Electrical impedance tomography using induced currents

The mathematical basis of a new imaging modality, induced current electrical impedance tomography (EIT), is investigated, The ultimate aim of this technique is the reconstruction of conductivity distribution of the human body, from voltage measurements made between electrodes placed on the surface, when currents are induced inside the body by applied time varying magnetic fields. In this study the two-dimensional problem is analyzed. A specific 9-coil system for generating nine different exciting magnetic fields (50 kHz) and 16 measurement electrodes around the object are assumed, The partial differential equation for the scaler potential function in the conductive medium is derived and finite element method (FEM) is used for its solution. Sensitivity matrix, which relates the perturbation in measurements to the conductivity perturbations, is calculated. Singular value decomposition of the sensitivity matrix shows that there are 135 independent measurements. It is found that measurements are less sensitive to changes in conductivity of the object's interior. While in this respect induced current EIT is slightly inferior to the technique of injected current EIT (using Sheffield protocol), its sensitivity matrix is better conditioned. The images obtained are found to be comparable to injected current EIT images In resolution. Design of a coil system for which parameters such as sensitivity to inner regions and condition number of the sensitivity matrix are optimum, remains to be made.     

Optimum Receiver Array Design for Magnetic Induction Tomography

Magnetic induction tomography (MIT) is an imaging modality that aims at mapping the distribution of the electrical conductivity inside the body. Eddy currents are induced in the body by magnetic induction and the resulting fields are measured by an array of receiver coils. In MIT, the location of the receivers affects the quality of the image reconstruction. In this paper, a fast deterministic algorithm was applied to obtain optimum receiver array designs for a given specific excitation. The design strategy is based on the iterative exclusion of receiver locations, which yield poor conductivity information, from the space spanning all possible locations until a feasible design is reached. The applicability of “regionally focused” MIT designs that increase the image resolution at a particular region was demonstrated. Currently used design geometries and the corresponding reconstructed images were compared to the images obtained by optimized designs. The eigenvalue analysis of the Hessian matrix showed that the algorithm tends to maintain identical conductivity information content sensed by the receivers. Although the method does not guarantee finding the optimum design globally, the results demonstrate the practical usability of this algorithm in MIT experimental designs.      

Electromagnetic impedance tomography (EMIT): a new method for impedance imaging

We propose a new impedance imaging method, electromagnetic impedance tomography (EMIT), in which the boundary electric potential measurements in electrical impedance tomography (EIT) are augmented by measurements of the exterior magnetic field induced by the currents excited in the object by the standard EIT procedures. These magnetic measurements can be obtained reliably and inexpensively by simple pickup coils located around the imaged cross section. We derive expressions for the forward problem and for the Jacobian of the measurements, and propose an iterative reconstruction algorithm using a squared error cost function. The performance of EMIT and EIT is compared in numerical simulations using a finite-element model for the conductivity distribution of several phantoms. Evaluation of the rank and condition of the Jacobian demonstrates that the additional magnetic measurements provided by a few pickup coils in EMIT turn an underdetermined EIT problem into a well-posed one with reasonable condition, or significantly improve the conditioning of the EIT problem when it is already fully determined. Reconstructions of various phantoms reveal that EMIT provides particularly significant visual and quantitative improvement (threefold to tenfold reduction in the root-mean-squared error) in the sensitivity at the center of the object, which is the area most difficult to image using EIT.     

电阻抗成像的修正阻尼最小二乘重建算法

本文给出了一种新的电阻抗成像的图像重建算法,该算法是对Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ类算法的改进。算法根据 目标函数的分析,将以前常用的,对正规方程组的求解。转化为 解一个条件数更好的超定方程组的最小二乘解。理论分析和数值试验都表明,这种新的重建算法较常用的Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ类算法,不仅数值稳定性有较大的提高,而且计算量有所减少,同时这种算法也适用于其他最小二乘问题的求解。     

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.     

