Three-dimensional electrical impedance tomography based on the complete electrode model

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

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

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

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

An EIT image reconstruction method based on DenseNet with multi-scale convolution

Electrical impedance tomography (EIT) is an imaging technique that non-invasively acquires the electrical conductivity distribution within a field. The ill-posed and nonlinear nature of the image reconstruction process results in lower quality of the obtained images. To solve this problem, an EIT image reconstruction method based on DenseNet with multi-scale convolution named MS-DenseNet is proposed. In the proposed method, three different multi-scale convolutional dense blocks are incorporated to replace the conventional dense blocks; they are placed in parallel to improve the generalization ability of the network. The connection layer between dense blocks adopts a hybrid pooling structure, which reduces the loss of information in the traditional pooling process. A learning rate setting achieves reduction in two stages and optimizes the fitting ability of the network. The input of the constructed network is the boundary voltage data, and the output is the conductivity distribution of the imaging area. The network was trained and tested on a simulated dataset, and it was further tested using actual measurement data. The images reconstructed via this method were evaluated by employing root mean square error, structural similarity index measure, mean absolute error and image correlation coefficient in comparison with conventional DenseNet and Gauss-Newton. The results show that the method improves the artifact and edge blur problems, achieves higher values on the image metrics and improves the EIT image quality.

Regularization Solver Guided FISTA for Electrical Impedance Tomography

Electrical impedance tomography (EIT) is non-destructive monitoring technology that can visualize the conductivity distribution in the observed area. The inverse problem for imaging is characterized by a serious nonlinear and ill-posed nature, which leads to the low spatial resolution of the reconstructions. The iterative algorithm is an effective method to deal with the imaging inverse problem. However, the existing iterative imaging methods have some drawbacks, such as random and subjective initial parameter setting, very time consuming in vast iterations and shape blurring with less high-order information, etc. To solve these problems, this paper proposes a novel fast convergent iteration method for solving the inverse problem and designs an initial guess method based on an adaptive regularization parameter adjustment. This method is named the Regularization Solver Guided Fast Iterative Shrinkage Threshold Algorithm (RS-FISTA). The iterative solution process under the L1-norm regular constraint is derived in the LASSO problem. Meanwhile, the Nesterov accelerator is introduced to accelerate the gradient optimization race in the ISTA method. In order to make the initial guess contain more prior information and be independent of subjective factors such as human experience, a new adaptive regularization weight coefficient selection method is introduced into the initial conjecture of the FISTA iteration as it contains more accurate prior information of the conductivity distribution. The RS-FISTA method is compared with the methods of Landweber, CG, NOSER, Newton-Raphson, ISTA and FISTA, six different distributions with their optimal parameters. The SSIM, RMSE and PSNR of RS-FISTA methods are 0.7253, 3.44 and 37.55, respectively. In the performance test of convergence, the evaluation metrics of this method are relatively stable at 30 iterations. This shows that the proposed method not only has better visualization, but also has fast convergence. It is verified that the RS-FISTA algorithm is the better algorithm for EIT reconstruction from both simulation and physical experiments.

Design of electrical impedance spectroscopy sensing surgical drill using computational modelling and experimental validation

Electrical Impedance Spectroscopy (EIS) sensing surgical instruments could provide valuable and real-time feedback to surgeons about hidden tissue boundaries, therefore reducing the risk of iatrogenic injuries. In this paper, we present an EIS sensing surgical drill as an example instrument and introduce a strategy to optimize the mono-polar electrode geometry using a finite element method (FEM)-based computational model and experimental validation. An empirical contact impedance model and an adaptive mesh refinement protocol were developed to accurately preserve the behaviour of sensing electrodes as they approach high impedance boundaries. Specifically, experiments with drill-bit, cylinder, and conical geometries suggested a 15%-35% increase in resistance as the sensing electrode approached a high impedance boundary. Simulations achieved a maximum mean experiment-to-simulation mismatch of +1.7% for the drill-bit and +/-11% range for other electrode geometries. The simulations preserved the increase in resistance behaviour near the high impedance boundary. This highly accurate simulation framework allows us a mechanism for optimizing sensor geometry without costly experimental evaluation.

