Methods for Compensating for Variable Electrode Contact in EIT

Electrical impedance tomography (EIT) is an imaging modality that currently shows promise for the detection and characterization of breast cancer. A very significant problem in EIT imaging is the proper modeling of the interface between the body and the electrodes. We have found empirically that it is very difficult, in a clinical setting, to assure that all electrodes make satisfactory contact with the body. In addition, we have observed a capacitive effect at the skin/electrode boundary that is spatially heterogeneous. To compensate for these problems, we have developed a hybrid nonlinear–linear reconstruction algorithm using the complete electrode model in which we first estimate electrode surface impedances, by means of a Levenberg–Marquardt iterative optimization procedure with an analytically computed Jacobian matrix. We, subsequently, use a linearized algorithm to perform a 3-D reconstruction of perturbations in both contact impedances, and in the spatial distributions of conductivity and permittivity. Results show that, with this procedure, artifacts due to electrodes making poor contact can be greatly reduced. If the experimental apparatus physically applies voltages and measures currents, we show that it is preferable to compute the reconstruction with respect to the Dirichlet-to-Neumann map rather than the Neumann-to-Dirichlet map if there is a significant possibility that electrodes will be fully disconnected. Finally, we test our electrode compensation algorithms for a set of clinical data, showing that we can significantly improve the fit of our model to the measurements by allowing the electrode surface impedances to vary.      

A confocal microwave imaging algorithm for breast cancer detection

We present a computationally efficient and robust image reconstruction algorithm for breast cancer detection using an ultrawideband confocal microwave imaging system. To test the efficacy of this approach, we have developed a two-dimensional (2-D) anatomically realistic MRI-derived FDTD model of the cancerous breast. The image reconstruction algorithm is applied to FDTD-computed backscatter signals, resulting in a microwave image that clearly identifies the presence and location of the malignant lesion. These simulations demonstrate the feasibility of detecting and imaging small breast tumors using this novel approach     

A reconstruction algorithm for breast cancer imaging with electrical impedance tomography in mammography geometry

The conductivity and permittivity of breast tumors are known to differ significantly from those of normal breast tissues, and electrical impedance tomography (EIT) is being studied as a modality for breast cancer imaging to exploit these differences. At present, X-ray mammography is the primary standard imaging modality used for breast cancer screening in clinical practice, so it is desirable to study EIT in the geometry of mammography. This paper presents a forward model of a simplified mammography geometry and a reconstruction algorithm for breast tumor imaging using EIT techniques. The mammography geometry is modeled as a rectangular box with electrode arrays on the top and bottom planes. A forward model for the electrical impedance imaging problem is derived for a homogeneous conductivity distribution and is validated by experiment using a phantom tank. A reconstruction algorithm for breast tumor imaging based on a linearization approach and the proposed forward model is presented. It is found that the proposed reconstruction algorithm performs well in the phantom experiment, and that the locations of a 5-mm-cube metal target and a 6-mm-cube agar target could be recovered at a target depth of 15 mm using a 32 electrode system.     

Real-Time Management of Faulty Electrodes in Electrical Impedance Tomography

Completely or partially disconnected electrodes are a fairly common occurrence in many electrical impedance tomography (EIT) clinical applications. Several factors can contribute to electrode disconnection: patient movement, perspiration, manipulations by clinical staff, and defective electrode leads or electronics. By corrupting several measurements, faulty electrodes introduce significant image artifacts. In order to properly manage faulty electrodes, it is necessary to: (1) account for invalid data in image reconstruction algorithms and (2) automatically detect faulty electrodes. This paper presents a two-part approach for real-time management of faulty electrodes based on the principle of voltage-current reciprocity. The first part allows accounting for faulty electrodes in EIT image reconstruction without a priori knowledge of which electrodes are at fault. The method properly weights each measurement according to its compliance with the principle of voltage-current reciprocity. Results show that the algorithm is able to automatically determine the valid portion of the data and use it to calculate high-quality images. The second part of the approach allows automatic real-time detection of at least one faulty electrode with 100% sensitivity and two faulty electrodes with 80% sensitivity enabling the clinical staff to fix the problem as soon as possible to minimize data loss.     

A robust image reconstruction algorithm and its parallel implementation in electrical impedance tomography

An efficient and robust image reconstruction algorithm for static impedance imaging using Hachtel's augmented matrix method was developed. This improved Newton-Raphson method produced more accurate images by reducing the undesirable effects of the ill-conditioned Hessian matrix. It is demonstrated that the electrical impedance tomography (EIT) system could produce two-dimensional static images from a physical phantom with 7% spatial resolution at the center and 5% at the periphery. Static EIT image reconstruction requires a large amount of computation. In order to overcome the limitations on reducing the computation time by algorithmic approaches, the improved Newton-Raphson algorithm was implemented on a parallel computer system. It is shown that the parallel computation could reduce the computation time from hours to minutes.     