Statistical estimation of resistance/conductance by electrical impedance tomography measurements

This paper is built upon the assumption that in electrical impedance tomography, vectors of voltages and currents are linearly dependent through a resistance matrix. This linear relationship was confirmed experimentally and may be derived analytically under certain assumptions regarding electrodes (Isaacson, 1991). Given measurement data consisting of voltages and currents, we treat this relationship as a linear statistical model. Thus, our goal is not to reconstruct the image but directly estimate its electromagnetic properties reflected in the resistance and/or conductance matrix using electrical impedance tomography (EIT) measurements of voltages and currents on the periphery of the body. Since no inverse problem is involved the algorithm for estimation merely reduces to one matrix inversion. We estimate the impedance resistance matrix using well established statistical inference techniques for linear regression models. We provide a comprehensive treatment for a two-dimensional homogeneous body of a circular shape, by which many concepts of electrical impedance tomography, such as width of electrodes, the difference between voltage-current and current-voltage systems are illustrated. Our theory may be applied to various tests including EIT hardware calibration and whether the medium is homogeneous. These tests are illustrated on phantom agar data.     

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.     

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     

Finite element implementation of Maxwell's equations for image reconstruction in electrical impedance tomography

Traditionally, image reconstruction in electrical impedance tomography (EIT) has been based on Laplace's equation. However, at high frequencies the coupling between electric and magnetic fields requires solution of the full Maxwell equations. In this paper, a formulation is presented in terms of the Maxwell equations expressed in scalar and vector potentials. The approach leads to boundary conditions that naturally align with the quantities measured by EIT instrumentation. A two-dimensional implementation for image reconstruction from EIT data is realized. The effect of frequency on the field distribution is illustrated using the high-frequency model and is compared with Laplace solutions. Numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation. The results show that scalar/vector potential reconstruction produces images which are essentially indistinguishable from a Laplace algorithm for frequencies below 1 MHz but superior at frequencies reaching 10 MHz.     

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.     

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.     

A Kalman filter approach to track fast impedance changes inelectrical impedance tomography

In electrical impedance tomography (EIT), an estimate for the cross-sectional impedance distribution is obtained from the body by using current and voltage measurements made from the boundary. All well-known reconstruction algorithms use a full set of independent current patterns for each reconstruction. In some applications, the impedance changes may be so fast that information on the time evolution of the impedance distribution is either lost or severely blurred. Here, the authors propose an algorithm for EIT reconstruction that is able to track fast changes in the impedance distribution. The method is based on the formulation of EIT as a state-estimation problem and the recursive estimation of the state with the aid of the Kalman filter. The performance of the proposed method is evaluated with a simulation of human thorax in a situation in which the impedances of the ventricles change rapidly. The authors show that with optimal current patterns and proper parameterization, the proposed approach yields significant enhancement of the temporal resolution over the conventional reconstruction strategy     

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.     

基于自适应并行结构的多模态生物特征识别

传统多模态生物特征识别方法当出现生物特征缺失时,识别性能会明显下降。针对此问题,提出一种融合人脸、虹膜和掌纹的自适应并行结构多模态生物识别方法。该方法在设计融合策略时,考虑到所有可能的输入缺失,构造并行结构的融合函数集,在实际应用时根据输入状态自适应的选择融合策略进行识别。实验仿真结果表明该方法既可提高识别可靠性又可实现当有生物特征缺失时的性能稳定。     

四探针和EIT测试微区薄层电阻的研究与进展

论述了一种测试大型硅片电阻率均匀性的新方法——电阻抗成像技术（EIT）。给出了四探针的基本原理,指出EIT的基本思想来源于四探针技术。对EIT的基本原理和重建算法在理论上进行了描述．提出可将其应用于微区薄层电阻测试,并对EIT在大型硅片微区薄层电阻率均匀性测试技术上的系统应用做了进一步探索。     

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.     

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.     

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.     

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