Electrical impedance tomography: regularized imaging and contrast detection

Noise-based correction for electrical impedance tomography

Objective.Noisy measurements frequently cause noisy and inaccurate images in impedance imaging. No post-processing technique exists to calculate the propagation of measurement noise and use this to suppress noise in the image. The objectives of this work were (1) to develop a post-processing method for noise-based correction (NBC) in impedance tomography, (2) to test whether NBC improves image quality in electrical impedance tomography (EIT), (3) to determine whether it is preferable to use correlated or uncorrelated noise for NBC, (4) to test whether NBC works within vivodata and (5) to test whether NBC is stable across model and perturbation geometries.Approach.EIT was performedin silicoin a 2D homogeneous circular domain and an anatomically realistic, heterogeneous 3D human head domain for four perturbations and 25 noise levels in each case. This was validated by performing EIT for four perturbations in a circular, saline tank in 2D as well as a human head-shaped saline tank with a realistic skull-like layer in 3D. Images were assessed on the error in the weighted spatial variance (WSV) with respect to the true, target image. The effect of NBC was also tested forin vivoEIT data of lung ventilation in a human thorax and cortical activity in a rat brain.Main results.On visual inspection, NBC maintained or increased image quality for all perturbations and noise levels in 2D and 3D, both experimentally andin silico. Analysis of the WSV showed that NBC significantly improved the WSV in nearly all cases. When the WSV was inferior with NBC, this was either visually imperceptible or a transformation between noisy reconstructions. Forin vivodata, NBC improved image quality in all cases and preserved the expected shape of the reconstructed perturbation.Significance.In practice, uncorrelated NBC performed better than correlated NBC and is recommended as a general-use post-processing technique in EIT.

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.

Non-invasive imaging of neural activity with magnetic detection electrical impedance tomography (MDEIT): a modelling study

Objectives.(1) Develop a computational pipeline for three-dimensional fast neural magnetic detection electrical impedance tomography (MDEIT), (2) determine whether constant current or constant voltage is preferable for MDEIT, (3) perform reconstructions of simulated neural activity in a human head model with realistic noise and compare MDEIT to EIT and (4) perform a two-dimensional study in a saline tank for MDEIT with optically pumped magnetometers (OPMs) and compare reconstruction algorithms.Approach.Forward modelling and image reconstruction were performed with a realistic model of a human head in three dimensions and at three noise levels for four perturbations representing neural activity. Images were compared using the error in the position and size of the reconstructed perturbations. Two-dimensional MDEIT was performed in a saline tank with a resistive perturbation and one OPM. Six reconstruction algorithms were compared using the error in the position and size of the reconstructed perturbations.Main results.A computational pipeline was developed in COMSOL Multiphysics, reducing the Jacobian calculation time from months to days. MDEIT reconstructed images with a lower reconstruction error than EIT with a mean difference of 7.0%, 5.5% and 11% for three noise cases representing current noise, reduced current source noise and reduced current source and magnetometer noise. A rank analysis concluded that the MDEIT Jacobian was less rank-deficient than the EIT Jacobian. Reconstructions of a phantom in a saline tank had a best reconstruction error of 13%, achieved using 0th-order Tikhonov regularisation with simulated noise-based correction.Significance.This study demonstrated that three-dimensional MDEIT for neural imaging is feasible and that MDEIT reconstructed superior images to EIT, which can be explained by the lesser rank deficiency of the MDEIT Jacobian. Reconstructions of a perturbation in a saline tank demonstrated a proof of principle for two-dimensional MDEIT with OPMs and identified the best reconstruction algorithm.

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

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

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.

An alternative excitation method for electrical impedance tomography

Electrical impedance tomography (EIT) can be utilized to image the conductivity distribution of material under test. The EIT measurements depend on the quality in the current injection and voltage measuring circuits. The current source plays a vital role in the EIT instruments. In most of the research studies, the push-pull current sources were employed for the source and sink signal generation. It usually requires frequent calibration to achieve proper functioning, especially for the sweeping frequency measurements. In this paper, an alternative excitation method has been proposed for simplifying the design of the current source in EIT instruments, which aims to achieve the performance of the push-pull current source by using a single-ended current source. It could offer the following advantages: (1) hardware simplification and (2) reduced requirements on current source calibration. The corrected measurements could be consistent with that using push-pull excitation, as confirmed by the numerical simulations. In addition, the reconstructed images have also been investigated to illustrate the effectiveness of the proposed method.