Electrical impedance tomography

Electrical impedance tomography (EIT) is an imaging modality that estimates the electrical properties at the interior of an object from measurements made on its surface. Typically, currents are injected into the object through electrodes placed on its surface, and the resulting electrode voltages are measured. An appropriate set of current patterns, with each pattern specifying the value of the current for each electrode, is applied to the object, and a reconstruction algorithm uses knowledge of the applied current patterns and the measured electrode voltages to solve the inverse problem, computing the electrical conductivity and permittivity distributions in the object. This article focuses on the type of EIT called adaptive current tomography (ACT) in which currents are applied simultaneously to all the electrodes. A number of current patterns are applied, where each pattern defines the current for each electrode, and the subsequent electrode voltages are measured to generate the data required for image reconstruction. A ring of electrodes may be placed in a single plane around the object, to define a two-dimensional problem, or in several layers of such rings, to define a three-dimensional problem. The reconstruction problem is described and two algorithms are discussed, a one-step, two-dimensional (2-D) Newton-Raphson algorithm and a one-step, full three-dimensional (3-D) reconstructor. Results from experimental data are presented which illustrate the performance of the algorithms     

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.     

Circular ultrasound compounding by designed matrix weighting

Spatial compounding is an imaging technique that aims to improve image contrast by combining partially decor-related images acquired at different angles or positions. In conventional spatial compounding, data sets are combined with equal weighting. Here, we describe an alternative method of reconstruction using algorithms which weight the data based on a "quality" matrix. The quality matrix is derived from beamforming characteristics. For each data set, the reliability of the data is assumed to vary spatially. By compounding the data based on the quality matrix, a complete image is formed. Here, we describe the construction of a rotational translation stage and tissue-mimicking phantoms that are used in conjunction with a commercial medical ultrasound machine to test our reconstruction algorithms. The new algorithms were found to increase the contrast-to-speckle ratio of simulated cysts and tumors by 61% from raw data, and to significantly increase edge definition of small embedded targets. The new method shows promise as a computationally efficient method of improving contrast and resolution in ultrasound images. The method should be particularly useful in breast imaging, where images from multiple angles can be acquired without interference from bone or air.     

Electrical impedance tomography problem with inaccurately known boundary and contact impedances

In electrical impedance tomography (EIT) electric currents are injected into a body with unknown electromagnetic properties through a set of contact electrodes at the boundary of the body. The resulting voltages are measured on the same electrodes and the objective is to reconstruct the unknown conductivity function inside the body based on these data. All the traditional approaches to the reconstruction problem assume that the boundary of the body and the electrode-skin contact impedances are known a priori. However, in clinical experiments one usually lacks the exact knowledge of the boundary and contact impedances, and therefore, approximate model domain and contact impedances have to be used in the image reconstruction. However, it has been noticed that even small errors in the shape of the computation domain or contact impedances can cause large systematic artefacts in the reconstructed images, leading to loss of diagnostically relevant information. In a recent paper (Kolehmainen , 2006), we showed how in the 2-D case the errors induced by the inaccurately known boundary can be eliminated as part of the image reconstruction and introduced a novel method for finding a deformed image of the original isotropic conductivity using the theory of TeichmÜller mappings. In this paper, the theory and reconstruction method are extended to include the estimation of unknown contact impedances. The method is implemented numerically and tested with experimental EIT data. The results show that the systematic errors caused by inaccurately known boundary and contact impedances can efficiently be eliminated by the reconstruction method.      

In Vivo Impedance Imaging With Total Variation Regularization

We show that electrical impedance tomography (EIT) image reconstruction algorithms with regularization based on the total variation (TV) functional are suitable for in vivo imaging of physiological data. This reconstruction approach helps to preserve discontinuities in reconstructed profiles, such as step changes in electrical properties at interorgan boundaries, which are typically smoothed by traditional reconstruction algorithms. The use of the TV functional for regularization leads to the minimization of a nondifferentiable objective function in the inverse formulation. This cannot be efficiently solved with traditional optimization techniques such as the Newton method. We explore two implementations methods for regularization with the TV functional: the lagged diffusivity method and the primal dual–interior point method (PD-IPM). First we clarify the implementation details of these algorithms for EIT reconstruction. Next, we analyze the performance of these algorithms on noisy simulated data. Finally, we show reconstructed EIT images of in vivo data for ventilation and gastric emptying studies. In comparison to traditional quadratic regularization, TV regulariza tion shows improved ability to reconstruct sharp contrasts.      