Characteristics and topic trends on electrical impedance tomography hardware publications

Objective: Electrical impedance tomography (EIT) is a technique to measure electrical properties of tissue. With the progress of modern integrated circuits and microchips, EIT instrumentation becomes an active research area to improve all aspects of device performance. Plenty of studies on EIT hardware have been presented in prestigious journals. This study explores publications on EIT hardware to identify the developing hotspots and trends.

Method: Publications covering EIT hardware on the Web of Science Core Collection (WoSCC) database from 1989 to 2021 were collected for bibliometric analysis. CiteSpace and VOS viewer were used to study the characteristics of the publications.

Main results: A total of 592 publications were analyzed, showing that the number of annual publications steadily increased. China, England, and South Korea were the most prolific countries on EIT hardware publications with productive native institutions and authors. Research topics spread out in “bio-electrical impedance imaging”, “hardware optimization”, “algorithms” and “clinical applications” (e.g., tissue, lung, brain, and oncology). Hardware research in “pulmonary” and “hemodynamic” applications focused on monitoring and were represented by silhouette recognition and dynamic imaging while research in “tumor and tissue” and “brain” applications focused on diagnosis and were represented by optimization of precision. Electrode development was a research focus through the years. Imaging precision and bioavailability of hardware optimization may be the future trend.

Conclusion: Overall, system performance, particularly in the areas of system bandwidth and precision in applications may be the future directions of hardware research.

Optimal Implementation Parameters of a Nonlinear Electrical Impedance Tomography Method Using the Complete Electrode Model

This study discusses a nonlinear electrical impedance tomography (EIT) technique under different analysis conditions to propose its optimal implementation parameters. The forward problem for calculating electric potential is defined by the complete electrode model. The inverse problem for reconstructing the target electrical conductivity profile is presented based on a partial-differential-equation-constrained optimization approach. The electrical conductivity profile is iteratively updated by solving the Karush-Kuhn-Tucker optimality conditions and using the conjugate gradient method with an inexact line search. Various analysis conditions such as regularization scheme, number of electrodes, current input patterns, and electrode arrangement were set differently, and the corresponding results were compared. It was found from this study that the proposed EIT method yielded appropriate inversion results with various parameter settings, and the optimal implementation parameters of the EIT method are presented. This study is expected to expand the utility and applicability of EIT for the non-destructive evaluation of structures.

Majorization–Minimization Total Variation Solution Methods for Electrical Impedance Tomography

Inverse problems arise in many areas of science and engineering, such as geophysics, biology, and medical imaging. One of the main imaging modalities that have seen a huge increase in recent years is the noninvasive, nonionizing, and radiation-free imaging technique of electrical impedance tomography (EIT). Other advantages of such a technique are the low cost and ubiquitousness. An imaging technique is used to recover the internal conductivity of a body using measurements from electrodes from the body’s surface. The standard procedure is to obtain measurements by placing electrodes in the body and measuring conductivity inside the object. A current with low frequency is applied on the electrodes below a threshold, rendering the technique harmless for the body, especially when applied to living organisms. As with many inverse problems, EIT suffers from ill-posedness, i.e., the reconstruction of internal conductivity is a severely ill-posed inverse problem and typically yields a poor-quality solution. Moreover, the desired solution has step changes in the electrical properties that are typically challenging to be reconstructed by traditional smoothing regularization methods. To counter this difficulty, one solves a regularized problem that is better conditioned than the original problem by imposing constraints on the regularization term. The main contribution of this work is to develop a general ℓp regularized method with total variation to solve the nonlinear EIT problem through a iteratively reweighted majorization–minimization strategy combined with the Gauss–Newton approach. The main idea is to majorize the linearized EIT problem at each iteration and minimize through a quadratic tangent majorant. Simulated numerical examples from complete electrode model illustrate the effectiveness of our approach.

Experimental Characterization Techniques for Solid-Liquid Slurry Flows in Pipelines: A Review

In industrial environments, having instrumentation able to attain fast, accurate, and autonomous measurements is pivotal to understanding the dynamics of liquid and particles during transport. Ideally, these instruments, consisting of either probes or sensors, should be robust, fast, and unintrusive, i.e., not cause interference on the very flows being monitored, and require minimal maintenance. Beyond monitoring, the process knowledge gained through real time inspection allows teams to make informed technical decisions based on particle behavior, i.e., settling of particles causing pipe wear and clustering or blockages that can damage the unit or cause shutdowns, both of which with economical drawbacks. The purpose of this review is to examine experimental measurement techniques used to characterize physical properties and operational parameters of solid-liquid slurry flows, focusing on non-ionizing radiation methods. With this text the intent is not to provide an exhaustive examination of each individual technique but rather an overview on the most pertinent types of instrumentation, which will be presented, in addition to application examples from the literature, while directing the reader for pertinent seminal and review papers for a more in-depth analysis.

