motion artifacts were introduced through pulsating mattress and deliberate body movements. The db8 wavelet was used to decompose the contaminated signals into several sublevels.

Results

In the simulation study, it was shown that, after being processed by DWT, the signal consistency improved by 92.98% for baseline drifting, 97.83% for the step-like artifact, and 62.83% for the spike-like artifact; the signal similarity improved by 77.49% for baseline drifting, 73.47% for the step-like artifact, and 2.35% for the spike-like artifact. Results from patient data demonstrated the EIT image errors decreased by 89.24% (baseline drifting), 88.45% (step-like artifact), and 97.80% (spike-like artifact), respectively; the data correlations between EIT images without artifacts and the processed were all > 0.95.

Conclusion

This study found that DWT is a universal and effective tool to detect and remove these motion artifacts.

Reconstruction of conductivity distribution with electrical impedance tomography based on hybrid regularization method

Purpose: Physiological or pathological variation would cause a change of conductivity. Electrical impedance tomography (EIT) is favorable in reconstructing conductivity distribution inside the detected area. However, the reconstruction is an ill-posed inverse problem and the spatial resolution of the reconstructed image is relatively poor. Approach: To deal with the problem, a regularization method is commonly applied. Traditional regularization methods have their own disadvantages. In this work, we develop an innovative hybrid regularization method to determine the conductivity distribution from the boundary measurement. To address the unwanted artifact observed in the total variation (TV) method, the proposed approach incorporates the TV method with the non-convex sparse penalty term-based wavelet transform. In the reconstruction, the sensitivity matrix is also normalized to increase the sensitivity of the measurement to the variation of the conductivity. The objective function is minimized with the split augmented Lagrangian shrinkage algorithm. Results: The feasibility of the proposed method is evaluated by numerical simulation and phantom experiment. The results verify that the reconstruction with the proposed method is more advantageous, as obvious improvement is observed in the reconstructed image. Conclusions: With the proposed method, the artifact can be effectively suppressed and the reconstructed image of conductivity distribution is improved. It has great potential in medical imaging, which would be helpful for the accurate diagnosis of disease.

Simultaneous Imaging of Bio- and Non-Conductive Targets by Combining Frequency and Time Difference Imaging Methods in Electrical Impedance Tomography

As a promising medical imaging modality, electrical impedance tomography (EIT) can image the electrical properties within a region of interest using electrical measurements applied at electrodes on the region boundary. This paper proposes to combine frequency and time difference imaging methods in EIT to simultaneously image bio- and non-conductive targets, where the image fusion is accomplished by applying a wavelet-based technique. To enable image fusion, both time and frequency difference imaging methods are investigated regarding the reconstruction of bio- or non-conductive inclusions in the target region at varied excitation frequencies, indicating that none of those two methods can tackle with the scenarios where both bio- and non-conductive inclusions exist. This dilemma can be resolved by fusing the time difference (td) and appropriate frequency difference (fd) EIT images since they are complementary to each other. Through simulation and in vitro experiment, it is demonstrated that the proposed fusion method can reasonably reconstruct both the bio- and non-conductive inclusions within the lung models established to simulate the ventilation process, which is expected to be beneficial for the diagnosis of lung-tissue related diseases by EIT.

Shape-Driven EIT Reconstruction Using Fourier Representations

Shape-driven approaches have been proposed as an effective strategy for the electrical impedance tomography (EIT) reconstruction problem in recent years. In order to augment the shape-driven approaches, we propose a new method that transforms the shape to be reconstructed as basic primitives directly modeled by using Fourier representations. To allow automatic topological changes between the basic primitives and surrounding objects simultaneously, Boolean operations are employed. The Boolean operations with direct representation of primitives can be utilized for dimensionality and ill-posedness reduction, enabling feasible shape and topology optimization with shape-driven approaches. As a proof of principle, we leverage the proposed method for two dimensional shape reconstruction in EIT with various conductivity distributions. We demonstrate that our method is able to improve EIT reconstructions by enabling accurate shape and topology optimization.

Development of a Portable, Reliable and Low-Cost Electrical Impedance Tomography System Using an Embedded System

Electrical impedance tomography (EIT) is a useful procedure with applications in industry and medicine, particularly in the lungs and brain area. In this paper, the development of a portable, reliable and low-cost EIT system for image reconstruction by using an embedded system (ES) is introduced herein. The novelty of this article is the hardware development of a complete low-cost EIT system, as well as three simple and efficient algorithms that can be implemented on ES. The proposed EIT system applies the adjacent voltage method, starting with an impedance acquisition stage that sends data to a Raspberry Pi 4 (RPi4) as ES. To perform the image reconstruction, a user interface was developed by using GNU Octave for RPi4 and the EIDORS library. A statistical analysis is performed to determine the best average value from the samples measured by using an analog-to-digital converter (ADC) with a capacity of 30 kSPS and 24-bit resolution. The tests for the proposed EIT system were performed using materials such as metal, glass and an orange to simulate its application in food industry. Experimental results show that the statistical median is more accurate with respect to the real voltage measurement; however, it represents a higher computational cost. Therefore, the mean is calculated and improved by discarding data values in a transitory state, achieving better accuracy than the median to determine the real voltage value, enhancing the quality of the reconstructed images. A performance comparison between a personal computer (PC) and RPi4 is presented. The proposed EIT system offers an excellent cost-benefit ratio with respect to a traditional PC, taking into account precision, accuracy, energy consumption, price, light weight, size, portability and reliability. The proposed EIT system has potential application in mechanical ventilation, food industry and structural health monitoring.

