Three-dimensional electrical impedance tomography based on thecomplete electrode model

In electrical impedance tomography an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. It is often assumed that the injected currents are confined to the two-dimensional (2-D) electrode plane and the reconstruction is based on 2-D assumptions. However, the currents spread out in three dimensions and, therefore, off-plane structures have significant effect on the reconstructed images. In this paper we propose a finite element-based method for the reconstruction of three-dimensional resistivity distributions. The proposed method is based on the so-called complete electrode model that takes into account the presence of the electrodes and the contact impedances. Both the forward and the inverse problems are discussed and results from static and dynamic (difference) reconstructions with real measurement data are given. It is shown that in phantom experiments with accurate finite element computations it is possible to obtain static images that are comparable with difference images that are reconstructed from the same object with the empty (saline filled) tank as a reference.     

A direct reconstruction algorithm for electrical impedance tomography

A direct (noniterative) reconstruction algorithm for electrical impedance tomography in the two-dimensional (2-D), cross-sectional geometry is reviewed. New results of a reconstruction of a numerically simulated phantom chest are presented. The algorithm is based on the mathematical uniqueness proof by A. I. Nachman [1996] for the 2-D inverse conductivity problem. In this geometry, several of the clinical applications include monitoring heart and lung function, diagnosis of pulmonary embolus, diagnosis of pulmonary edema, monitoring for internal bleeding, and the early detection of breast cancer.     

Weighted least-squares criteria for electrical impedance tomography

Methods are developed for the design of electrical impedance tomographic reconstruction algorithms with specified properties. Assuming a starting model with constant conductivity or some other specified background distribution, an algorithm with the following properties is found. (1) The optimum constant for the starting model is determined automatically. (2) The weighted least-squares error between the predicted and measured power dissipation data is as small as possible. (3) The variance of the reconstructed conductivity from the starting model is minimized. (4) Potential distributions with the largest volume integral of gradient squared have the least influence on the reconstructed conductivity, and therefore distributions most likely to be corrupted by contact impedance effects are deemphasized. (5) Cells that dissipate the most power during the current injection tests tend to deviate least from the background value. For a starting model with nonconstant conductivity, the reconstruction algorithm has analogous properties.     

Reconstructions of chest phantoms by the D-bar method for electrical impedance tomography

The problem this paper addresses is how to use the two-dimensional D-bar method for electrical impedance tomography with experimental data collected on finitely many electrodes covering a portion of the boundary of a body. This requires an approximation of the Dirichlet-to-Neumann, or voltage-to-current density map, defined on the entire boundary of the region, from a finite number of matrix elements of the current-to-voltage map. Reconstructions from experimental data collected on a saline filled tank containing agar heart and lung phantoms are presented, and the results are compared to reconstructions by the NOSER algorithm on the same data.     

A neural network image reconstruction technique for electrical impedance tomography

Reconstruction of images in electrical impedance tomography requires the solution of a nonlinear inverse problem on noisy data. This problem is typically ill-conditioned and requires either simplifying assumptions or regularization based on a priori knowledge. The authors present a reconstruction algorithm using neural network techniques which calculates a linear approximation of the inverse problem directly from finite element simulations of the forward problem. This inverse is adapted to the geometry of the medium and the signal-to-noise ratio (SNR) used during network training. Results show good conductivity reconstruction where measurement SNR is similar to the training conditions. The advantages of this method are its conceptual simplicity and ease of implementation, and the ability to control the compromise between the noise performance and resolution of the image reconstruction.     

On optimal current patterns for electrical impedance tomography

We develop a statistical criterion for optimal patterns in planar circular electrical impedance tomography. These patterns minimize the total variance of the estimation for the resistance or conductance matrix. It is shown that trigonometric patterns (Isaacson, 1986), originally derived from the concept of distinguishability, are a special case of our optimal statistical patterns. New optimal random patterns are introduced. Recovering the electrical properties of the measured body is greatly simplified when optimal patterns are used. The Neumann-to-Dirichlet map and the optimal patterns are derived for a homogeneous medium with an arbitrary distribution of the electrodes on the periphery. As a special case, optimal patterns are developed for a practical EIT system with a finite number of electrodes. For a general nonhomogeneous medium, with no a priori restriction, the optimal patterns for the resistance and conductance matrix are the same. However, for a homogeneous medium, the best current pattern is the worst voltage pattern and vice versa. We study the effect of the number and the width of the electrodes on the estimate of resistivity and conductivity in a homogeneous medium. We confirm experimentally that the optimal patterns produce minimum conductivity variance in a homogeneous medium. Our statistical model is able to discriminate between a homogenous agar phantom and one with a 2 mm air hole with error probability (p-value) 1/1000.     

