Tikhonov regularization and prior information in electrical impedance tomography

TSS-ConvNet for electrical impedance tomography image reconstruction

Objective.The objective of this study was to propose a novel data-driven method for solving ill-posed inverse problems, particularly in certain conditions such as time-difference electrical impedance tomography for detecting the location and size of bubbles inside a pipe.Approach.We introduced a new layer architecture composed of three paths: spatial, spectral, and truncated spectral paths. The spatial path processes information locally, whereas the spectral and truncated spectral paths provide the network with a global receptive field. This unique architecture helps eliminate the ill-posedness and nonlinearity inherent in the inverse problem. The three paths were designed to be interconnected, allowing for an exchange of information on different receptive fields with varied learning abilities. Our network has a bottleneck architecture that enables it to recover signal information from noisy redundant measurements. We named our proposed model truncated spatial-spectral convolutional neural network (TSS-ConvNet).Main results.Our model demonstrated superior accuracy with relatively high resolution on both simulation and experimental data. This indicates that our approach offers significant potential for addressing ill-posed inverse problems in complex conditions effectively and accurately.Significance.The TSS-ConvNet overcomes the receptive field limitation found in most existing models that only utilize local information in Euclidean space. We trained the network on a large dataset covering various configurations with random parameters to ensure generalization over the training samples.

Posterior Approximate Clustering-Based Sensitivity Matrix Decomposition for Electrical Impedance Tomography

This paper introduces a sensitivity matrix decomposition regularization (SMDR) method for electric impedance tomography (EIT). Using k-means clustering, the EIT-reconstructed image can be divided into four clusters, derived based on image features, representing posterior information. The sensitivity matrix is then decomposed into distinct work areas based on these clusters. The elimination of smooth edge effects is achieved through differentiation of the images from the decomposed sensitivity matrix and further post-processing reliant on image features. The algorithm ensures low computational complexity and avoids introducing extra parameters. Numerical simulations and experimental data verification highlight the effectiveness of SMDR. The proposed SMDR algorithm demonstrates higher accuracy and robustness compared to the typical Tikhonov regularization and the iterative penalty term-based regularization method (with an improvement of up to 0.1156 in correlation coefficient). Moreover, SMDR achieves a harmonious balance between image fidelity and sparsity, effectively addressing practical application requirements.

Electrical impedance tomography for pulmonary function monitoring without dorsal electrodes

Electrical impedance tomography (EIT) is a non-invasive technology that can visualize conductivity changes inside human body in real time using multiple surface electrodes. For convenience of wearing and application, if no electrodes are attached to the back, a commonly used image reconstruction approach produces poor images of dorsal region. In this study, we developed a special current injection and voltage measurement pattern to well reconstruct the conductivity distribution inside the body even in the absence of dorsal electrodes. The proposed method has proven through numerical and phantom experiments.

Research Trends and Hotspots of Medical Electrical Impedance Tomography Algorithms: A Bibliometric Analysis From 1987 to 2021

Electrical impedance tomography (EIT) is a gradually maturing medical imaging technique that relies on computational algorithms for reconstructing and visualizing internal conductivity distributions within the human body. To provide a comprehensive and objective understanding of the current state and trends in the EIT algorithm research, we conducted bibliometric analysis on a 25-year EIT algorithm research dataset sourced from Web of Science Core Collections. We visualized publication characteristics, collaboration patterns, keywords, and co-cited references. The results indicate a steady increase in annual publications over recent decades. The United States, United Kingdom, China, and South Korea contributed 60% of the articles collaboratively. Keyword analysis unveiled three distinct stages in the evolution of EIT algorithm research: the establishment of fundamental algorithm frameworks, optimization for improved imaging performance, and the development of algorithms for clinical applications. Additionally, there has been a shift in research focus from traditional theories to the incorporation of new methods, such as artificial intelligence. Co-cited references suggest that integrating EIT with other established imaging techniques may emerge as a new trend in EIT algorithm research. In summary, EIT algorithms have been a consistent research focus, with current efforts centered on optimizing algorithms to enhance imaging performance. The emerging research trend involves utilizing more diverse and intersecting algorithms.

Image Reconstruction Using Supervised Learning in Wearable Electrical Impedance Tomography of the Thorax

Electrical impedance tomography (EIT) is a non-invasive technique for visualizing the internal structure of a human body. Capacitively coupled electrical impedance tomography (CCEIT) is a new contactless EIT technique that can potentially be used as a wearable device. Recent studies have shown that a machine learning-based approach is very promising for EIT image reconstruction. Most of the studies concern models containing up to 22 electrodes and focus on using different artificial neural network models, from simple shallow networks to complex convolutional networks. However, the use of convolutional networks in image reconstruction with a higher number of electrodes requires further investigation. In this work, two different architectures of artificial networks were used for CCEIT image reconstruction: a fully connected deep neural network and a conditional generative adversarial network (cGAN). The training dataset was generated by the numerical simulation of a thorax phantom with healthy and illness-affected lungs. Three kinds of illnesses, pneumothorax, pleural effusion, and hydropneumothorax, were modeled using the electrical properties of the tissues. The thorax phantom included the heart, aorta, spine, and lungs. The sensor with 32 area electrodes was used in the numerical model. The ECTsim custom-designed toolbox for Matlab was used to solve the forward problem and measurement simulation. Two artificial neural networks were trained with supervision for image reconstruction. Reconstruction quality was compared between those networks and one-step algebraic reconstruction methods such as linear back projection and pseudoinverse with Tikhonov regularization. This evaluation was based on pixel-to-pixel metrics such as root-mean-square error, structural similarity index, 2D correlation coefficient, and peak signal-to-noise ratio. Additionally, the diagnostic value measured by the ROC AUC metric was used to assess the image quality. The results showed that obtaining information about regional lung function (regions affected by pneumothorax or pleural effusion) is possible using image reconstruction based on supervised learning and deep neural networks in EIT. The results obtained using cGAN are strongly better than those obtained using a fully connected network, especially in the case of noisy measurement data. However, diagnostic value estimation showed that even algebraic methods allow us to obtain satisfactory results.