Retrieval of the conductivity spectrum of tissuesin vitrowith novel multimodal tomography

OBJECTIVE

Imaging of tissue engineered three-dimensional (3D) specimens is challenging due to their thickness. We propose a novel multimodal imaging technique to obtain multi-physical 3D images and the electrical conductivity spectrum of tissue engineered specimensin vitro.

APPROACH

We combine simultaneous recording of rotational multifrequency electrical impedance tomography (R-mfEIT) with optical projection tomography (OPT). Structural details of the specimen provided by OPT are used here as geometrical priors for R-mfEIT.

MAIN RESULTS

This data fusion enables accurate retrieval of the conductivity spectrum of the specimen. We demonstrate experimentally the feasibility of the proposed technique using a potato phantom, adipose and liver tissues, and stem cells in biomaterial spheroids. The results indicate that the proposed technique can distinguish between viable and dead tissues and detect the presence of stem cells.

SIGNIFICANCE

This technique is expected to become a valuable tool for monitoring tissue engineered specimens' growth and viabilityin vitro.

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.

A Three Dimensional Calderon-Based Method for EIT on the Cylindrical Geometry

OBJECTIVE

Electrical impedance tomography (EIT) is an imaging modality in which voltage data arising from currents applied on the boundary are used to reconstruct the conductivity distribution in the interior. This paper provides a novel direct (noniterative) 3-D reconstruction algorithm for EIT in the cylindrical geometry.

METHODS

The algorithm is based on Calderón's method [Calderón, 1980], and is implemented for data collected on two or four rows of electrodes on the boundary of a cylinder.

RESULTS

The effectiveness of the method to localize inhomogeneities in the plane of the electrodes and in the z-direction is demonstrated on simulated and experimental data.

CONCLUSIONS AND SIGNIFICANCE

The results from simulated and experimental data show that the method is effective for distinguishing in-plane and nearby out-of-plane inhomogeneities with good spatial resolution in the vertical z direction with computational efficiency.

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.

Sparse image reconstruction of intracerebral hemorrhage with electrical impedance tomography

Purpose: Intracerebral hemorrhage (ICH) is a common disease that is known for its high morbidity, high mortality, and high disability. The fast and accurate detection of ICH is essential for the acute care of patients. Electrical impedance tomography (EIT) offers an alternative with which pathological tissues can be detected by reconstructing conductivity variation. Nevertheless, the sensitive field of EIT is greatly affected by medium distribution, which is referred to as soft-field effect. In addition, the image reconstruction is a severely ill-posed inverse problem. Furthermore, due to the low conductivity of skull, the sensitivity in the sensing area is extremely low. Therefore, the reconstruction of ICH with EIT is great challenge. Approach: A sparse image reconstruction method is proposed for EIT to visualize the conductivity variation caused by ICH. To reduce the impact of soft-field effect, the normalization of sensitivity distribution is conducted for monolayer and three-layer head model. In addition, a constrained sparse L 1 -norm minimization model is developed for the image reconstruction. Augmented Lagrangian multiplier method and alternating minimization scheme are adopted to solve the proposed model. Results: The results show that the sensitivity in the sensing area is largely enhanced. Numerical simulation based on monolayer head model and three-layer head model is respectively carried out. Both the reconstructed images and the quantitative evaluations show that image reconstructed by the proposed method is much better than that reconstructed by traditional Tikhonov method. The reconstructions evaluated under the impact of noise also show that the proposed method has superior anti-noise performance. Conclusions: With the proposed method, the quality of the reconstructed image would be greatly improved. It is an effective approach for imaging ICH with EIT technique.

