Electrical impedance tomography problem with inaccurately known boundary and contact impedances

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.

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

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

Advances in electrical impedance tomography-based brain imaging

Novel advances in the field of brain imaging have enabled the unprecedented clinical application of various imaging modalities to facilitate disease diagnosis and treatment. Electrical impedance tomography (EIT) is a functional imaging technique that measures the transfer impedances between electrodes on the body surface to estimate the spatial distribution of electrical properties of tissues. EIT offers many advantages over other neuroimaging technologies, which has led to its potential clinical use. This qualitative review provides an overview of the basic principles, algorithms, and system composition of EIT. Recent advances in the field of EIT are discussed in the context of epilepsy, stroke, brain injuries and edema, and other brain diseases. Further, we summarize factors limiting the development of brain EIT and highlight prospects for the field. In epilepsy imaging, there have been advances in EIT imaging depth, from cortical to subcortical regions. In stroke research, a bedside EIT stroke monitoring system has been developed for clinical practice, and data support the role of EIT in multi-modal imaging for diagnosing stroke. Additionally, EIT has been applied to monitor the changes in brain water content associated with cerebral edema, enabling the early identification of brain edema and the evaluation of mannitol dehydration. However, anatomically realistic geometry, inhomogeneity, cranium completeness, anisotropy and skull type, etc., must be considered to improve the accuracy of EIT modeling. Thus, the further establishment of EIT as a mature and routine diagnostic technique will necessitate the accumulation of more supporting evidence.

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.

Measurement-Based Domain Parameter Optimization in Electrical Impedance Tomography Imaging

This paper discusses the optimization of domain parameters in electrical impedance tomography-based imaging. Precise image reconstruction requires accurate, well-correlated physical and numerical finite element method (FEM) models; thus, we employed the Nelder–Mead algorithm and a complete electrode model to evaluate the individual parameters, including the initial conductivity, electrode misplacement, and shape deformation. The optimization process was designed to calculate the parameters of the numerical model before the image reconstruction. The models were verified via simulation and experimental measurement with single source current patterns. The impact of the optimization on the above parameters was reflected in the applied image reconstruction process, where the conductivity error dropped by 6.16% and 11.58% in adjacent and opposite driving, respectively. In the shape deformation, the inhomogeneity area ratio increased by 11.0% and 48.9%; the imprecise placement of the 6th electrode was successfully optimized with adjacent driving; the conductivity error dropped by 12.69%; and the inhomogeneity localization exhibited a rise of 66.7%. The opposite driving option produces undesired duality resulting from the measurement pattern. The designed optimization process proved to be suitable for correlating the numerical and the physical models, and it also enabled us to eliminate imaging uncertainties and artifacts.

Trends and recent development of the microelectrode arrays (MEAs)

In this paper, we reviewed the history of microelectrode arrays (MEAs), compared different microfabrication techniques applied to modern MEAs in terms of their material characters, device properties and application scenarios. Then we discussed the biocompatibility of different MEAs as well as corresponding strategy of improvement. At last, we analyzed the growing trend of MEAs' technical route, expected application of MEAs in the field of Electrical impedance tomography (EIT).

Capacitively Coupled Electrical Impedance Tomography for Brain Imaging

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

Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks

The mathematical problem for electrical impedance tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features, such as clear organ boundaries. Convolutional neural networks provide a powerful framework for post-processing such convolved direct reconstructions. In this paper, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems.

Torso shape detection to improve lung monitoring

OBJECTIVE

Newborns with lung immaturity often require continuous monitoring and treatment of their lung ventilation in intensive care units, especially if born preterm. Recent studies indicate that electrical impedance tomography (EIT) is feasible in newborn infants and children, and can quantitatively identify changes in regional lung aeration and ventilation following alterations to respiratory conditions. Information on the patient-specific shape of the torso and its role in minimizing the artefacts in the reconstructed images can improve the accuracy of the clinical parameters obtained from EIT. Currently, only idealized models or those segmented from CT scans are usually adopted.

APPROACH

This study presents and compares two methodologies that can detect the patient-specific torso shape by means of wearable devices based on (1) previously reported bend sensor technology, and (2) a novel approach based on the use of accelerometers.

MAIN RESULTS

The reconstruction of different phantoms, taking into account anatomical asymmetries and different sizes, are produced for comparison.

SIGNIFICANCE

As a result, the accelerometers are more versatile than bend sensors, which cannot be used on bigger cross-sections. The computational study estimates the optimal number of accelerometers required in order to generate an image reconstruction comparable to the use of a CT scan as the forward model. Furthermore, since the patient position is crucial to monitoring lung ventilation, the orientation of the phantoms is automatically detected by the accelerometer-based method.