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.

Distributed Strain Monitoring Using Nanocomposite Paint Sensing Meshes

Strain measurements are vital for monitoring the load-bearing capacity and safety of structures. A common approach is to affix strain gages onto structural surfaces. On the other hand, most aerospace, automotive, civil, and mechanical structures are painted and coated, often with many layers, prior to their deployment. There is an opportunity to design smart and multifunctional paints that can be directly pre-applied onto structural surfaces to serve as a sensing layer among their other layers of functional paints. Therefore, the objective of this study was to design a strain-sensitive paint that can be used for structural monitoring. Carbon nanotubes (CNT) were dispersed in paint by high-speed shear mixing, while paint thinner was employed for adjusting the formulation's viscosity and nanomaterial concentration. The study started with the design and fabrication of the CNT-based paint. Then, the nanocomposite paint's electromechanical properties and its sensitivity to applied strains were characterized. Third, the nanocomposite paint was spray-coated onto patterned substrates to form "Sensing Meshes" for distributed strain monitoring. An electrical resistance tomography (ERT) measurement strategy and algorithm were utilized for reconstructing the conductivity distribution of the Sensing Meshes, where the magnitude of conductivity (or resistivity) corresponded to the magnitude of strain, while strain directionality was determined based on the strut direction in the mesh.

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.

Continuous Multi-DoF Wrist Kinematics Estimation Based on a Human-Machine Interface With Electrical-Impedance-Tomography

This study proposed a multiple degree-of-freedom (DoF) continuous wrist angle estimation approach based on an electrical impedance tomography (EIT) interface. The interface can inspect the spatial information of deep muscles with a soft elastic fabric sensing band, extending the measurement scope of the existing muscle-signal-based sensors. The designed estimation algorithm first extracted the mutual correlation of the EIT regions with a kernel function, and second used a regularization procedure to select the optimal coefficients. We evaluated the method with different features and regression models on 12 healthy subjects when they performed six basic wrist joint motions. The average root-mean-square error of the 3-DoF estimation task was 7.62°, and the average R² was 0.92. The results are comparable to state-of-the-art with sEMG signals in multi-DoF tasks. Future endeavors will be paid in this new direction to get more promising results.

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.

Feasibility of Temperature Control by Electrical Impedance Tomography in Hyperthermia

We present a simulation study investigating the feasibility of electrical impedance tomography (EIT) as a low cost, noninvasive technique for hyperthermia (HT) treatment monitoring and adaptation. Temperature rise in tissues leads to perfusion and tissue conductivity changes that can be reconstructed in 3D by EIT to noninvasively map temperature and perfusion. In this study, we developed reconstruction methods and investigated the achievable accuracy of EIT by simulating HT treatmentlike scenarios, using detailed anatomical models with heterogeneous conductivity distributions. The impact of the size and location of the heated region, the voltage measurement signal-to-noise ratio, and the reference model personalization and accuracy were studied. Results showed that by introducing an iterative reconstruction approach, combined with adaptive prior regions and tissue-dependent penalties, planning-based reference models, measurement-based reweighting, and physics-based constraints, it is possible to map conductivity-changes throughout the heated domain, with an accuracy of around 5% and cm-scale spatial resolution. An initial exploration of the use of multifrequency EIT to separate temperature and perfusion effects yielded promising results, indicating that temperature reconstruction accuracy can be in the order of 1 ∘C. Our results suggest that EIT can provide valuable real-time HT monitoring capabilities. Experimental confirmation in real-world conditions is the next step.