Imaging Conductivity Changes in Monolayer Graphene Using Electrical Impedance Tomography

Recently, graphene has gained a lot of attention in the electronic industry due to its unique properties and has paved the way for realizing novel devices in the field of electronics. For the development of new device applications, it is necessary to grow large wafer-sized monolayer graphene samples. Among the methods to synthesize large graphene films, chemical vapor deposition (CVD) is one of the promising and common techniques. However, during the growth and transfer of the CVD graphene monolayer, defects such as wrinkles, cracks, and holes appear on the graphene surface. These defects can influence the electrical properties and it is of interest to know the quality of graphene samples non-destructively. Electrical impedance tomography (EIT) can be applied as an alternate method to determine conductivity distribution non-destructively. The EIT inverse problem of reconstructing conductivity is highly non-linear and is heavily dependent on measurement accuracy and modeling errors related to an accurate knowledge of electrode location, contact resistances, the exact outer boundary of the graphene wafer, etc. In practical situations, it is difficult to eliminate these modeling errors as complete knowledge of the electrode contact impedance and outer domain boundary is not fully available, and this leads to an undesirable solution. In this paper, a difference imaging approach is proposed to estimate the conductivity change of graphene with respect to the reference distribution from the data sets collected before and after the change. The estimated conductivity change can be used to locate the defects on the graphene surface caused due to the CVD transfer process or environment interaction. Numerical and experimental results with graphene sample of size 2.5 × 2.5 cm are performed to determine the change in conductivity distribution and the results show that the proposed difference imaging approach handles the modeling errors and estimates the conductivity distribution with good accuracy.

Supervised Descent Learning for Thoracic Electrical Impedance Tomography

OBJECTIVE

The absolute image reconstruction problem of electrical impedance tomography (EIT) is ill-posed. Traditional methods usually solve a nonlinear least squares problem with some kind of regularization. These methods suffer from low accuracy, poor anti-noise performance, and long computation time. Besides, the integration of a priori information is not very flexible. This work tries to solve EIT inverse problem using a machine learning algorithm for the application of thorax imaging.

METHODS

We developed the supervised descent learning EIT (SDL-EIT) inversion algorithm based on the idea of supervised descent method (SDM). The algorithm approximates the mapping from measured data to the conductivity image by a series of descent directions learned from training samples. We designed a training data set in which the thorax contour, and some general structure of lungs, and heart are embedded. The algorithm is implemented in both two-, and three-dimensional cases, and is evaluated using synthetic, and measured thoracic data. Results, and conclusion: For synthetic data, SDL-EIT shows better accuracy, and anti-noise performance compared with traditional Gauss-Newton inversion (GNI) method. For measured data, the result of SDL-EIT is reasonable compared with computed tomography (CT) scan image.

SIGNIFICANCE

Using SDL-EIT, prior information can be easily integrated through the specifically designed training data set, and the image reconstruction process can be accelerated. The algorithm is effective in inverting measured thoracic data. It is a potential algorithm for human thorax imaging.

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.

Large-Area Carbon Nanotube-Based Flexible Composites for Ultra-Wide Range Pressure Sensing and Spatial Pressure Mapping

Flexible pressure sensors are of broad interest for applications including human-machine interfaces, wearable electronics, and object/motion detection. However, complexities associated with constituent materials, fabrication processes, sensing mechanisms, and hardwiring often hinder the large-scale applications of using high performance pressure sensors reported in the literature. Here we demonstrate a large-area, highly flexible, conformable, and mechanically robust pressure sensor using a silicone elastomer with an embedded nonwoven textile carrier coated with carbon nanotubes. The selected silicone polymer allows through-thickness deformability of the sensor while the high modulus textile carrier ensures in-plane stiffness and stability. The sensor has an initial electrical conductivity of 4.4 ± 0.38 S/m and is fabricated using a straightforward dip coating and polymer infusion process and can be easily scaled-up for large-scale applications. On the basis of its hierarchical composite structure, this piezoresistive pressure sensor possesses extremely high resilience under compression, a repeatable monotonic positive pressure correlation, and an ultrawide elastic working range (5.5 ± 0.5 MPa) that can be segmentally linearized. A true two-dimensional modality for spatial pressure mapping is realized by utilizing electrical impedance tomography (EIT) and demonstrated to yield conductivity maps that can estimate the location, shape, and amplitude of both localized and distributed pressure with simple contact areas.