Reconstruction of three-dimensional data for electrical impedance tomography

A two-dimensional reconstruction algorithm based on a modified version of the method of sensitivity regions is used to reconstruct data obtained from a three-dimensional finite element model. By using data obtained from off-drive-plane measurements an improved image of changes in resistivity on the drive plane is obtained.<>     

A real-time electrical impedance tomography system for clinicaluse-design and preliminary results

An instrument is described which produces images of the electrical impedance distribution within the body at a rate of 25 frames per second, allowing lung ventilation and lung perfusion to be observed in real time. The instrument makes impedance measurements using an array of 16 electrodes on the surface of the body, and reconstructs the images using a weighted backprojection technique. The design of the data acquisition electronics and the reconstruction and display processor are described. Some preliminary in vitro and in vivo results from the system are presented     

A broadband high-frequency electrical impedance tomography system for breast imaging.

Bio-electric impedance signatures arise primarily from differences in cellular morphologies within an organ and can be used to differentiate benign and malignant pathologies, specifically in the breast. Electrical impedance tomography (EIT) is an imaging modality that determines the impedance distribution within tissue and has been used in prior work to map the electrical properties of breast at signal frequencies ranging from a few kHz to 1 MHz. It has been suggested that by extending the frequency range, additional information of clinical significance may be obtained. We have, therefore, developed a new EIT system for breast imaging which covers the frequency range from 10 kHz to 10 MHz. The instrument developed here is a distributed processor tomograph with 64 channels, capable of generating and measuring voltages and currents. Electrical benchmarking has shown the system to have a SNR greater than 94 dB up to 2 MHz, 90 dB up to 7 MHz, and 65 dB at 10 MHz. In addition, the system measures impedances to an accuracy of 99.7 % and has channel-to-channel variations of less than 0.05 %. Phantom imaging has demonstrated the ability to image across the entire frequency range in both single- and multiplane configurations. Further, 96 women have participated safely in breast exams with the system and the associated conductivity spectra obtained from 3-D image reconstructions range from 0.0237 S/m at 10 kHz to 0.2174 S/m at 10 MHz. These findings are consistent with impedance values reported in the literature.     

A four-shell diffusion phantom of the head for electrical impedance tomography

A four-shell head phantom has been built and characterized. Its structure is similar to that of nonhomogeneous concentric shell domains used by numerical solvers that better approximate current distribution than phantoms currently used to validate electrical impedance tomography systems. Each shell represents a head tissue, namely, skin, skull, cerebrospinal fluid, and brain. A novel technique, which employs a volume conductive impermeable film, has been implemented to prevent ion diffusion between different agar regions without affecting current distribution inside the phantom. Comparisons between simulations and phantom measurements performed over four days are given to prove both the adherence to the model in the frequency range between 10 kHz and 1 MHz and its long-term stability.     

A reconstruction algorithm for electrical impedance tomography data collected on rectangular electrode arrays

A three-dimensional reconstruction algorithm in electrical impedance imaging is presented for determining the conductivity distribution beneath the surface of a medium, given surface voltage data measured on a rectangular array of electrodes. Such an electrode configuration may be desirable for using electrical impedence tomography to detect tumors in the human breast. The algorithm is based on linearizing the conductivity about a constant value. Here, we describe a simple implementation of the algorithm on a four-electrode--by-four-electrode array and the reconstructions obtained from numerical and experimental tank data. The results demonstrate significantly better spatial resolution in the plane of the electrodes than with respect to depth.     

Optimal experiments in electrical impedance tomography

Electrical impedance tomography (EIT) is a noninvasive imaging technique which aims to image the impedance within a body from electrical measurements made on the surface. The reconstruction of impedance images is a ill-posed problem which is both extremely sensitive to noise and highly computationally intensive. The authors define an experimental measurement in EIT and calculate optimal experiments which maximize the distinguishability between the region to be imaged and a best-estimate conductivity distribution. These optimal experiments can be derived from measurements made on the boundary. The analysis clarifies the properties of different voltage measurement schemes. A reconstruction algorithm based on the use of optimal experiments is derived. It is shown to be many times faster than standard Newton-based reconstruction algorithms, and results from synthetic data indicate that the images that it produces are comparable.     

An image reconstruction algorithm for three-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) has been studied by many authors and in most of this work it has been considered to be a two-dimensional problem. Many groups are now turning their attention to the full three-dimensional case in which the computational demands become much greater. It is interesting to look for ways to reduce this demand and in this paper we describe an implementation of an algorithm that is able to achieve this by precomputing many of the quantities needed in the image reconstruction. The algorithm is based on a method called NOSER introduced some years ago by Cheney et al. [3]. In this paper we have significantly extended the method by introducing a more realistic electrode model into the analysis. We have given explicit formulae for the quantities involved so that the reader can reproduce our results.     