Impact of model shape mismatch on reconstruction quality in electrical impedance tomography

Electrical impedance tomography (EIT) is a low-cost, noninvasive and radiation free medical imaging modality for monitoring ventilation distribution in the lung. Although such information could be invaluable in preventing ventilator-induced lung injury in mechanically ventilated patients, clinical application of EIT is hindered by difficulties in interpreting the resulting images. One source of this difficulty is the frequent use of simple shapes which do not correspond to the anatomy to reconstruct EIT images. The mismatch between the true body shape and the one used for reconstruction is known to introduce errors, which to date have not been properly characterized. In the present study we, therefore, seek to 1) characterize and quantify the errors resulting from a reconstruction shape mismatch for a number of popular EIT reconstruction algorithms and 2) develop recommendations on the tolerated amount of mismatch for each algorithm. Using real and simulated data, we analyze the performance of four EIT reconstruction algorithms under different degrees of shape mismatch. Results suggest that while slight shape mismatch is well tolerated by all algorithms, using a circular shape severely degrades their performance.     

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.     

Electrical impedance tomography for imaging tissue electroporation

Electroporation is a method to introduce molecules, such as gene constructs or small drugs, into cells by temporarily permeating the cell membrane with electric pulses. In molecular medicine and biotechnology, tissue electroporation is performed with electrodes placed in the target area of the body. Currently, tissue electroporation, as with all other methods of molecular medicine, is performed without real-time control or near-term information regarding the extent and degree of electroporation. This paper expands the work from our previous study by implementing new ex vivo experimental data with "front-tracking" analysis for the image reconstruction algorithm. The experimental data is incorporated into numerical simulations of electroporation procedures and images are generated using the new reconstruction algorithm to demonstrate that electrical impedance tomography (EIT) can produce an image of the electroporated area. Combining EIT with electroporation could become an important biotechnological and medical technique to introduce therapeutic molecules into cells in tissue at predetermined areas of the body.     

Assessment of Terahertz Imaging for Excised Breast Cancer Tumors with Image Morphing

This paper presents an image morphing algorithm for quantitative evaluation methodology of terahertz (THz) images of excised breast cancer tumors. Most current studies on the assessment of THz imaging rely on qualitative evaluation, and there is no established benchmark or procedure to quantify the THz imaging performance. The proposed morphing algorithm provides a tool to quantitatively align the THz image with the histopathology image. Freshly excised xenograft murine breast cancer tumors are imaged using the pulsed THz imaging and spectroscopy system in the reflection mode. Upon fixing the tumor tissue in formalin and embedding in paraffin, a formalin-fixed paraffin-embedded (FFPE) tissue block is produced. A thin slice of the block is prepared for the pathology image while another THz reflection image is produced directly from the block. We developed an algorithm of mesh morphing using homography mapping of the histopathology image to adjust the alignment, shape, and resolution to match the external contour of the tissue in the THz image. Unlike conventional image morphing algorithms that rely on internal features of the source and target images, only the external contour of the tissue is used to avoid bias. Unsupervised Bayesian learning algorithm is applied to THz images to classify the tissue regions of cancer, fat, and muscles present in xenograft breast tumors. The results demonstrate that the proposed mesh morphing algorithm can provide more effective and accurate evaluation of THz imaging compared with existing algorithms. The results also showed that while THz images of FFPE tissue are highly in agreement with pathology images, challenges remain in assessing THz imaging of fresh tissue.     

Magnetic resonance electrical impedance tomography (MREIT): simulation study of J-substitution algorithm

We developed a new image reconstruction algorithm for magnetic resonance electrical impedance tomography (MREIT). MREIT is a new EIT imaging technique integrated into magnetic resonance imaging (MRI) system. Based on the assumption that internal current density distribution is obtained using magnetic resonance imaging (MRI) technique, the new image reconstruction algorithm called J-substitution algorithm produces cross-sectional static images of resistivity (or conductivity) distributions. Computer simulations show that the spatial resolution of resistivity image is comparable to that of MRI. MREIT provides accurate high-resolution cross-sectional resistivity images making resistivity values of various human tissues available for many biomedical applications.     