Development of an electrical impedance tomography set-up for the quantification of mineralization in biopolymer scaffolds

Objective. 3D cell cultures are becoming a fundamental resource forin-vitrostudies, as they mimic more closelyin-vivobehavior. The analysis of these constructs, however, generally rely on destructive techniques, that prevent the monitoring over time of the same construct, thus increasing the results variability and the resources needed for each experiment.Approach. In this work, we focus on mineralization, a crucial process during maturation of artificial bone models, and propose electrical impedance tomography (EIT) as an alternative non-destructive approach. In particular, we discuss the development of an integrated hardware/software system capable of acquiring experimental data from 3D scaffolds and reconstructing the corresponding conductivity maps. We also show how the same software can test how the measurement is affected by biological features such as scaffold shrinking during the culture.Main results. An initial validation, comprising the acquisition of both a non-conductive phantom and alginate/gelatin scaffolds with known calcium content will be presented, together with thein-silicostudy of a cell-induced mineralization process. This analysis will allow for an initial verification of the systems functionality while limiting the effects of biological variability due to cell number and activity.Significance. Our results show the potential of EIT for the non-destructive quantification of matrix mineralization in 3D scaffolds, and open to the possible long term monitoring of this fundamental hallmark of osteogenic differentiation in hybrid tissue engineered constructs.

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.

Review of Structural Health Monitoring Methods Regarding a Multi-Sensor Approach for Damage Assessment of Metal and Composite Structures

Structural health monitoring (SHM) is the continuous on-board monitoring of a structure's condition during operation by integrated systems of sensors. SHM is believed to have the potential to increase the safety of the structure while reducing its deadweight and downtime. Numerous SHM methods exist that allow the observation and assessment of different damages of different kinds of structures. Recently data fusion on different levels has been getting attention for joint damage evaluation by different SHM methods to achieve increased assessment accuracy and reliability. However, little attention is given to the question of which SHM methods are promising to combine. The current article addresses this issue by demonstrating the theoretical capabilities of a number of prominent SHM methods by comparing their fundamental physical models to the actual effects of damage on metal and composite structures. Furthermore, an overview of the state-of-the-art damage assessment concepts for different levels of SHM is given. As a result, dynamic SHM methods using ultrasonic waves and vibrations appear to be very powerful but suffer from their sensitivity to environmental influences. Combining such dynamic methods with static strain-based or conductivity-based methods and with additional sensors for environmental entities might yield a robust multi-sensor SHM approach. For demonstration, a potent system of sensors is defined and a possible joint data evaluation scheme for a multi-sensor SHM approach is presented.

Cardiac radiofrequency ablation tracking using electrical impedance tomography

There is a need for accessible high speed imaging of Radiofrequency (RF) cardiac electrosurgery to improve safety and efficacy of the ablation time course, where lesion information is critical to safety and efficacy but currently lacking in real time. In this paper, Electrical Impedance Tomography (EIT) using existing cardiac EP electrodes was optimised to confirm (1) that removal of measurements with low signal sensitivity leads to improved images and (2) that multiple signal thresholds are needed to track the lesion accurately over time. A novel ventricle-shaped gel phantom with realistic fluid flow to mimic blood flow, lung ventilation and myocardium conductivity was developed to study the capability and motivate transition to in-vivo measurements. When using 8 external (ECG) electrodes, 4 internal coronary sinus electrodes and 4 RF catheter-based electrodes, the optimal setup for sensitivity and dynamic tracking was 77 measurements within an error of 20%. Higher thresholds were more suitable for the earlier phase of the ablation when lesions are small while lower thresholds suited later phases. Patient-specific thresholds could be optimised in pre-surgical planning where detailed anatomical images are available. While the error reported in this initial study appears large, it is a major advance over the current situation for the cardiologist where no real-time lesion visualization is accessible in a regular EP suite/cath lab.

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.

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.

An on-line processing strategy for head movement interferences removal of dynamic brain electrical impedance tomography based on wavelet decomposition

BACKGROUND

Head movement interferences are a common problem during prolonged dynamic brain electrical impedance tomography (EIT) clinical monitoring. Head movement interferences mainly originate from body movements of patients and nursing procedures performed by medical staff, etc. These body movements will lead to variation in boundary voltage signals, which affects image reconstruction.