A Hydrogel-Based Electronic Skin for Touch Detection Using Electrical Impedance Tomography

Recent advancement in wearable and robot-assisted healthcare technology gives rise to the demand for smart interfaces that allow more efficient human-machine interaction. In this paper, a hydrogel-based soft sensor for subtle touch detection is proposed. Adopting the working principle of a biomedical imaging technology known as electrical impedance tomography (EIT), the sensor produces images that display the electrical conductivity distribution of its sensitive region to enable touch detection. The sensor was made from a natural gelatin hydrogel whose electrical conductivity is considerably less than that of human skin. The low conductivity of the sensor enabled a touch-detection mechanism based on a novel short-circuiting approach, which resulted in the reconstructed images being predominantly affected by the electrical contact between the sensor and fingertips, rather than the conventionally used piezoresistive response of the sensing material. The experimental results indicated that the proposed sensor was promising for detecting subtle contacts without the necessity of exerting a noticeable force on the sensor.

On the Image Reconstruction of Capacitively Coupled Electrical Resistance Tomography (CCERT) with Entropy Priors

Regularization with priors is an effective approach to solve the ill-posed inverse problem of electrical tomography. Entropy priors have been proven to be promising in radiation tomography but have received less attention in the literature of electrical tomography. This work aims to investigate the image reconstruction of capacitively coupled electrical resistance tomography (CCERT) with entropy priors. Four types of entropy priors are introduced, including the image entropy, the projection entropy, the image-projection joint entropy, and the cross-entropy between the measurement projection and the forward projection. Correspondingly, objective functions with the four entropy priors are developed, where the first three are implemented under the maximum entropy strategy and the last one is implemented under the minimum cross-entropy strategy. Linear back-projection is adopted to obtain the initial image. The steepest descent method is utilized to optimize the objective function and obtain the final image. Experimental results show that the four entropy priors are effective in regularization of the ill-posed inverse problem of CCERT to obtain a reasonable solution. Compared with the initial image obtained by linear back projection, all the four entropy priors make sense in improving the image quality. Results also indicate that cross-entropy has the best performance among the four entropy priors in the image reconstruction of CCERT.

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.

Fast absolute 3D CGO-based electrical impedance tomography on experimental tank data

Objective.To present the first 3D CGO-based absolute EIT reconstructions from experimental tank data.Approach.CGO-based methods for absolute EIT imaging are compared to traditional TV regularized non-linear least squares reconstruction methods. Additional robustness testing is performed by considering incorrect modeling of domain shape.Main Results.The CGO-based methods are fast, and show strong robustness to incorrect domain modeling comparable to classic difference EIT imaging and fewer boundary artefacts than the TV regularized non-linear least squares reference reconstructions.Significance.This work is the first to demonstrate fully 3D CGO-based absolute EIT reconstruction on experimental data and also compares to TV-regularized absolute reconstruction. The speed (1-5 s) and quality of the reconstructions is encouraging for future work in absolute EIT.

Multi-Defect Detection in Additively Manufactured Lattice Structures Using 3D Electrical Resistance Tomography

Cellular lattice structures possess high strength-to-weight ratios suitable for advanced lightweight engineering applications. However, their quality and mechanical performance can degrade because of defects introduced during manufacturing or in-service. Their complexity and small length scale features make defects difficult to detect using conventional nondestructive evaluation methods. Here we propose a current injection-based method, electrical resistance tomography (ERT), that can be used to detect damaged struts in conductive cellular lattice structures with their intrinsic electromechanical properties. The reconstructed conductivity distributions from ERT can reveal the severity and location of damaged struts without having to probe each strut. However, the low central sensitivity of ERT may result in image artifacts and inaccurate localization of damaged struts. To address this issue, this study introduces an absolute, high throughput, conductivity reconstruction algorithm for 3D ERT. The algorithm incorporates a strut-based normalized sensitivity map to compensate for lower interior sensitivity and suppresses reconstruction artifacts. Numerical simulations and experiments on fabricated representative cellular lattice structures were performed to verify the ability of ERT to quantitatively identify single and multiple damaged struts. The improved performance of this method compared with classical ERT was observed, based on greatly decreased imaging and reconstructed value errors.

Case-Specific Focal Sensor Design for Cardiac Electrical Impedance Tomography

Electrical impedance tomography (EIT) is a non-invasive detection technology that uses the electrical response value at the boundary of an observation field to image the conductivity changes in an area. When EIT is applied to the thoracic cavity of the human body, the conductivity change caused by the heartbeat will be concentrated in a sub-region of the thoracic cavity, that is, the heart region. In order to improve the spatial resolution of the target region, two sensor optimization methods based on conformal mapping theory were proposed in this study. The effectiveness of the proposed method was verified by simulation and phantom experiment. The qualitative analysis and quantitative index evaluation of the reconstructed image showed that the optimized model could achieve higher imaging accuracy of the heart region compared with the standard sensor. The reconstruction results could effectively reflect the periodic diastolic and systolic movements of the heart and had a better ability to recognize the position of the heart in the thoracic cavity.