Introduction of Sample Based Prior into the D-Bar Method Through a Schur Complement Property

Electrical impedance tomography (EIT) is a non-invasive medical imaging technique in which images of the conductivity in a region of interest in the body are computed from measurements of voltages on electrodes arising from low-frequency, low-amplitude applied currents. Mathematically, the inverse conductivity problem is nonlinear and ill-posed, and the reconstructions have characteristically low spatial resolution. One approach to improve the spatial resolution of EIT images is to include anatomically and physiologically-based prior information in the reconstruction algorithm. Statistical inversion theory provides a means of including prior information from a representative sample population. In this paper, a method is proposed to introduce statistical prior information into the D-bar method based on Schur complement properties. The method presents an improvement of the image obtained by the D-bar method by maximizing the conditional probability density function of an image that is consistent with a prior information and the model, given a D-bar image computed from the voltage measurements. Experimental phantoms show an improved spatial resolution by the use of the proposed method for the D-bar image reconstructions.

Shape-Driven Difference Electrical Impedance Tomography

This work proposes a novel shape-driven reconstruction approach for difference electrical impedance tomography (EIT). In the proposed approach, the reconstruction problem is formulated as a shape reconstruction problem and solved via an explicit and geometrical methodology, where the geometry of the embedded inclusions is represented by a shape and topology description function (STDF). To incorporate more geometry and prior information directly into the reconstruction and to provide better flexibility in the solution process, the concept of a moving morphable component (MMC) is applied here implying that MMC is treated as the basic building block of the embedded inclusions. Simulations, phantom studies, and in vivo pig data are used to test the proposed approach for the most popular biomedical application of EIT - lung imaging - and the performance is compared with the conventional linear approach. In addition, the modality's robustness is studied in cases where (i) modeling errors are caused by inhomogeneity in the background conductivity, and (ii) uncertainties in the contact impedances and reference state are present. The results of this work indicate that the proposed approach is tolerant to modeling errors and is fairly robust to typical EIT uncertainties, producing greatly improved image quality compared to the conventional linear approach.

Shape Reconstruction Using Boolean Operations in Electrical Impedance Tomography

In this work, we propose a new shape reconstruction framework rooted in the concept of Boolean operations for electrical impedance tomography (EIT). Within the framework, the evolution of inclusion shapes and topologies are simultaneously estimated through an explicit boundary description. For this, we use B-spline curves as basic shape primitives for shape reconstruction and topology optimization. The effectiveness of the proposed approach is demonstrated using simulated and experimentally-obtained data (testing EIT lung imaging). In the study, improved preservation of sharp features is observed when employing the proposed approach relative to the recently developed moving morphable components-based approach. In addition, robustness studies of the proposed approach considering background inhomogeneity and differing numbers of B-spline curve control points are performed. It is found that the proposed approach is tolerant to modeling errors caused by background inhomogeneity and is also quite robust to the selection of control points.

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.

CT Image-Guided Electrical Impedance Tomography for Medical Imaging

This study presents a computed tomography (CT) image-guided electrical impedance tomography (EIT) method for medical imaging. CT is a robust imaging modality for accurately reconstructing the density structure of the region being scanned. EIT can detect electrical impedance abnormalities to which CT scans may be insensitive, but the poor spatial resolution of EIT is a major concern for medical applications. A cross-gradient method has been introduced for oil and gas exploration to jointly invert multiple geophysical datasets associated with different medium properties in the same geological structure. In this study, we develop a CT image-guided EIT (CEIT) based on the cross-gradient method. We assume that both CT scanning and EIT imaging are conducted for the same medical target. A CT scan is first acquired to help solve the subsequent EIT imaging problem. During EIT imaging, we apply cross gradients between the CT image and the electrical conductivity distribution to iteratively constrain the conductivity inversion. The cross-gradient based method allows the mutual structures of different physical models to be referenced without directly affecting the polarity and amplitude of each model during the inversion. We apply the CEIT method to both numerical simulations and phantom experiments. The effectiveness of CEIT is demonstrated in comparison with conventional EIT. The comparison shows that the CEIT method can significantly improve the quality of conductivity images.