METHODS

This study employed a data preprocessing method based on wavelet decomposition to inhibit head movement interferences in brain EIT data. Mixed Gaussian models were applied to describe the distribution characteristics of brain EIT data. We identified head movement signal through the differences in distribution characteristics of corresponding wavelet decomposition coefficients between head movement artifacts and normal signals, and then managed the contaminated data with improved on-line wavelet processing methods.

RESULTS

To validate the efficacy of the method, simulated signal experiments and human data experiments were performed. In the simulation experiment, the simulated movement artifact was significantly reduced and data quality was improved with indicators' increase in PRD and correlation coefficient. Human data experiments demonstrated that this method effectively suppressed head movement in signals and reduce artifacts resulting from head movement artifacts in images.

CONCLUSION

In this paper, we proposed an on-line strategy to manage the head movement interferences from the brain EIT data based on the distribution characteristics of wavelet coefficients. Our strategy is capable of reducing the movement interference in the data and improving the reconstructed images. This work would improve the clinical practicability of brain EIT and contribute to its further promotion.

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.

Enhancing Sharp Features by Locally Relaxing Regularization for Reconstructed Images in Electrical Impedance Tomography

Image reconstruction in EIT is an inverse problem, which is ill posed and hence needs regularization. Regularization brings stability to reconstructed EIT image with respect to noise in the measured data. But this is at the cost of smoothening of sharp edges and high curvature details of shapes in the image, affecting the quality. We propose a novel iterative regularization method based on detection of probable location of the inclusion, for locally relaxing the regularization by appropriate amount, to overcome this problem. Local relaxation around inclusion allows reconstruction of its high curvature shape details or sharp features at the same time giving benefits of higher regularization in remaining areas of the image. The proposed method called DeTER is implemented using a small plug-in to EIDORS (Electrical Impedance and Diffused Optical Reconstruction Software) in a MATLAB environment. Parameters like CNR, correlation coefficients of shape descriptor functions and relative size of reconstructed targets have been computed to evaluate the effectiveness of the technique. The performance of DeTER is tested and verified on simulated data added with Gaussian noise for inclusions of different shapes. Both conducting and nonconducting inclusions are considered. The method is validated using open EIT data shared by 'Finnish inverse problem society' and also by reconstructing image of internal void of a papaya fruit from the data acquired by an EIT system developed in our laboratory. The reconstructed images corresponding to the open EIT data clearly show the shapes similar to original objects, with sharp edges and curvature details. The shapes obtained in the papaya image are shown to correspond to the actual void using shape descriptor function. The results demonstrate that the proposed method enhances the sharp features in the reconstructed image with few iterations without causing geometric distortions like smoothening or rounding of the edges.

Extended Joint Sparsity Reconstruction for Spatial and Temporal ERT Imaging

Electrical resistance tomography (ERT) is an imaging technique to recover the conductivity distribution with boundary measurements via attached electrodes. There are a wide range of applications using ERT for image reconstruction or parameter calculation due to high speed data collection, low cost, and the advantages of being non-invasive and portable. Although ERT is considered a high temporal resolution method, a temporally regularized method can greatly enhance such a temporal resolution compared to frame-by-frame reconstruction. In some of the cases, especially in the industrial applications, dynamic movement of an object is critical. In practice, it is desirable for monitoring and controlling the dynamic process. ERT can determine the spatial conductivity distribution based on previous work, and ERT potentially shows good performance in exploiting temporal information as well. Many ERT algorithms reconstruct images frame by frame, which is not optimal and would assume that the target is static during collection of each data frame, which is inconsistent with the real case. Although spatiotemporal-based algorithms can account for the temporal effect of dynamic movement and can generate better results, there is not that much work aimed at analyzing the performance in the time domain. In this paper, we discuss the performance of a novel spatiotemporal total variation (STTV) algorithm in both the spatial and temporal domain, and Temporal One-Step Tikhonov-based algorithms were also employed for comparison. The experimental results show that the STTV has a faster response time for temporal variation of the moving object. This robust time response can contribute to a much better control process which is the main aim of the new generation of process tomography systems.

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.

Ex Vivo Modeling of Perioperative Air Leaks in Porcine Lungs

OBJECTIVE

A novel ex vivo model is described to advance the understanding of prolonged air leaks, one of the most common postoperative complications following thoracic resection procedures.