Improved resolution of D-bar images of ventilation using a Schur complement property and an anatomical atlas

BACKGROUND

Electrical impedance tomography (EIT) is a nonionizing imaging technique for real-time imaging of ventilation of patients with respiratory distress. Cross-sectional dynamic images are formed by reconstructing the conductivity distribution from measured voltage data arising from applied alternating currents on electrodes placed circumferentially around the chest. Since the conductivity of lung tissue depends on air content, blood flow, and the presence of pathology, the dynamic images provide regional information about ventilation, pulsatile perfusion, and abnormalities. However, due to the ill-posedness of the inverse conductivity problem, EIT images have a coarse spatial resolution. One method of improving the resolution is to include prior information in the reconstruction.

PURPOSE

In this work, we propose a technique in which a statistical prior built from an anatomical atlas is used to postprocess EIT reconstructions of human chest data. The effectiveness of the method is demonstrated on data from two patients with cystic fibrosis.

METHODS

A direct reconstruction algorithm known as the D-bar method was used to compute a two-dimensional reconstruction of the conductivity distribution in the plane of the electrodes. Reconstructions using one step in an iterative (regularized) Newton's method were also computed for comparison. An anatomical atlas consisting of 1589 synthetic EIT images computed from X-ray computed tomography (CT) scans of 74 adult male subjects was computed for use as a statistical prior. The resolution of the D-bar images was then improved by maximizing the conditional probability density function of an image that is consistent with the a priori information and the statistical model. A new method to evaluate the accuracy of the EIT images using CT scans of the imaged patient as ground truth is presented. The novel approach is tested on data from two patients with cystic fibrosis.

RESULTS AND CONCLUSIONS

The D-bar images resulted in better structural similarity index measures (SSIM) and multiscale (MS) SSIM measures for both subjects using the mask or amplitude evaluation approach than the one-step (regularized) Newton's method. Further improvement was achieved using the Schur complement (SC) approach, with MS-SSIM values of 0.718 and 0.682 using SC evaluated with the mask and amplitude approach, respectively, for Patient 1, and MS-SSIM values of 0.726 and 0.692 using SC evaluated with the mask and amplitude approach, respectively, for Patient 2. The results from applying an anatomical atlas and statistical prior to EIT data from two patients with cystic fibrosis suggest that the spatial resolution of the EIT image can be improved to reveal pathology that may be difficult to discern in the original EIT image. The novel metric of evaluation is consistent with the appearance of improved spatial resolution and provides a new way to evaluate the accuracy of EIT reconstructions when a CT scan is available.

Optimization of Critical Parameters of Deep Learning for Electrical Resistivity Tomography to Identifying Hydrate

As a new energy source, gas hydrates have attracted worldwide attention, but their exploration and development face enormous challenges. Thus, it has become increasingly crucial to identify hydrate distribution accurately. Electrical resistivity tomography (ERT) can be used to detect the distribution of hydrate deposits. An ERT inversion network (ERTInvNet) based on a deep neural network (DNN) is proposed, with strong learning and memory capabilities to solve the ERT nonlinear inversion problem. 160,000 samples about hydrate distribution are generated by numerical simulation, of which 10% are used for testing. The impact of different deep learning parameters (such as loss function, activation function, and optimizer) on the performance of ERT inversion is investigated to obtain a more accurate hydrate distribution. When the Logcosh loss function is enabled in ERTInvNet, the average correlation coefficient (CC) and relative error (RE) of all samples in the test sets are 0.9511 and 0.1098. The results generated by Logcosh are better than MSE, MAE, and Huber. ERTInvNet with Selu activation function can better learn the nonlinear relationship between voltage and resistivity. Its average CC and RE of all samples in the test set are 0.9449 and 0.2301, the best choices for Relu, Selu, Leaky_Relu, and Softplus. Compared with Adadelta, Adagrad, and Aadmax, Adam has the best performance in ERTInvNet with the optimizer. Its average CC and RE of all samples in the test set are 0.9449 and 0.2301, respectively. By optimizing the critical parameters of deep learning, the accuracy of ERT in identifying hydrate distribution is improved.

Experimental Investigation into Three-Dimensional Spatial Distribution of the Fracture-Filling Hydrate by Electrical Property of Hydrate-Bearing Sediments

As a future clean energy resource, the exploration and exploitation of natural gas hydrate are favorable for solving the energy crisis and improving environmental pollution. Detecting the spatial distribution of natural gas hydrate in the reservoir is of great importance in natural gas hydrate exploration and exploitation. Fracture-filling hydrate, one of the most common types of gas hydrate, usually appears as a massive or layered accumulation below the seafloor. This paper aims to detect the spatial distribution variation of fracture-filling hydrate in sediments using the electrical property in the laboratory. Massive hydrate and layered hydrate are formed in the electrical resistivity tomography device with a cylindrical array. Based on the electrical resistivity tomography data during the hydrate formation process, the three-dimensional resistivity images of the massive hydrate and layered hydrate are established by using finite element forward, Gauss–Newton inversion, and inverse distance weighted interpolation. Massive hydrate is easier to identify than layered hydrate because of the big difference between the massive hydrate area and surrounding sediments. The diffusion of salt ions in sediments makes the boundary of massive hydrate and layered hydrate change with hydrate formation. The average resistivity values of massive hydrate (50 Ω⋅m) and layered hydrate (1.4 Ω⋅m) differ by an order of magnitude due to the difference in the morphology of the fracture. Compared with the theoretical resistivity, it is found that the resistivity change of layered hydrate is in accordance with the change tendency of the theoretical value. The formation characteristic of massive hydrate is mainly affected by the pore water distribution and pore microstructure of hydrate. The hydrate formation does not necessarily cause the increase in resistivity, but the increase of resistivity must be due to the formation of hydrate. The decrease of resistivity in fine-grains is not obvious due to the cation adsorption of clay particles. These results provide a feasible approach to characterizing the resistivity and growth characteristics of fracture-filling hydrate reservoirs and provide support for the in-situ visual detection of fracture-filling hydrate.