Unification of optimal targeting methods in transcranial electrical stimulation

One of the major questions in high-density transcranial electrical stimulation (TES) is: given a region of interest (ROI) and electric current limits for safety, how much current should be delivered by each electrode for optimal targeting of the ROI? Several solutions, apparently unrelated, have been independently proposed depending on how "optimality" is defined and on how this optimization problem is stated mathematically. The least squares (LS), weighted LS (WLS), or reciprocity-based approaches are the simplest ones and have closed-form solutions. An extended optimization problem can be stated as follows: maximize the directional intensity at the ROI, limit the electric fields at the non-ROI, and constrain total injected current and current per electrode for safety. This problem requires iterative convex or linear optimization solvers. We theoretically prove in this work that the LS, WLS and reciprocity-based closed-form solutions are specific solutions to the extended directional maximization optimization problem. Moreover, the LS/WLS and reciprocity-based solutions are the two extreme cases of the intensity-focality trade-off, emerging under variation of a unique parameter of the extended directional maximization problem, the imposed constraint to the electric fields at the non-ROI. We validate and illustrate these findings with simulations on an atlas head model. The unified approach we present here allows a better understanding of the nature of the TES optimization problem and helps in the development of advanced and more effective targeting strategies.

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.

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.

A Review of Electrical Impedance Tomography in Lung Applications: Theory and Algorithms for Absolute Images

Electrical Impedance Tomography (EIT) is under fast development, the present paper is a review of some procedures that are contributing to improve spatial resolution and material properties accuracy, admitivitty or impeditivity accuracy. A review of EIT medical applications is presented and they were classified into three broad categories: ARDS patients, obstructive lung diseases and perioperative patients. The use of absolute EIT image may enable the assessment of absolute lung volume, which may significantly improve the clinical acceptance of EIT. The Control Theory, the State Observers more specifically, have a developed theory that can be used for the design and operation of EIT devices. Electrode placement, current injection strategy and electrode electric potential measurements strategy should maximize the number of observable and controllable directions of the state vector space. A non-linear stochastic state observer, the Unscented Kalman Filter, is used directly for the reconstruction of absolute EIT images. Historically, difference images were explored first since they are more stable in the presence of modelling errors. Absolute images require more detailed models of contact impedance, stray capacitance and properly refined finite element mesh where the electric potential gradient is high. Parallelization of the forward program computation is necessary since the solution of the inverse problem often requires frequent solutions of the forward problem. Several reconstruction algorithms benefit by the Bayesian inverse problem approach and the concept of prior information. Anatomic and physiologic information are used to form the prior information. An already tested methodology is presented to build the prior probability density function using an ensemble of CT scans and in vivo impedance measurements. Eight absolute EIT image algorithms are presented.

Focusing Sensor Design for Open Electrical Impedance Tomography Based on Shape Conformal Transformation

Electrical Impedance Tomography (EIT) is a non-invasive detection method to image the conductivity changes inside an observation region by using the electrical measurements at the boundary of this region. In some applications of EIT, the observation domain is infinite and is only accessible from one side, which leads to the so-called open EIT (OEIT) problem. Compared with conventional EIT problems, the observation region in OEIT can only be measured from limited projection directions, which makes high resolution imaging much more challenging. To improve the imaging quality of OEIT, a focusing sensor design strategy is proposed based on shape conformal theory. The conformal bijection is used to map a standard EIT sensor defined at a unit circle to a focusing OEIT sensor defined at an upper half plane. A series of numerical and experimental testes are conducted. Compared with the traditional sensor structure, the proposed focusing sensor has higher spatial resolution at the near-electrode region and is good at distinguishing multi-inclusions which are close to each other.

AN EXPERIMENTAL ANALYSIS AND VALIDATION OF ELECTRICAL IMPEDANCE TOMOGRAPHY TECHNIQUE FOR MEDICAL OR INDUSTRIAL APPLICATION

Electrical impedance tomography is a recently established technique by which impedance of an object (medical or nonmedical applications) is measured data from the surface of the object, and a numerically simulated reconstruction of the object internal shape of the image can be obtained. This imaging technique based on boundary or surface voltage is measured when the different current pattern is injected into it. For current pulse, we are creating a voltage controlled current source, which is based on the different RC circuits, according to current amplitude and frequency values. The current source used in inject the current pulse of the various phantoms. The current position and measuring voltage is controlled by the created control unit or programmable system on chip (PSOC) of the proposed EIT system. After that image reconstruction of the cross-sectional image of resistivity requires sufficient data collection from used phantoms, which is based on finite element method (FEM) method and Tikhonov regularization method with helps of graphical user interface (GUI) on MatLab. The objective of the GUI was to produce an image (2D/3D), impedance distribution graph, and the FEM mesh model according to used electrode combinations from the various phantoms. EIT system has a great potential for imaging modality, is non-invasive, radiation-free, and inexpensive for medical applications.