METHODS

As an alternative to in vivo testing, an ex vivo model simulating the various physiologic environments experienced by an isolated lung during the perioperative period was designed and built. Isolated porcine lungs were perfused and ventilated during open chest and closed chest simulations, mimicking intra and postoperative ventilation conditions. To assess and validate system capabilities, nine porcine lungs were tested by creating a standardized injury to create an approximately 250 cc/min air leak. Air leak rates, physiologic ventilation, and perfusion parameters were continuously monitored, while gas transfer analysis was performed on selected lungs. Segmental ventilation was monitored using electrical impedance tomography.

RESULTS

The evaluated lungs produced flow-volume and pressure-volume loops that approximated standard clinical representations under positive (mechanical) and negative (physiological) pressure ventilation modalities. Leak rate was averaged across the ventilation phases, and sharp increases in leak rate were observed between positive and negative pressure phases, suggesting that differences or changes in ventilation mechanics may strongly influence leak development.

CONCLUSION

The successful design and validation of a novel ex vivo lung model was achieved. Model output paralleled clinical observations. Pressure modality may also play a significant role in air leak severity.

SIGNIFICANCE

This work provides a foundation for future studies aimed at increasing the understanding of air leaks to better inform means of mitigating the risk of air leaks under clinically relevant conditions.

Accuracy and reliability of noninvasive stroke volume monitoring via ECG-gated 3D electrical impedance tomography in healthy volunteers

Cardiac output (CO) and stroke volume (SV) are parameters of key clinical interest. Many techniques exist to measure CO and SV, but are either invasive or insufficiently accurate in clinical settings. Electrical impedance tomography (EIT) has been suggested as a noninvasive measure of SV, but inconsistent results have been reported. Our goal is to determine the accuracy and reliability of EIT-based SV measurements, and whether advanced image reconstruction approaches can help to improve the estimates. Data were collected on ten healthy volunteers undergoing postural changes and exercise. To overcome the sensitivity to heart displacement and thorax morphology reported in previous work, we used a 3D EIT configuration with 2 planes of 16 electrodes and subject-specific reconstruction models. Various EIT-derived SV estimates were compared to reference measurements derived from the oxygen uptake. Results revealed a dramatic impact of posture on the EIT images. Therefore, the analysis was restricted to measurements in supine position under controlled conditions (low noise and stable heart and lung regions). In these measurements, amplitudes of impedance changes in the heart and lung regions could successfully be derived from EIT using ECG gating. However, despite a subject-specific calibration the heart-related estimates showed an error of 0.0 ± 15.2 mL for absolute SV estimation. For trending of relative SV changes, a concordance rate of 80.9% and an angular error of -1.0 ± 23.0° were obtained. These performances are insufficient for most clinical uses. Similar conclusions were derived from lung-related estimates. Our findings indicate that the key difficulty in EIT-based SV monitoring is that purely amplitude-based features are strongly influenced by other factors (such as posture, electrode contact impedance and lung or heart conductivity). All the data of the present study are made publicly available for further investigations.

A novel post-processing scheme for two-dimensional electrical impedance tomography based on artificial neural networks

OBJECTIVE

Electrical Impedance Tomography (EIT) is a powerful non-invasive technique for imaging applications. The goal is to estimate the electrical properties of living tissues by measuring the potential at the boundary of the domain. Being safe with respect to patient health, non-invasive, and having no known hazards, EIT is an attractive and promising technology. However, it suffers from a particular technical difficulty, which consists of solving a nonlinear inverse problem in real time. Several nonlinear approaches have been proposed as a replacement for the linear solver, but in practice very few are capable of stable, high-quality, and real-time EIT imaging because of their very low robustness to errors and inaccurate modeling, or because they require considerable computational effort.

METHODS

In this paper, a post-processing technique based on an artificial neural network (ANN) is proposed to obtain a nonlinear solution to the inverse problem, starting from a linear solution. While common reconstruction methods based on ANNs estimate the solution directly from the measured data, the method proposed here enhances the solution obtained from a linear solver.