Adversarial Resolution Enhancement for Electrical Capacitance Tomography Image Reconstruction

High-quality image reconstruction is essential for many electrical capacitance tomography (CT) applications. Raw capacitance measurements are used in the literature to generate low-resolution images. However, such low-resolution images are not sufficient for proper functionality of most systems. In this paper, we propose a novel adversarial resolution enhancement (ARE-ECT) model to reconstruct high-resolution images of inner distributions based on low-quality initial images, which are generated from the capacitance measurements. The proposed model uses a UNet as the generator of a conditional generative adversarial network (CGAN). The generator’s input is set to the low-resolution image rather than the typical random input signal. Additionally, the CGAN is conditioned by the input low-resolution image itself. For evaluation purposes, a massive ECT dataset of 320 K synthetic image–measurement pairs was created. This dataset is used for training, validating, and testing the proposed model. New flow patterns, which are not exposed to the model during the training phase, are used to evaluate the feasibility and generalization ability of the ARE-ECT model. The superiority of ARE-ECT, in the efficient generation of more accurate ECT images than traditional and other deep learning-based image reconstruction algorithms, is proved by the evaluation results. The ARE-ECT model achieved an average image correlation coefficient of more than 98.8% and an average relative image error about 0.1%.

A fast Tikhonov regularization method based on homotopic mapping for electrical resistance tomography

Electrical resistance tomography (ERT) is considered a novel sensing technique for monitoring conductivity distribution. Image reconstruction of ERT is an ill-posed inverse problem. In this paper, an improved regularization reconstruction method is presented to solve this issue. We adopted homotopic mapping to choose the regularization parameter of the iterative Tikhonov algorithm. The standard normal distribution function was used to continuously adjust the regularization parameter. Subsequently, the resultant image vector was deployed as the initial value of the iterative Tikhonov algorithm to improve the image quality. Finally, the improved method was combined with a projection algorithm based on the Krylov subspace, which was also effective in reducing the computational time. Both simulation and experimental results indicated that the new algorithm could improve the real-time performance and imaging quality.

Adaptively Regularized Bases-Expansion Subspace Optimization Methods for Electrical Impedance Tomography

OBJECTIVE

In this work, to deal with the difficulties in choosing regularization weighting parameters and low spatial resolution problems in difference electrical impedance tomography (EIT), we propose two adaptively regularized bases-expansion subspace optimization methods (AR-BE-SOMs).

METHODS

Firstly, an adaptive L1-norm based total variation (TV) regularization is introduced under the framework of BE-SOM. Secondly, besides the additive regularization, an adaptive weighted L2-norm multiplicative regularization is further proposed. The regularized objective functions are optimized by conjugate gradient method, where the unknowns in both methods are update alternatively between induced contrast current (ICC) and conductivity domain.

CONCLUSION

Both numerical and experimental tests are conducted to validate the proposed methods, where AR-BE-SOMs show better edge-preserving, anti-noise performance, lower relative errors, and higher structure similarity indexes than BE-SOM.

SIGNIFICANCE

Unlike the common regularization techniques in EIT, the proposed regularization factors can be obtained adaptively during the optimization process. More importantly, ARBE-SOMs perform well in reconstructions of some challenging geometry with sharp corners such as the heart and lung phantoms, deformation phantoms, triangles and even rectangles. It is expected that the proposed AR-BE-SOMs will find their applications for high-quality lung health monitoring and other clinical applications.

A Rotational Invariant Neural Network for Electrical Impedance Tomography Imaging without Reference Voltage: RF-REIM-NET

Background: Electrical Impedance Tomography (EIT) is a radiation-free technique for image reconstruction. However, as the inverse problem of EIT is non-linear and ill-posed, the reconstruction of sharp conductivity images poses a major problem. With the emergence of artificial neural networks (ANN), their application in EIT has recently gained interest. Methodology: We propose an ANN that can solve the inverse problem without the presence of a reference voltage. At the end of the ANN, we reused the dense layers multiple times, considering that the EIT exhibits rotational symmetries in a circular domain. To avoid bias in training data, the conductivity range used in the simulations was greater than expected in measurements. We also propose a new method that creates new data samples from existing training data. Results: We show that our ANN is more robust with respect to noise compared with the analytical Gauss–Newton approach. The reconstruction results for EIT phantom tank measurements are also clearer, as ringing artefacts are less pronounced. To evaluate the performance of the ANN under real-world conditions, we perform reconstructions on an experimental pig study with computed tomography for comparison. Conclusions: Our proposed ANN can reconstruct EIT images without the need of a reference voltage.

Robust imaging using electrical impedance tomography: review of current tools

Electrical impedance tomography (EIT) is a medical imaging technique with many advantages and great potential for development in the coming years. Currently, some limitations of EIT are related to the ill-posed nature of the problem. These limitations are translated on a practical level by a lack of genericity of the developed tools. In this paper, the main robust data acquisition and processing tools for EIT proposed in the scientific literature are presented. Their relevance and potential to improve the robustness of EIT are analysed, in order to conclude on the feasibility of a robust EIT tool capable of providing resistivity or difference of resistivity mapping in a wide range of applications. In particular, it is shown that certain measurement acquisition tools and algorithms, such as faulty electrode detection algorithm or particular electrode designs, can ensure the quality of the acquisition in many circumstances. Many algorithms, aiming at processing acquired data, are also described and allow to overcome certain difficulties such as an error in the knowledge of the position of the boundaries or the poor conditioning of the inverse problem. They have a strong potential to faithfully reconstruct a quality image in the presence of disturbances such as noise or boundary modelling error.