An efficient forward solver in electrical impedance tomography by spectral element method

In electrical impedance tomography (EIT), a forward solver capable of predicting the voltages on electrodes for a given conductivity distribution is essential for reconstruction. The EIT forward solver is normally based on the conventional finite element method (FEM). One of the major problems of three-dimensional (3-D) EIT is its high demand in computing power and memory since high precision is required for obtaining a small secondary field which is typical for a small anomaly. This accuracy requirement is also set by the level of noise in the real data; although currently the noise level is still an issue, future EIT systems should significantly reduce the noise level to be capable of detecting very small anomalies. To accurately simulate the forward solution with the FEM, a mesh with large number of nodes and elements is usually needed. To overcome this problem, we proposed the spectral element method (SEM) for EIT forward problem. With the introduction of SEM, a smaller number of nodes and hence less computational time and memory are needed to achieve the same or better accuracy in the forward solution than the FEM. Numerical results demonstrate the efficiency of the SEM in 3-D EIT simulation.     

Measuring lung resistivity using electrical impedance tomography

We propose the use of electrical impedance tomography (EIT) imaging techniques in the measurement of lung resistivity for detection and monitoring of apnea and edema. In EIT, we inject currents into a subject using multiple electrodes and measure boundary voltages to reconstruct a cross-sectional image of internal resistivity distribution. We found that a simplified, therefore fast, version of the impedance imaging method can be used for detection and monitoring of apnea and edema. We have showed the feasibility of this method through computer simulations and human experiments. We speculate that the EIT imaging technique will be more reliable than the current impedance apnea monitoring method, since we are monitoring the change of internal lung resistivity. However, more study is required to verify that this method performs better in the presence of motion artifact than the conventional two-electrode impedance apnea monitoring method. Future work should include experiments which carefully simulate different kinds of motion artifacts.     

Increasing image resolution in electrical impedance tomography

An effective approach to increase the image resolution in static electrical impedance tomography is proposed, in which the image with local high resolution is reconstructed by fine meshing only the impedance abnormal element in the finite element model based on a genetic algorithm. Experimental results from a laboratory phantom are presented     

Using compound electrodes in electrical impedance tomography

A compound electrode composed of a large outer electrode to inject current and a small inner electrode to sense voltage was developed and used to measure voltages from a physical phantom. The measured voltages were smaller in amplitude than those from conventional electrodes, demonstrating that the compound electrode can minimize contact impedance voltage drop from the measured data. A finite-element model was used for the compound electrode and incorporated into the regularized Newton-Raphson reconstruction algorithm. A sensitivity study showed that the reconstructed resistivity distributions are less dependent on the unknown contact resistance values for a compound electrode than a conventional electrode and that the use of a compound electrode results in improved images for the reconstruction algorithm     

Anatomically constrained electrical impedance tomography forthree-dimensional anisotropic bodies

As shown previously for two-dimensional geometries, anisotropy effects should not be ignored in electrical impedance tomography (EIT) and structural information is important for the reconstruction of anisotropic conductivities. Here, we describe the static reconstruction of an anisotropic conductivity distribution for the more realistic three-dimensional (3-D) case. Boundaries between different conductivity regions are anatomically constrained using magnetic resonance imaging (MRI) data. The values of the conductivities are then determined using gradient-type-algorithms in a nonlinear-indirect approach. At each iteration, the forward problem is solved by the finite element method. The approach is used to reconstruct the 3-D conductivity profile of a canine torso. Both computational performance and simulated reconstruction results are presented together with a detailed study on the sensitivity of the prediction error with respect to different parameters. In particular, the use of an intracavity catheter to better extract interior conductivities is demonstrated     

Tissue spectroscopy with electrical impedance tomography: computersimulations

A method is proposed by which bioelectrical spectroscopy could be combined with electrical impedance tomography (EIT) to provide noninvasive characterization of tissue. Multifrequency (2-200 kHz) EIT measurements were simulated with a numerical model for a volume of porcine liver immersed in an electrolytic tank. From the reconstructed EIT images the tissue characterization method was then applied enabling a plot of complex resistivity to be drawn for any selected pixel in the image. Simulations were performed for a small volume of degraded tissue embedded in the normal tissue to examine its effect on the derived spectroscopic parameters. The method could have an application in transplant surgery for screening organs for tissue degradation     

MPSO-MNR算法及噪声对该算法在EIT成像中的影响

针对现有电阻抗成像算法的局限,在此将修正的粒子群算法与牛顿拉夫孙结合算法,形成MPSO-MNR算法。对二维圆形求解区域,采用有限元剖分,在三角电流驱动模式下,应用提出的MPSO-MNR算法进行电阻抗重构,并研究了噪声对重构结果的影响。数值仿真结果表明：MPSO-MNR算法能够准确重构解域内电阻抗分布;噪声影响成像的质量,随着噪声的增加（信噪比的减少）,重构目标的边界、背景变得逐渐模糊。MPSO-MNR算法避免要求迭代初值接近真值,并具有较快收敛的特点,在一定的噪声范围内,可用于电阻抗重构。