CONCLUSION

Applying a linear reconstruction algorithm before applying an ANN reduces the effects of noise and modeling errors. Hence, this approach significantly reduces the error associated with solving 2D inverse problems using machine-learning-based algorithms.

SIGNIFICANCE

This work presents radical enhancements in the stability of nonlinear methods for biomedical EIT applications.

Ventilation inhomogeneity in obstructive lung diseases measured by electrical impedance tomography: a simulation study

Electrical impedance tomography (EIT) has mostly been used in the Intensive Care Unit (ICU) to monitor ventilation distribution but is also promising for the diagnosis in spontaneously breathing patients with obstructive lung diseases. Beside tomographic images, several numerical measures have been proposed to quantitatively assess the lung state. In this study two common measures, the 'Global Inhomogeneity Index' and the 'Coefficient of Variation' were compared regarding their capability to reflect the severity of lung obstruction. A three-dimensional simulation model was used to simulate obstructed lungs, whereby images were reconstructed on a two-dimensional domain. Simulations revealed that minor obstructions are not adequately recognized in the reconstructed images and that obstruction above and below the electrode plane may result in misleading values of inhomogeneity measures. EIT measurements on several electrode planes are necessary to apply these measures in patients with obstructive lung diseases in a promising manner.

Primal-dual approach to optical tomography with discretized path integral with efficient formulations

We propose an efficient optical tomography with discretized path integral. We first introduce the primal-dual approach to solve the inverse problem formulated as a constraint optimization problem. Next, we develop efficient formulations for computing Jacobian and Hessian of the cost function of the constraint nonlinear optimization problem. Numerical experiments show that the proposed formulation is faster ([Formula: see text]) than the previous work with the log-barrier interior point method ([Formula: see text]) for the Shepp-Logan phantom with a grid size of [Formula: see text], while keeping the quality of the estimation results (root-mean-square error increasing by up to 12%).

A Versatile Noise Performance Metric for Electrical Impedance Tomography Algorithms

Electrical impedance tomography (EIT) is an emerging technology for real-time monitoring of patients under mechanical ventilation. EIT has the potential to offer continuous medical monitoring while being noninvasive, radiation free, and low cost. Due to their ill-posedness, image reconstruction typically uses regularization, which implies a hyperparameter controlling the tradeoff between noise rejection and resolution or other accuracies. In order to compare reconstruction algorithms, it is common to choose hyperparameter values such that the reconstructed images have equal noise performance (NP), i.e., the amount of measurement noise reflected in the images. For EIT many methods have been suggested, but none work well when the data originate from different measurement setups, such as for different electrode positions or measurement patterns. To address this issue, we propose a new NP metric based on the average signal-to-noise ratio in the image domain. The approach is validated for EIT using simulation experiments on a human thorax model and measurements on a resistor phantom. Results show that the approach is robust to the measurement configuration (i.e., number and position of electrodes, skip pattern) and the reconstruction algorithm used. We propose this novel approach as a way to select optimized measurement configurations and algorithms.

Lobe based image reconstruction in Electrical Impedance Tomography

PURPOSE

Electrical Impedance Tomography (EIT) is an imaging modality used to generate two-dimensional cross-sectional images representing impedance change in the thorax. The impedance of lung tissue changes with change in air content of the lungs; hence, EIT can be used to examine regional lung ventilation in patients with abnormal lungs. In lung EIT, electrodes are attached around the circumference of the thorax to inject small alternating currents and measure resulting voltages. In contrast to X-ray computed tomography (CT), EIT images do not depict a thorax slice of well defined thickness, but instead visualize a lens-shaped region around the electrode plane, which results from diffuse current propagation in the thorax. Usually, this is considered a drawback, since image interpretation is impeded if 'off-plane' conductivity changes are projected onto the reconstructed two-dimensional image. In this paper we describe an approach that takes advantage of current propagation below and above the electrode plane. The approach enables estimation of the individual conductivity change in each lung lobe from boundary voltage measurements. This could be used to monitor disease progression in patients with obstructive lung diseases, such as chronic obstructive pulmonary disease (COPD) or cystic fibrosis (CF) and to obtain a more comprehensive insight into the pathophysiology of the lung.