Electrical impedance tomography: regularized imaging and contrast detection

Dynamic electrical impedance tomography (EIT) images changes in the conductivity distribution of a medium from low frequency electrical measurements made at electrodes on the medium surface. Reconstruction of the conductivity distribution is an under-determined and ill-posed problem, typically requiring either simplifying assumptions or regularization based on a priori knowledge. This paper presents a maximum a posteriori (MAP) approach to linearized image reconstruction using knowledge of the noise variance of the measurements and the covariance of the conductivity distribution. This approach has the advantage of an intuitive interpretation of the algorithm parameters as well as fast (near real time) image reconstruction. In order to compare this approach to existing algorithms, the authors develop figures of merit to measure the reconstructed image resolution, the noise amplification of the image reconstruction, and the fidelity of positioning in the image. Finally, the authors develop a communications systems approach to calculate the probability of detection of a conductivity contrast in the reconstructed image as a function of the measurement noise and the reconstruction algorithm used.     

静态阻抗断层图像重建新方法

阻抗断层图像重建是一个严重病态的非线性的逆问题,特别是在静态阻抗断层成像中,由于其图像重建模型误差和测量噪声的影响更为严重,因此常用的基于目标函数梯度信息不断迭代的改进的Newton-Raphson类重建算法,即使使用正则化技术,其稳定性仍较差,甚至发散.本文提出一种全新的静态阻抗断层图像重建方法,它利用基于生物自然选择与遗传机理的遗传算法去搜索阻抗图像重建问题的最优解,无需正则化技术,也不会象改进的Newton-Raphson类算法那样易陷入局部最优解.实验结果也表明基于遗传算法的图像重建方法重建的静态阻抗断层图像,其成像精度和空间分辨率都大大好于改进的Newton-Raphson类重建算法.     

A versatile high-permittivity phantom for EIT

Phantoms are frequently used in medical imaging systems to test hardware, reconstruction algorithms, and the interpretation of data. This report describes and characterizes the use of powdered graphite as a means of adding a significant reactive component or permittivity to useful phantom media for electrical impedance imaging. The phantom materials produced have usable complex admittivity at the electrical impedance tomography (EIT) frequencies from a few kilohertz to 1 MHz, as measured by our EIT system (ACT4) and by a commercial bioimpedance analyzer (BIS 4000, Xitron). We have also studied a commercial ultrasound coupling gel, which is highly electrically conductive and semisolid but that permits objects to move within it. The mixture of agar–graphite and gel–graphite, increases in permittivity and conductivity are proportional to the graphite concentration. We also report the use of a porous polymer membrane to simulate skin. A thin layer of this membrane increased resistance and the characteristic frequency of the phantoms, providing a promising candidate to simulate the effect of skin and the layered structure of a breast or other anatomical structure. The graphite also provides a realistic level of “speckle” in ultrasound images of the phantom, which may be useful in developing dual-mode imaging systems with ultrasound and the EIT.      

Noninvasive imaging of bioimpedance distribution by means of current reconstruction magnetic resonance electrical impedance tomography

We have developed a novel magnetic resonance electrical impedance tomography (MREIT) algorithm-current reconstruction MREIT algorithm-for noninvasive imaging of electrical impedance distribution of a biological system using only one component of magnetic flux density. The newly proposed algorithm uses the inverse of Biot-Savart Law to reconstruct the current density distribution, and then, uses a modified J-substitution algorithm to reconstruct the conductivity image. A series of computer simulations has been conducted to evaluate the performance of the proposed current reconstruction MREIT algorithm with simulation settings for breast cancer imaging applications, with consideration of measurement noise, current injection strength, size of simulated tumors, spatial resolution, and position dependency. The present simulation results are highly promising, demonstrating the high spatial resolution, high accuracy in conductivity reconstruction, and robustness against noise of the proposed algorithm for imaging electrical impedance of a biological system. The present MREIT method may have potential applications to breast cancer imaging and imaging of other organs.     

Confocal microwave imaging for breast cancer detection: delay-multiply-and-sum image reconstruction algorithm

A new image reconstruction algorithm, termed as delay-multiply-and-sum (DMAS), for breast cancer detection using an ultra-wideband confocal microwave imaging technique is proposed. In DMAS algorithm, the backscattered signals received from numerical breast phantoms simulated using the finite-difference time-domain method are time shifted, multiplied in pair, and the products are summed to form a synthetic focal point. The effectiveness of the DMAS algorithm is shown by applying it to backscattered signals received from a variety of numerical breast phantoms. The reconstructed images illustrate improvement in identification of embedded malignant tumors over the delay-and-sum algorithm. Successful detection and localization of tumors as small as 2 mm in diameter are also demonstrated.