A High Accuracy Voltage Approximation Model Based on Object-oriented Sensitivity Matrix Estimation (OO-SME Model) in Electrical Impedance Tomography

The image reconstruction in electrical impedance tomography (EIT) has low accuracy due to the approximation error between the measured voltage change and the approximated voltage change, from which the object cannot be accurately reconstructed and quantitatively evaluated. A voltage approximation model based on object-oriented sensitivity matrix estimation (OO-SME model) is proposed to reconstruct the image with high accuracy. In the OO-SME model, a sensitivity matrix of the object-field is estimated, and the sensitivity matrix change from the background-field to the object-field is estimated to optimize the approximated voltage change, from which the approximation error is eliminated to improve the reconstruction accuracy. Against the existing linear and nonlinear models, the approximation error in the OO-SME model is eliminated, thus an image with higher accuracy is reconstructed. The simulation shows that the OO-SME model reconstructs a more accurate image than the existing models for quantitative evaluation. The relative accuracy (RA) of reconstructed conductivity is increased up to 83.98% on average. The experiment of lean meat mass evaluation shows that the RA of lean meat mass is increased from 7.70% with the linear model to 54.60% with the OO-SME model. It is concluded that the OO-SME model reconstructs a more accurate image to evaluate the object quantitatively than the existing models.

A Point-Matching Method of Moment with Sparse Bayesian Learning Applied and Evaluated in Dynamic Lung Electrical Impedance Tomography

Dynamic lung imaging is a major application of Electrical Impedance Tomography (EIT) due to EIT's exceptional temporal resolution, low cost and absence of radiation. EIT however lacks in spatial resolution and the image reconstruction is very sensitive to mismatches between the actual object's and the reconstruction domain's geometries, as well as to the signal noise. The non-linear nature of the reconstruction problem may also be a concern, since the lungs' significant conductivity changes due to inhalation and exhalation. In this paper, a recently introduced method of moment is combined with a sparse Bayesian learning approach to address the non-linearity issue, provide robustness to the reconstruction problem and reduce image artefacts. To evaluate the proposed methodology, we construct three CT-based time-variant 3D thoracic structures including the basic thoracic tissues and considering 5 different breath states from end-expiration to end-inspiration. The Graz consensus reconstruction algorithm for EIT (GREIT), the correlation coefficient (CC), the root mean square error (RMSE) and the full-reference (FR) metrics are applied for the image quality assessment. Qualitative and quantitative comparison with traditional and more advanced reconstruction techniques reveals that the proposed method shows improved performance in the majority of cases and metrics. Finally, the approach is applied to single-breath online in-vivo data to qualitatively verify its applicability.

ConcrEITS: An Electrical Impedance Interrogator for Concrete Damage Detection Using Self-Sensing Repairs

Concrete infrastructure requires continuous monitoring to ensure any new damage or repair failures are detected promptly. A cost-effective combination of monitoring and maintenance would be highly beneficial in the rehabilitation of existing infrastructure. Alkali-activated materials have been used as concrete repairs and as sensing elements for temperature, moisture, and chlorides. However, damage detection using self-sensing repairs has yet to be demonstrated, and commercial interrogation solutions are expensive. Here, we present the design of a low-cost tomographic impedance interrogator, denoted the “ConcrEITS”, capable of crack detection and location in concrete using conductive repair patches. Results show that for pure material blocks ConcrEITS is capable of measuring 4-probe impedance with a root mean square error of ±5.4% when compared to a commercially available device. For tomographic measurements, ConcrEITS is able to detect and locate cracks in patches adhered to small concrete beam samples undergoing 4-point bending. In all six samples tested, crack locations were clearly identified by the contour images gained from tomographic reconstruction. Overall, this system shows promise as a cost-effective combined solution for monitoring and maintenance of concrete infrastructure. We believe further up-scaled testing should follow this research before implementing the technology in a field trial.

3D ELECTRICAL IMPEDANCE TOMOGRAPHY RECONSTRUCTIONS FROM SIMULATED ELECTRODE DATA USING DIRECT INVERSION texp AND CALDERÓN METHODS

The first numerical implementation of a t ^exp method in 3D using simulated electrode data is presented. Results are compared to Calderón's method as well as more common TV and smoothness regularization-based methods. The t ^exp method for EIT is based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. In 2D, t ^exp methods have shown great promise for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D t ^exp and Calderón methods are demonstrated to provide comparable quality to their 2D counterparts, and hold promise for real-time reconstructions due to their fast, non-optimized, computational cost.

Calderón's Method with a Spatial Prior for 2-D EIT Imaging of Ventilation and Perfusion

Bedside imaging of ventilation and perfusion is a leading application of 2-D medical electrical impedance tomography (EIT), in which dynamic cross-sectional images of the torso are created by numerically solving the inverse problem of computing the conductivity from voltage measurements arising on electrodes due to currents applied on electrodes on the surface. Methods of reconstruction may be direct or iterative. Calderón’s method is a direct reconstruction method based on complex geometrical optics solutions to Laplace’s equation capable of providing real-time reconstructions in a region of interest. In this paper, the importance of accurate modeling of the electrode location on the body is demonstrated on simulated and experimental data, and a method of including a priori spatial information in dynamic human subject data is presented. The results of accurate electrode modeling and a spatial prior are shown to improve detection of inhomogeneities not included in the prior and to improve the resolution of ventilation and perfusion images in a human subject.

An efficient Point-Matching Method-of-Moments for 2D and 3D Electrical Impedance Tomography Using Radial Basis functions

AbstractObjective: The inverse problem of computing conductivity distributions in 2D and 3D objects interrogated by low frequency electrical signals, which is called Electrical Impedance Tomography (EIT), is treated using a Method-of-Moment technique.