Real-Time Implementation of Calderón's Method on Subject-Specific Domains

A real-time implementation of Calderón's method for the reconstruction of a 2-D conductivity from electrical impedance tomography data is presented, in which domain-specific modeling is taken into account. This is the first implementation of Calderón's method that accounts for correct modeling of non-symmetric domain boundaries in image reconstruction. The domain-specific Calderón's method is derived and reconstructions from experimental tank data are presented, quantifying the distortion when correct modeling is not included in the reconstruction algorithm. Reconstructions from human subject volunteers are presented, demonstrating the method's effectiveness for imaging changes due to ventilation and perfusion in the human thorax.

Compensation for large thorax excursions in EIT imaging

Besides the application of EIT in the intensive care unit it has recently also been used in spontaneously breathing patients suffering from asthma bronchiole, cystic fibrosis (CF) or chronic obstructive pulmonary disease (COPD). In these cases large thorax excursions during deep inspiration, e.g. during lung function testing, lead to artifacts in the reconstructed images. In this paper we introduce a new approach to compensate for image artifacts resulting from excursion induced changes in boundary voltages. It is shown in a simulation study that boundary voltage change due to thorax excursion on a homogeneous model can be used to modify the measured voltages and thus reduce the impact of thorax excursion on the reconstructed images. The applicability of the method on human subjects is demonstrated utilizing a motion-tracking-system. The proposed technique leads to fewer artifacts in the reconstructed images and improves image quality without substantial increase in computational effort, making the approach suitable for real-time imaging of lung ventilation. This might help to establish EIT as a supplemental tool for lung function tests in spontaneously breathing patients to support clinicians in diagnosis and monitoring of disease progression.

Improving image quality in EIT imaging by measurement of thorax excursion

Electrical Impedance Tomography (EIT) is used to visualize the regional ventilation of the lungs using voltage measurements on the surface of the thorax. Unfortunately the image reconstruction process is sensitive to shape deformation. During breathing the inevitable expansion of the thorax influences measured boundary voltages which leads to artifacts in the reconstructed images. A camera based motion-tracking-system was used to measure thorax excursion during breathing and systematically modify measured voltages. Results indicate that image artefacts can be reduced if the measured voltages are modified based on the measured thorax excursion.

Resolution Guarantees in Electrical Impedance Tomography

Electrical impedance tomography (EIT) uses current-voltage measurements on the surface of an imaging subject to detect conductivity changes or anomalies. EIT is a promising new technique with great potential in medical imaging and non-destructive testing. However, in many applications, EIT suffers from inconsistent reliability due to its enormous sensitivity to modeling and measurement errors. In this work, we show that it is principally possible to give rigorous resolution guarantees in EIT even in the presence of systematic and random measurement errors. We derive a constructive criterion to decide whether a desired resolution can be achieved in a given measurement setup. Our results cover the case where anomalies of a known minimal contrast in a subject with imprecisely known background conductivity are to be detected from noisy measurements on a number of electrodes with imprecisely known contact impedances. The considered settings are still idealized in the sense that the shape of the imaging subject has to be known and the allowable amount of uncertainty is rather low. Nevertheless, we believe that this may be a starting point to identify new applications and to design and optimize measurement setups in EIT.

An image reconstruction algorithm for 3-D electrical impedance mammography

The Sussex MK4 electrical impedance mammography system is especially designed for 3-D breast screening. It aims to diagnose breast cancer at an early stage when it is most treatable. Planar electrodes are employed in this system. The challenge with planar electrodes is the inaccuracy and poor sensitivity in the vertical direction for 3-D imaging. An enhanced image reconstruction algorithm using a duo-mesh method is proposed to improve the vertical accuracy and sensitivity. The novel part of the enhanced image reconstruction algorithm is the correction term. To evaluate the new algorithm, an image processing based error analysis method is presented, which not only can precisely assess the error of the reconstructed image but also locate the center and outline the center and outline the shape of the objects of interest. Although the enhanced image reconstruction algorithm and the image processing based error analysis method are designed for the Sussex MK4 system, they are applicable to all electrical impedance tomography systems, regardless of the hardware design. To validate the enhanced algorithm, performance results from simulations, phantoms and patients are presented.

Calderón's method on an elliptical domain

One possible application for electrical impedance tomography is in medical imaging where lung and heart function may be monitored. One drawback of current algorithms is that they are implemented for use in a circular domain, but a human thorax is more elliptical than circular. In this paper, a reconstruction algorithm based on the work of Calderón (1980 Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro) pp 65-75) on the inverse conductivity problem is derived for an elliptical domain. It is explained how this reconstruction algorithm uses a transformed Dirichlet-to-Neumann map. Experimental results from an elliptical tank are given to show how correct domain modelling reduces the artefacts produced by this version of Calderón's reconstruction algorithm.