Three-Dimensional Electrical Impedance Tomography With Multiplicative Regularization

OBJECTIVE

The multiplicative regularization scheme is applied to three-dimensional electrical impedance tomography (EIT) image reconstruction problem to alleviate its ill-posedness.

METHODS

A cost functional is constructed by multiplying the data misfit functional with the regularization functional. The regularization functional is based on a weighted L²-norm with the edge-preserving characteristic. Gauss-Newton method is used to minimize the cost functional. A method based on the discrete exterior calculus (DEC) theory is introduced to formulate the discrete gradient and divergence operators related to the regularization on unstructured meshes.

RESULTS

Both numerical and experimental results show good reconstruction accuracy and anti-noise performance of the algorithm. The reconstruction results using human thoracic data show promising applications in thorax imaging.

CONCLUSION

The multiplicative regularization can be applied to EIT image reconstruction with promising applications in thorax imaging.

SIGNIFICANCE

In the multiplicative regularization scheme, there is no need to set an artificial regularization parameter in the cost functional. This helps to reduce the workload related to choosing a regularization parameter which may require expertise and many numerical experiments. The DEC-based method provides a systematic and rigorous way to formulate operators on unstructured meshes. This may help EIT image reconstructions using regularizations imposing structural or spatial constraints.

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

This paper presents a novel difference imaging approach based on the recently developed parametric level set (PLS) method for estimating the change in a target conductivity from electrical impedance tomography measurements. As in conventional difference imaging, the reconstruction of conductivity change is based on data sets measured from the surface of a body before and after the change. The key feature of the proposed approach is that the conductivity change to be reconstructed is assumed to be piecewise constant, while the geometry of the anomaly is represented by a shape-based PLS function employing Gaussian radial basis functions (GRBFs). The representation of the PLS function by using GRBF provides flexibility in describing a large class of shapes with fewer unknowns. This feature is advantageous, as it may significantly reduce the overall number of unknowns, improve the condition number of the inverse problem, and enhance the computational efficiency of the technique. To evaluate the proposed PLS-based difference imaging approach, results obtained via simulation, phantom study, and in vivo pig data are studied. We find that the proposed approach tolerates more modeling errors and leads to a significant improvement in image quality compared with the conventional linear approach.

Image Reconstruction in Electrical Impedance Tomography Based on Structure-Aware Sparse Bayesian Learning

Electrical impedance tomography (EIT) is developed to investigate the internal conductivity changes of an object through a series of boundary electrodes, and has become increasingly attractive in a broad spectrum of applications. However, the design of optimal tomography image reconstruction algorithms has not achieved the adequate level of progress and matureness. In this paper, we propose an efficient and high-resolution EIT image reconstruction method in the framework of sparse Bayesian learning. Significant performance improvement is achieved by imposing structure-aware priors on the learning process to incorporate the prior knowledge that practical conductivity distribution maps exhibit clustered sparsity and intra-cluster continuity. The proposed method not only achieves high-resolution estimation and preserves the shape information even in low signal-to-noise ratio scenarios but also avoids the time-consuming parameter tuning process. The effectiveness of the proposed algorithm is validated through comparisons with state-of-the-art techniques using extensive numerical simulation and phantom experiment results.

A Parametric Level Set Method for Electrical Impedance Tomography

This paper presents an image reconstruction method based on parametric level set (PLS) method using electrical impedance tomography. The conductivity to be reconstructed was assumed to be piecewise constant and the geometry of the anomaly was represented by a shape-based PLS function, which we represent using Gaussian radial basis functions (GRBF). The representation of the PLS function significantly reduces the number of unknowns, and circumvents many difficulties that are associated with traditional level set (TLS) methods, such as regularization, re-initialization and use of signed distance function. PLS reconstruction results shown in this article are some of the first ones using experimental EIT data. The performance of the PLS method was tested with water tank data for two-phase visualization and with simulations which demonstrate the most popular biomedical application of EIT: lung imaging. In addition, robustness studies of the PLS method w.r.t width of the Gaussian function and GRBF centers were performed on simulated lung imaging data. The experimental and simulation results show that PLS method has significant improvement in image quality compared with the TLS reconstruction.