METHODS

A Point-Matching-Method-of-Moment technique is used to formulate a global integral equation solver. Radial Basis Functions are adopted to express the conductivity distribution. Single-step quadratic-norm (L2) and iterative total variation (L1) regularization techniques are exploited to solve the inverse problem.

RESULTS

Simulation and experimental tests on a circular reconstruction domain show satisfactory performance in deriving conductivity distribution, achieving a Correlation Coefficient (CC) up to 0:863 for 70 dB voltage SNR and 0:842 for 40 dB voltage SNR. The proposed methodology with L2-norm regularization provided better results than traditional iterative Gauss-Newtons approach, whereas with L1-norm regularization it showed promising performance. Moreover, 3D reconstructions on a cylindrical cavity demonstrated superior results near the electrodes planes compared to those of the conventional linearized approach. Finally, application to EIT medical data for dynamic lung imaging successfully revealed the breath-cycle conductivity changes.

CONCLUSION

The results show that the proposed method can be effective for both 2D and 3D EIT and applicable to many applications.

SIGNIFICANCE

Strong conductivity variations are successfully tackled with a very good Correlation Coefficient. In contrast to conventional EIT solutions based on weak-form and linearization on small conductivity changes, the proposed method requires only one step to converge with L2-norm regularization. The proposed method with L1-norm regularization also achieves good reconstruction quality with a low number of iterations.

Evaluation of Thoracic Equivalent Multiport Circuits Using an Electrical Impedance Tomography Hardware Simulation Interface

Electrical impedance tomography is a low-cost, safe, and high temporal resolution medical imaging modality which finds extensive application in real-time thoracic impedance imaging. Thoracic impedance changes can reveal important information about the physiological condition of patients’ lungs. In this way, electrical impedance tomography can be a valuable tool for monitoring patients. However, this technique is very sensitive to measurement noise or possible minor signal errors, coming from either the hardware, the electrodes, or even particular biological signals. Thus, the design of a good performance electrical impedance tomography hardware setup which properly interacts with the tissue examined is both an essential and a challenging concept. In this paper, we adopt an extensive simulation approach, which combines the system’s analogue and digital hardware, along with equivalent circuits of 3D finite element models that represent thoracic cavities. Each thoracic finite element model is created in MATLAB based on existing CT images, while the tissues’ conductivity and permittivity values for a selected frequency are acquired from a database using Python. The model is transferred to a multiport RLC network, embedded in the system’s hardware which is simulated at LT SPICE. The voltage output data are transferred to MATLAB where the electrical impedance tomography signal sampling and digital processing is also simulated. Finally, image reconstructions are performed in MATLAB, using the EIDORS library tool and considering the signal noise levels and different electrode and signal sampling configurations (ADC bits, sampling frequency, number of taps).

Fusing electrical and elasticity imaging

Electrical and elasticity imaging are promising modalities for a suite of different applications, including medical tomography, non-destructive testing and structural health monitoring. These emerging modalities are capable of providing remote, non-invasive and low-cost opportunities. Unfortunately, both modalities are severely ill-posed nonlinear inverse problems, susceptive to noise and modelling errors. Nevertheless, the ability to incorporate complimentary datasets obtained simultaneously offers mutually beneficial information. By fusing electrical and elastic modalities as a joint problem, we are afforded the possibility to stabilize the inversion process via the utilization of auxiliary information from both modalities as well as joint structural operators. In this study, we will discuss a possible approach to combine electrical and elasticity imaging in a joint reconstruction problem giving rise to novel multi-modality applications for use in both medical and structural engineering. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

In-vivoviscoelastic properties estimation in subcutaneous adipose tissue by integration of poroviscoelastic-mass transport model (pve-MTM) into wearable electrical impedance tomography (w-EIT)

In-vivoviscoelastic properties have been estimated in human subcutaneous adipose tissue (SAT) by integration of poroviscoelastic-mass transport model (pve-MTM) into wearable electrical impedance tomography (w-EIT) under the influence of external compressive pressure-P.Thepve-MTM predicts the ion concentration distributioncmod(t)by coupling the poroviscoelastic and mass transport model to describe the hydrodynamics, rheology, and transport phenomena inside SAT. Thew-EIT measures the time-difference conductivity distribution∆γ(t)in SAT resulted from the ion transport. Based on the integration, the two viscoelastic properties which are viscoelastic shear modulus of SATGvand relaxation time of SATτvare estimated by applying an iterative curve-fitting between the normalized average ion concentration distributioncˆmod(t)predicted frompve-MTM and the experimental normalized average ion concentration distributioncˆexp(t)derived fromw-EIT. Thein-vivoexperiments were conducted by applying external compressive pressure-Pon human calf boundary to induce interstitial fluid flow and ion movement in SAT. As a result, the value ofGvwas range from 4.9-6.3 kPa and the value ofτvwas range from 27.50-38.5 s with the value of average goodness-of-fit curve fittingR² > 0.76. These values ofGvandτvwere compared to the human and animal tissue from the literature in order to verify this method. The results frompve-MTM provide evidence thatGvandτvplay a role in the predicted value ofcˆmod.

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.