Induced-Current Learning Method for Nonlinear Reconstructions in Electrical Impedance Tomography

Electrical impedance tomography (EIT) is an attractive technique that aims to reconstruct the unknown electrical property in a domain from the surface electrical measurements. In this work, the induced-current learning method (ICLM) is proposed to solve nonlinear electrical impedance tomography (EIT) problems. Specifically, the cascaded end-to-end convolutional neural network (CEE-CNN) architecture is designed to implement the ICLM. The CEE-CNN greatly decreases the nonlinearities in EIT problems by designing a combined objective function and introducing multiple labels. A noticeable characteristic of the proposed CNN scheme is that the input parameters are chosen as both induced contrast current (ICC) and the updated electrical field from a spectral analysis and the output is chosen as ICC, which is fundamentally different from prevailing CNN schemes. Further, several skip connections are introduced to focus on learning only the unknown part of ICC. ICLM is verified with both numerical and experimental tests on typical EIT problems, and it is found that ICLM is able to solve typical EIT problems in less than 1 second with high image qualities. More importantly, it is also highly robust to measurement noises and modeling errors, such as inaccurate boundary data.

A Shape-Based Statistical Inversion Method for EIT/URT Dual-Modality Imaging

A shape-based statistical inversion method is proposed for Electrical Impedance Tomography (EIT) and Ultrasound Reflection Tomography (URT) dual-modality imaging. It is promising to improve the imaging accuracy in inclusion detection problems. The proposed image reconstruction method is based on the statistical shape inversion framework. The likelihood function is derived from EIT and URT forward models. The prior distribution is constructed using the Markov random field (MRF) prior. The measurement uncertainty is modeled by conditional error model method. The statistical shape inversion problem is solved by the Maximum a posterior (MAP) method with conventional error model. A set of numerical and experimental tests are carried out to evaluate the performance of the proposed method. The results show that the proposed EIT/URT dual-modality imaging method has obvious improvement in imaging accuracy compared to the traditional single-modality EIT and URT methods.

A Moving Morphable Components Based Shape Reconstruction Framework for Electrical Impedance Tomography

This paper presents a new computational framework in electrical impedance tomography (EIT) for shape reconstruction based on the concept of moving morphable components (MMC). In the proposed framework, the shape reconstruction problem is solved in an explicit and geometrical way. Compared with the traditional pixel or shape-based solution framework, the proposed framework can incorporate more geometry and prior information into shape and topology optimization directly and therefore render the solution process more flexibility. It also has the afford potential to substantially reduce the computational burden associated with shape and topology optimization. The effectiveness of the proposed approach is tested with noisy synthetic data and experimental data, which demonstrates the most popular biomedical application of EIT: lung imaging. In addition, robustness studies of the proposed approach considering modeling errors caused by non-homogeneous background, varying initial guesses, differing numbers of candidate shape components, and differing exponent in the shape and topology description function are performed. The simulation and experimental results show that the proposed approach is tolerant to modeling errors and is fairly robust to these parameter choices, offering significant improvements in image quality in comparison to the conventional absolute reconstructions using smoothness prior regularization and total variation regularization.

B-Spline-Based Sharp Feature Preserving Shape Reconstruction Approach for Electrical Impedance Tomography

This paper presents a B-spline-based shape reconstruction approach for electrical impedance tomography (EIT). In the proposed approach, the conductivity distribution to be reconstructed is assumed to be piecewise constant. The geometry of the inclusions is parameterized using B-spline curves, and the EIT forward solver is modified as a set of control points representing the inclusions' boundary to the data on the domain boundary. The low-order representation decreases the computational demand and reduces the ill-posedness of the EIT reconstruction problem. The performance of the proposed B-spline-based approach is tested with simulations that demonstrate the most popular biomedical application of EIT: lung imaging. The approach is experimentally validated using water tank data. In addition, robustness studies of the proposed approach considering varying initial guesses, inaccurately known contact impedances, differing numbers of control points, and degree of B-spline are performed. The simulation and experimental results show that the B-spline-based approach offers improvements in image quality in comparison to the traditional Fourier series-based reconstruction approach, as measured by quantitative metrics such as relative size coverage ratio and relative contrast. Inasmuch, the proposed approach is demonstrated to offer clear improvement in the ability to preserve the sharp properties of the inclusions to be imaged.

Development of a Wearable Electrical Impedance Tomographic Sensor for Gesture Recognition With Machine Learning

A wearable electrical impedance tomographic (wEIT) sensor with 8 electrodes is developed to realize gesture recognition with machine learning algorithms. To optimize the wEIT sensor, gesture recognition rates are compared by using a series of electrodes with different materials and shapes. To improve the gesture recognition rates, several Machine Learning algorithms are used to recognize three different gestures with the obtained voltage data. To clarify the gesture recognition mechanism, an electrical model of the electrode-skin contact impedance is established. Experimental results show that: rectangular copper electrodes realize the highest recognition rate; the existence of the electrode-skin contact impedance could improve the gesture recognition rate; Medium Gaussian SVM (Support Vector Machine) algorithm is the optimal algorithm with an average recognition rate of 95%.

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.