Shape deformation in two-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) uses measurements from surface electrodes to reconstruct an image of the conductivity of the contained medium. However, changes in measurements result from both changes in internal conductivity and changes in the shape of the medium relative to the electrode positions. Failure to account for shape changes results in a conductivity image with significant artifacts. Previous work to address shape changes in EIT has shown that in some cases boundary shape and electrode location can be uniquely determined for isotropic conductivities; however, for geometrically conformal changes, this is not possible. This prior work has shown that the shape change problem can be partially addressed. In this paper, we explore the limits of compensation for boundary movement in EIT using three approaches. First, a theoretical model was developed to separate a deformation vector field into conformal and nonconformal components, from which the reconstruction limits may be determined. Next, finite element models were used to simulate EIT measurements from a domain whose boundary has been deformed. Finally, an experimental phantom was constructed from which boundary deformation measurements were acquired. Results, both in simulation and with experimental data, suggest that some electrode movement and boundary distortions can be reconstructed based on conductivity changes alone while reducing image artifacts in the process.

Influence of crystalloid and colloid fluid infusion and blood withdrawal on pulmonary bioimpedance in an animal model of mechanical ventilation

Electrical impedance tomography (EIT) is considered useful for monitoring regional ventilation and aeration in intensive-care patients during mechanical ventilation. Changes in their body fluid state modify the electrical properties of lung tissue and may interfere with the EIT measurements of lung aeration. The aim of our study was to assess the effects of crystalloid and colloid infusion and blood withdrawal on bioimpedance determined by EIT in a chest cross-section. Fourteen anaesthetized mechanically ventilated pigs were subjected to interventions affecting the volume state (crystalloid and colloid infusion, blood withdrawal). Six animals received additional crystalloid fluids (fluid group) whereas eight did not (no-fluid group). Global and regional relative impedance changes (RIC, dimensionless unit) were determined by backprojection at end-expiration. Regional ventilation distribution was analyzed by calculating the tidal RIC in the same regions. Colloid infusion led to a significant fall in the global end-expiratory RIC (mean differences: fluid: -91.2, p < 0.001, no-fluid: -38.9, p < 0.001), which was partially reversed after blood withdrawal (mean differences, fluid: +45.1, p = 0.047 and no-fluid: +26.2, p = 0.009). The RIC was significantly lower in the animals with additional crystalloids (mean group difference: 45.5, p < 0.001). Global and regional tidal volumes were not significantly affected by the fluid and volume states.

Statistical estimation of EIT electrode contact impedance using magic Toeplitz matrix

The goal of the paper is to propose a fast and reliable method of simultaneous estimation of conductivity and electrode contact impedances for a homogeneous 2D disk. Magic Toeplitz matrix as the Neumann-to-Dirichlet map with finite width electrodes plays the central role in our linear model, called the gapZ model. This model enables testing of various hypotheses using the F-test, such as the uniformity of electrode impedances and their statistical significance. The gapZ model is compared with the finite element approximation, and illustrated and validated with a phantom tank experiment filled with saline. Further this model was illustrated with the patient breast EIT data to identify bad contact electrodes.

Compensation of modelling errors due to unknown domain boundary in electrical impedance tomography

Electrical impedance tomography is a highly unstable problem with respect to measurement and modeling errors. This instability is especially severe when absolute imaging is considered. With clinical measurements, accurate knowledge about the body shape is usually not available, and therefore an approximate model domain has to be used in the computational model. It has earlier been shown that large reconstruction artefacts result if the geometry of the model domain is incorrect. In this paper, we adapt the so-called approximation error approach to compensate for the modeling errors caused by inaccurately known body shape. This approach has previously been shown to be applicable to a variety of modeling errors, such as coarse discretization in the numerical approximation of the forward model and domain truncation. We evaluate the approach with a simulated example of thorax imaging, and also with experimental data from a laboratory setting, with absolute imaging considered in both cases. We show that the related modeling errors can be efficiently compensated for by the approximation error approach. We also show that recovery from simultaneous discretization related errors is feasible, allowing the use of computationally efficient reduced order models.

Arbitrary geometry patient interfaces for breast cancer detection and monitoring with electrical impedance tomography

Electrical impedance tomography (EIT) is a promising technology enabling the detection or observation of many biological processes. This is typically accomplished by applying currents at known locations on an outer surface (in this case skin) and measuring voltages at other locations. This information is then used to determine electrical properties of tissue found between the electrodes by solving the associated Laplace equation. Such problems depend upon knowing the exact boundary conditions (BC). Unfortunately BCs are not always easily determined and approximations are accepted out of necessity due to problem complexity or time constraints. The EIT group at Dartmouth College has developed two new patient interfaces for breast cancer detection and monitoring both of which speed acquisition time and allow for precision BC information in natural and arbitrary geometries. Preliminary experimental results are presented.