METHODS

Electrode voltages resulting from different conductivities in each lung lobe were simulated utilizing a realistic 3D finite element model (FEM) of the human thorax and the lungs. Overall 200 different patterns of conductivity change were simulated. A 'lobe reconstruction' algorithm was developed, applying patient-specific anatomical information in the reconstruction process. A standard EIT image reconstruction algorithm and the proposed 'lobe reconstruction' algorithm were used to estimate conductivity change in the lobes. The agreement between simulated and reconstructed conductivity change in particular lobes were compared using Bland-Altman plots, correlation plots and linear regression. To test the applicability of the approach in a realistic scenario, EIT measurements of a patient suffering from cystic fibrosis (CF) were carried out.

RESULTS

Conductivity changes in each lobe generate specific patterns of voltage change. These can be used to estimate the conductivity change in lobes from measured boundary voltage. The correlation coefficient between simulated and reconstructed conductivity change in particular lobes is r > 0.89 for all lobes. Unknown position of the electrode plane leads to over- or underestimation of reconstructed conductivity change. Slight mismatches (± 5% of the forward model height) between the actual position of the electrode plane and the position used in the reconstruction model lead to regression coefficients of 0.7 to 1.3 between simulated and reconstructed conductivity change in the lobes.

CONCLUSION

The presented approach enhances common reconstruction methods by providing information about anatomically assignable units and thus facilitates image interpretation, since impedance change and thus ventilation of each lobe is directly determined in the reconstructions.

Regional regularization method for ECT based on spectral transformation of Laplacian

Image reconstruction in electrical capacitance tomography is an ill-posed inverse problem, and regularization techniques are usually used to solve the problem for suppressing noise. An anisotropic regional regularization algorithm for electrical capacitance tomography is constructed using a novel approach called spectral transformation. Its function is derived and applied to the weighted gradient magnitude of the sensitivity of Laplacian as a regularization term. With the optimum regional regularizer, the a priori knowledge on the local nonlinearity degree of the forward map is incorporated into the proposed online reconstruction algorithm. Simulation experimentations were performed to verify the capability of the new regularization algorithm to reconstruct a superior quality image over two conventional Tikhonov regularization approaches. The advantage of the new algorithm for improving performance and reducing shape distortion is demonstrated with the experimental data.

Structural-functional lung imaging using a combined CT-EIT and a Discrete Cosine Transformation reconstruction method

Lung EIT is a functional imaging method that utilizes electrical currents to reconstruct images of conductivity changes inside the thorax. This technique is radiation free and applicable at the bedside, but lacks of spatial resolution compared to morphological imaging methods such as X-ray computed tomography (CT). In this article we describe an approach for EIT image reconstruction using morphologic information obtained from other structural imaging modalities. This leads to recon- structed images of lung ventilation that can easily be superimposed with structural CT or MRI images, which facilitates image interpretation. The approach is based on a Discrete Cosine Transformation (DCT) of an image of the considered transversal thorax slice. The use of DCT enables reduction of the dimensionality of the reconstruction and ensures that only conductivity changes of the lungs are reconstructed and displayed. The DCT based approach is well suited to fuse morphological image information with functional lung imaging at low computational costs. Results on simulated data indicate that this approach preserves the morphological structures of the lungs and avoids blurring of the solution. Images from patient measurements reveal the capabilities of the method and demonstrate benefits in possible applications.

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.

A comparison framework for temporal image reconstructions in electrical impedance tomography

Electrical impedance tomography (EIT) provides low-resolution images of internal conductivity distributions, but is able to achieve relatively high temporal resolutions. Most EIT image reconstruction algorithms do not explicitly account for the temporal constraints on the measurements or physiological processes under investigation. Instead, algorithms typically assume both that the conductivity distribution does not change during the acquisition of each EIT data frame, and that frames can be reconstructed independently, without consideration of the correlation between images. A failure to account for these temporal effects will result in aliasing-related artefacts in images. Several methods have been proposed to compensate for these effects, including interpolation of raw data, and reconstruction algorithms using Kalman and temporal filtering. However, no systematic work has been performed to understand the severity of the temporal artefacts nor the extent to which algorithms can account for them. We seek to address this need by developing a temporal comparison framework and figures of merit to assess the ability of reconstruction algorithms to account for temporal effects. Using this approach, we compare combinations of three reconstruction algorithms using three EIT data frame types: perfect, realistic and interpolated. The results show that, without accounting for temporal effects, artefacts are present in images for dynamic conductivity contrasts at frequencies 10-20 times slower than the frame rate. The proposed methods show some improvements in reducing these artefacts.