Reproducible 3D printed head tanks for electrical impedance tomography with realistic shape and conductivity distribution

OBJECTIVE

Electrical impedance tomography (EIT) has many promising applications in brain injury monitoring. To evaluate both instrumentation and reconstruction algorithms, experiments are first performed in head tanks. Existing methods, whilst accurate, produce a discontinuous conductivity, and are often made by hand, making it hard for other researchers to replicate.

APPROACH

We have developed a method for constructing head tanks directly in a 3D printer. Conductivity was controlled through perforations in the skull surface, which allow for saline to pass through. Varying the diameter of the holes allowed for the conductivity to be controlled with 3% error for the target conductivity range. Taking CT and MRI segmentations as a basis, this method was employed to create an adult tank with a continuous conductivity distribution, and a neonatal tank with fontanelles.

MAIN RESULTS

Using 3D scanning a geometric accuracy of 0.21 mm was recorded, equal to that of the precision of the 3D printer used. Differences of 6.1%  ±  6.4% (n  =  11 in 4 tanks) compared to simulations were recorded in c. 800 boundary voltages. This may be attributed to the morphology of the skulls increasing tortuosity effects and hole misalignment. Despite significant differences in errors between three repetitions of the neonatal tank, images of a realistic perturbation could still be reconstructed with different tanks used for the baseline and perturbation datasets.

SIGNIFICANCE

These phantoms can be reproduced by any researcher with access to a 'hobbyist' 3D printer in a matter of days. All design files have been released using an open source license to encourage reproduction and modification.

Absolute Reconstructions Using Rotational Electrical Impedance Tomography for Breast Cancer Imaging

A rotational Electrical Impedance Tomography (rEIT) methodology is described and shown to produce spatially accurate absolute reconstructions with improved image contrast and an improved ability to distinguish closely spaced inclusions compared to traditional EIT on data recorded from cylindrical and breast-shaped tanks. Rotations of the tank without altering the interior conductivity distribution are used to produce the rEIT data. Quantitatively, rEIT was able to distinguish two inclusions that were 1.5 cm closer together than traditional EIT could achieve for inclusions placed 2 to 3 cm from the center for the cylindrical tank, and rEIT was able to distinguish two tumor-like inclusions where traditional EIT could not reliably do so. Mathematical analysis showed that rEIT improves the number of stable singular vectors by up to 4.2 and 4.7 times than that of traditional EIT for the cylindrical and breast-shaped tanks, respectively, which is an indication of improved resolution. Direct investigations into measurements revealed minimum rotation angles that should yield data uncorrupted by noise. Two inverse approaches (one that inverts then fuses the data (I/DF) and one that fuses the data then inverts (DF/I)) and two mesh modeling approaches were considered. It was found that DF/I produces far better results compared to I/DF and a rotated-mesh approach produces further improvements. The ability to obtain improved absolute reconstructions using rEIT on a practical clinical scenario (breast-shaped tank experiment) is an important step towards using rEIT to improve previous EIT results in medical applications.

Efficient Simultaneous Reconstruction of Time-Varying Images and Electrode Contact Impedances in Electrical Impedance Tomography

OBJECTIVE

In electrical impedance tomography (EIT), we apply patterns of currents on a set of electrodes at the external boundary of an object, measure the resulting potentials at the electrodes, and, given the aggregate dataset, reconstruct the complex conductivity and permittivity within the object. It is possible to maximize sensitivity to internal conductivity changes by simultaneously applying currents and measuring potentials on all electrodes but this approach also maximizes sensitivity to changes in impedance at the interface.

METHODS

We have, therefore, developed algorithms to assess contact impedance changes at the interface as well as to efficiently and simultaneously reconstruct internal conductivity/permittivity changes within the body. We use simple linear algebraic manipulations, the generalized singular value decomposition, and a dual-mesh finite-element-based framework to reconstruct images in real time. We are also able to efficiently compute the linearized reconstruction for a wide range of regularization parameters and to compute both the generalized cross-validation parameter as well as the L-curve, objective approaches to determining the optimal regularization parameter, in a similarly efficient manner.

RESULTS

Results are shown using data from a normal subject and from a clinical intensive care unit patient, both acquired with the GE GENESIS prototype EIT system, demonstrating significantly reduced boundary artifacts due to electrode drift and motion artifact.