A deep neural network for estimating the bladder boundary using electrical impedance tomography

OBJECTIVE

Accurate bladder size estimation is an important clinical parameter that assists physicians, enabling them to provide better treatment for patients who are suffering from urinary incontinence. Electrical impedance tomography (EIT) is a non-invasive medical imaging method that estimates organ boundaries assuming that the electrical conductivity values of the background, bladder, and adjacent tissues inside the pelvic domain are known a priori. However, the performance of a traditional EIT inverse algorithm such as the modified Newton-Raphson (mNR) for shape estimation exhibits severe convergence problems as it heavily depends on the initial guess and often fails to estimate complex boundaries that require greater numbers of Fourier coefficients to approximate the boundary shape. Therefore, in this study a deep neural network (DNN) is introduced to estimate the urinary bladder boundary inside the pelvic domain.

APPROACH

We designed a five-layer DNN which was trained with a dataset of 15 subjects that had different pelvic boundaries, bladder shapes, and conductivity. The boundary voltage measurements of the pelvic domain are defined as input and the corresponding Fourier coefficients that describe the bladder boundary as output data. To evaluate the DNN, we tested with three different sizes of urinary bladder.

MAIN RESULTS

Numerical simulations and phantom experiments were performed to validate the performance of the proposed DNN model. The proposed DNN algorithm is compared with the radial basis function (RBF) and mNR method for bladder shape estimation. The results show that the DNN has a low root mean square error for estimated boundary coefficients and better estimation of bladder size when compared to the mNR and RBF.

SIGNIFICANCE

We apply the first DNN algorithm to estimate the complex boundaries such as the urinary bladder using EIT. Our work provides a novel efficient EIT inverse solver to estimate the bladder boundary and size accurately. The proposed DNN algorithm has advantages in that it is simple to implement, and has better accuracy and fast estimation.

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.

A second order Calderón's method with a correction term and a priori information

Calderón's method is a direct linearized reconstruction method for the inverse conductivity problem with the attribute that it can provide absolute images of both conductivity and permittivity with no need for forward modeling. In this work, an explicit relationship between Calderón's method and the D-bar method is provided, facilitating a "higher-order" Calderón's method in which a correction term is included, derived from the relationship to the D-bar method. Furthermore, a method of including a spatial prior is provided. These advances are demonstrated on simulated data and on tank data collected with the ACE1 EIT system.

Cardiac eigen imaging: a novel method to isolate cardiac activity in thoracic electrical impedance tomography

OBJECTIVE

As the global burden of cardiovascular disease increases, proactive cardiovascular healthcare by means of accurate, precise, continuous, and non-invasive monitoring is becoming crucial. However, no current device is able to provide cardiac hemodynamic monitoring with the aforementioned criterion. Electrical impedance tomography (EIT) is an inexpensive, non-invasive imaging modality that can provide real-time images of internal conductivity distributions that describe physiological activity. This work explores and compares a standard approach of regular cardiac gated averaging (RCGA) and a newly developed method, cardiac eigen-imaging (CEI), based on the singular value decomposition (SVD) to isolate cardiac activity in thoracic EIT.

APPROACH

EIT and heart-rate (HR) data were collected from 20 heart-failure patients preceding echocardiography. Features from RCGA and CEI images were correlated with stroke volume (SV) from echocardiography and image reconstruction parameters were optimized using leave-one-out (LOO) cross-validation.

MAIN RESULTS

CEI per-pixel-based features achieved a Pearson correlation coefficient of 0.80 with SV relative to 0.72 with RCGA. CEI had 33 high-correlating pixels while RCGA had 8. High-correlating pixels tend to concentrate in the right-ventricle (RV) when referenced to a general chest model.

SIGNIFICANCE

While both RCGA and CEI images had high-correlating pixels, CEI had higher correlations, a larger number of high-correlating pixels, and unlike RCGA is not dependent on the quality of the HR data collected. The observed performance of the CEI approach represents a promising step forward for EIT-based cardiac monitoring in either clinical or ambulatory settings.

Data preprocessing methods for electrical impedance tomography: a review

OBJECTIVE

Electrical impedance tomography (EIT) is a promising measurement technique in applications, especially in industrial monitoring and clinical diagnosis. However, two major drawbacks exist that limit the spatial resolution of reconstructed EIT images, i.e. the 'soft field' effect and the ill-posed problem. In recent years, apart from the development of reconstruction algorithms, some preprocessing methods for measured data or sensitivity maps have also been proposed to reduce these negative effects. It is necessary to find the optimal preprocessing method for various EIT reconstruction algorithms.

APPROACH

In this paper, seven typical data preprocessing methods for EIT are reviewed. The image qualities obtained using these methods are evaluated and compared in simulations, and their applicable ranges and combination effects are summarized.

MAIN RESULTS

The results show that all the reviewed methods can enhance the quality of EIT reconstructed images to different extents, and there is an optimal one under any given reconstruction algorithm. In addition, most of the reviewed methods do not work well when using the Tikhonov regularization algorithm.

SIGNIFICANCE

This paper introduces the preprocessing method to EIT, and the quality of reconstructed images obtained using these methods is evaluated through simulations. The results can provide a reference for practical applications.

A Review on Electrical Impedance Tomography Spectroscopy

Electrical Impedance Tomography Spectroscopy (EITS) enables the reconstruction of material distributions inside an object based on the frequency-dependent characteristics of different substances. In this paper, we present a review of EITS focusing on physical principles of the technology, sensor geometries, existing measurement systems, reconstruction algorithms, and image representation methods. In addition, a novel imaging method is proposed which could fill some of the gaps found in the literature. As an example of an application, EITS of ice and water mixtures is used.

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.

Neural network-based supervised descent method for 2D electrical impedance tomography

OBJECTIVE

In this work, we study the application of the neural network-based supervised descent method (NN-SDM) for 2D electrical impedance tomography.

APPROACH

The NN-SDM contains two stages: offline training and online prediction. In the offline stage, neural networks are iteratively applied to learn a sequence of descent directions for minimizing the objective function, where the training data set is generated in advance according to prior information or historical data. In the online stage, the trained neural networks are directly used to predict the descent directions.