Functional validation and comparison framework for EIT lung imaging

INTRODUCTION

Electrical impedance tomography (EIT) is an emerging clinical tool for monitoring ventilation distribution in mechanically ventilated patients, for which many image reconstruction algorithms have been suggested. We propose an experimental framework to assess such algorithms with respect to their ability to correctly represent well-defined physiological changes. We defined a set of clinically relevant ventilation conditions and induced them experimentally in 8 pigs by controlling three ventilator settings (tidal volume, positive end-expiratory pressure and the fraction of inspired oxygen). In this way, large and discrete shifts in global and regional lung air content were elicited.

METHODS

We use the framework to compare twelve 2D EIT reconstruction algorithms, including backprojection (the original and still most frequently used algorithm), GREIT (a more recent consensus algorithm for lung imaging), truncated singular value decomposition (TSVD), several variants of the one-step Gauss-Newton approach and two iterative algorithms. We consider the effects of using a 3D finite element model, assuming non-uniform background conductivity, noise modeling, reconstructing for electrode movement, total variation (TV) reconstruction, robust error norms, smoothing priors, and using difference vs. normalized difference data.

RESULTS AND CONCLUSIONS

Our results indicate that, while variation in appearance of images reconstructed from the same data is not negligible, clinically relevant parameters do not vary considerably among the advanced algorithms. Among the analysed algorithms, several advanced algorithms perform well, while some others are significantly worse. Given its vintage and ad-hoc formulation backprojection works surprisingly well, supporting the validity of previous studies in lung EIT.

Trackability evaluation of reconstruction algorithms to the change of measured objects in electrical tomography

The continuous monitoring of the changing process is an important application field of electrical tomography (ET). In this changing process, the size, position and shape of measured objects are always alterative. The trackability of algorithms to the change of measured objects is important to the application of ET. The single object model group and two-object-model group were established to simulate the change of measured objects. The single object model group includes the circle model group and square model group. The suitable evaluation parameters were designed to evaluate the trackability of the different algorithms quantitatively, which includes the single image parameter and group parameter. Evaluation software was developed, which can generate measured boundary data of different models, complete reconstructed image greying, calculate evaluation parameters and plot parameter curves, etc. Furthermore, the trackability of ten selected algorithms was evaluated by this evaluation software. The results show that the trackability of the different algorithms is different in the evaluation of the different model group. Therefore, the different model group should be established according to the application requirement. Then the suitable algorithm for a particular application could be chosen through the evaluation process.

Evaluation and real-time monitoring of data quality in electrical impedance tomography

Electrical impedance tomography (EIT) is a noninvasive method to image conductivity distributions within a body. One promising application of EIT is to monitor ventilation in patients as a real-time bedside tool. Thus, it is essential that an EIT system reliably provide meaningful information, or alert clinicians when this is impossible. Because the reconstructed images are very sensitive to system instabilities (primarily from electrode connection variability and movement), EIT systems should continuously monitor and, if possible, correct for such errors. Motivated by this requirement, we describe a novel approach to quantitatively measure EIT data quality. Our goals are to define the requirements of a data quality metric, develop a metric q which meets these requirements, and an efficient way to calculate it. The developed metric q was validated using data from saline tank experiments and a retrospective clinical study. Additionally, we show that q may be used to compare the performance of EIT systems using phantom measurements. Results suggest that the calculated metric reflects well the quality of reconstructed EIT images for both phantom and clinical data. The proposed measure can thus be used for real-time assessment of EIT data quality and, hence, to indicate the reliability of any derived physiological information.