EIT image reconstruction based on a hybrid FE-EFG forward method and the complete-electrode model

This paper presents the application of the hybrid finite element-element free Galerkin (FE-EFG) method for the forward and inverse problems of electrical impedance tomography (EIT). The proposed method is based on the complete electrode model. Finite element (FE) and element-free Galerkin (EFG) methods are accurate numerical techniques. However, the FE technique has meshing task problems and the EFG method is computationally expensive. In this paper, the hybrid FE-EFG method is applied to take both advantages of FE and EFG methods, the complete electrode model of the forward problem is solved, and an iterative regularized Gauss-Newton method is adopted to solve the inverse problem. The proposed method is applied to compute Jacobian in the inverse problem. Utilizing 2D circular homogenous models, the numerical results are validated with analytical and experimental results and the performance of the hybrid FE-EFG method compared with the FE method is illustrated. Results of image reconstruction are presented for a human chest experimental phantom.

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

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

Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

This study proposes a method to improve performance of sparse recovery inverse solvers in 3D electrical impedance tomography (3D EIT), especially when the volume under study contains small-sized inclusions, e.g. 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum. Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously made by the quadratic solver. Finally, a sparse inverse solver is applied solely to the sampled finite elements, with the solution to the CS as its initial guess. The results show the great potential of the proposed CS-based sparse recovery in improving accuracy of sparse solution to the large-size 3D EIT.

An instrumental electrode model for solving EIT forward problems

An instrumental electrode model (IEM) capable of describing the performance of electrical impedance tomography (EIT) systems in the MHz frequency range has been proposed. Compared with the commonly used Complete Electrode Model (CEM), which assumes ideal front-end interfaces, the proposed model considers the effects of non-ideal components in the front-end circuits. This introduces an extra boundary condition in the forward model and offers a more accurate modelling for EIT systems. We have demonstrated its performance using simple geometry structures and compared the results with the CEM and full Maxwell methods. The IEM can provide a significantly more accurate approximation than the CEM in the MHz frequency range, where the full Maxwell methods are favoured over the quasi-static approximation. The improved electrode model will facilitate the future characterization and front-end design of real-world EIT systems.

A new head phantom with realistic shape and spatially varying skull resistivity distribution

Brain electrical impedance tomography (EIT) is an emerging method for monitoring brain injuries. To effectively evaluate brain EIT systems and reconstruction algorithms, we have developed a novel head phantom that features realistic anatomy and spatially varying skull resistivity. The head phantom was created with three layers, representing scalp, skull, and brain tissues. The fabrication process entailed 3-D printing of the anatomical geometry for mold creation followed by casting to ensure high geometrical precision and accuracy of the resistivity distribution. We evaluated the accuracy and stability of the phantom. Results showed that the head phantom achieved high geometric accuracy, accurate skull resistivity values, and good stability over time and in the frequency domain. Experimental impedance reconstructions performed using the head phantom and computer simulations were found to be consistent for the same perturbation object. In conclusion, this new phantom could provide a more accurate test platform for brain EIT research.

Toward microendoscopic electrical impedance tomography for intraoperative surgical margin assessment

No clinical protocols are routinely used to intraoperatively assess surgical margin status during prostate surgery. Instead, margins are evaluated through pathological assessment of the prostate following radical prostatectomy, when it is too late to provide additional surgical intervention. An intraoperative device potentially capable of assessing surgical margin status based on the electrical property contrast between benign and malignant prostate tissue has been developed. Specifically, a microendoscopic electrical impedance tomography (EIT) probe has been constructed to sense and image, at near millimeter resolution, the conductivity contrast within heterogeneous biological tissues with the goal of providing surgeons with real-time assessment of margin pathologies. This device consists of a ring of eight 0.6-mm diameter electrodes embedded in a 5-mm diameter probe tip to enable access through a 12-mm laparoscopic port. Experiments were performed to evaluate the volume of tissue sensed by the probe. The probe was also tested with inclusions in gelatin, as well as on a sample of porcine tissue with clearly defined regions of adipose and muscle. The probe's area of sensitivity consists of a circular area of 9.1 mm(2) and the maximum depth of sensitivity is approximately 1.5 mm. The probe is able to distinguish between high contrast muscle and adipose tissue on a sub-mm scale (∼500 μm). These preliminary results suggest that EIT is possible in a probe designed to fit within a 12-mm laparoscopic access port.