MAIN RESULTS

Numerical and experimental results are reported to assess the efficiency and accuracy of the NN-SDM for both model-based and pixel-based inversions. In addition, the performance of the NN-SDM is compared with the linear SDM (LSDM), an end-to-end neural network (E2E-NN) and the Gauss-Newton (GN) method. The results demonstrate that the NN-SDM achieves faster convergence than the LSDM and GN method, and achieves a stronger generalization ability than the E2E-NN.

SIGNIFICANCE

The NN-SDM combines the strong non-linear fitting ability of the neural network and good generalization capability of the supervised descent method (SDM), which also provides good flexibility to incorporate prior information and accelerates the convergence of iteration.

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.

Optimal similarity norm for electrical tomography based on Bregman divergence

Electrical Tomography (ET) is an advanced visualization technique, which can reconstruct all targets in an investigated field based on boundary measurements. Since the spatial resolution in the ET process can be greatly affected by the selected similarity norm, different norms may result in different ET time and spatial resolutions. In the tomographic applications nowadays, Bregman divergence (BD) has attracted increasing attention. BDs are a family of generalized similarity norm, and they can measure the similarity/difference between any two targets more accurately. Specifically, the mostly used similarity norm in the ET process (e.g., L₂-norm) is only a special case of the BD family. As the key step of applying BD to the ET process, an execution method is proposed in this paper, together with the selection criteria for the optimal norm in the BD family. Simulations and experiments were conducted, and the results show that the use of an optimal BD can effectively improve the spatial resolution of an ET image.

DYNAMIC OPTIMIZED PRIORS FOR D-BAR RECONSTRUCTIONS OF HUMAN VENTILATION USING ELECTRICAL IMPEDANCE TOMOGRAPHY

A method of including dynamic spatial priors in the 2-D D-bar reconstruction algorithm is presented for use on time-difference reconstructions of human subject thoracic data. The conductivity values for the prior are updated at each frame in the reconstruction using an optimization method applied to the scattering transform. The updates of the dynamic spatial priors are guided by a principle component analysis of the data to determine the timepoint in the ventilatory (or cardiac) cycle. The effectiveness of the method is demonstrated on human subject ventilatory data.

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.

A theoretical study on real time monitoring of single cell mitosis with micro electrical impedance tomography

Real time monitoring of cell division, mitosis, at the single cell level, has value for many biomedical applications; such as developing optimal cancer treatments that target the cell division process. The goal of this theoretical study is to explore the feasibility of using Micro Electrical Impedance Tomography (MEIT) for real time monitoring of mitosis in a single cell, through imaging. MEIT employs a micro (single cell) scale electrode cage with electrodes placed around the cell. The electrodes deliver subsensory current and the consequential voltages on the electrodes are measured. An inverse image reconstruction algorithm uses the electric data from the electrodes to generate a map of electrical conductivity distribution in the chamber, which is the image. EIT is a well-known medical imaging technology that is simple to use but lacks good resolution. Therefore, it is not a-priori obvious that EIT has sufficient resolution to monitor single cell mitosis. To accomplish the goal of this study we have developed a mathematical model of MEIT of single cell mitosis, in which an in silico experiment provided the data for the MEIT image reconstruction. This theoretical study shows that MEIT can detect the outlines of the dividing cell during the various stages of mitosis (metaphase, anaphase and telophase) and, therefore, has potential as a technology for real time monitoring of single cell mitosis.

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.

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.

Capacitively Coupled Electrical Impedance Tomography for Brain Imaging

Electrical impedance tomography (EIT) is considered as a potential candidate for brain stroke imaging due to its compactness and potential use in bedside and emergency settings. The electrode-skin contact impedance and low conductivity of skull pose some practical challenges to the EIT head imaging. This paper studies the application of capacitively coupled electrical impedance tomography (CCEIT) in brain imaging for the first time. CCEIT is a new contactless EIT technique which uses voltage excitation without direct contact with the skin, as oppose to directly injecting the current to the skin in EIT. Because the safety issue of a new technique should be strictly treated, simulation work based on a simplified head model was carried out to investigate the safety aspects of CCEIT. By comparing with the standard EIT excited by a typical safe current level used in brain imaging, the safe excitation reference of CCEIT is obtained. This is done by comparing the maximum level of internal electrical field (internal current density) of EIT and that of CCEIT. Simulation results provide useful knowledge of excitation signal level of CCEIT and also show a critical comparison with traditional EIT. Practical experiments were carried out with a 12-electrode CCEIT phantom, saline, and carrot samples. Experimental results show the feasibility and potential of CCEIT for stroke imaging. In this paper, the anomaly diameter resolution is 10 mm (1/18 of the phantom diameter), which indicates that small-volume stroke could be detected. This is achieved by a low excitation voltage of 1 V, showing the possibility of even better performance when higher but yet safe level of excitation voltages is used.

Mapping the conductivity of graphene with Electrical Resistance Tomography

Electronic applications of large-area graphene films require rapid and accurate methods to map their electrical properties. Here we present the first electrical resistance tomography (ERT) measurements on large-area graphene samples, obtained with a dedicated measurement setup and reconstruction software. The outcome of an ERT measurement is a map of the graphene electrical conductivity. The same setup allows to perform van der Pauw (vdP) measurements of the average conductivity. We characterised the electrical conductivity of chemical-vapour deposited graphene samples by performing ERT, vdP and scanning terahertz time-domain spectroscopy (TDS), the last one by means of a commercial instrument. The measurement results are compared and discussed, showing the potential of ERT as an accurate and reliable technique for the electrical characterization of graphene samples.