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.     

A quantitative method based on total relative change for dynamic electrical impedance tomography

We proposed a new method based on total relative change (TRC) from measured boundary voltages to quantify the volume changes of fluid during electrical impedance tomography (EIT) monitoring. The results showed that TRC linearly correlated with the volume of infused saline solution into a phantom, and the slope of TRC changes was approximately linear with the infusion speed. A inserted copper tube at different positions did not affect TRC significantly. The linear relationship between TRC and volume change indicates that TRC could be a good quantitative index for dynamic EIT.     

A comparison of techniques to optimize measurement of voltage changes in electrical impedance tomography by minimizing phase shift errors

In electrical impedance tomography, errors due to stray capacitance may be reduced by optimization of the reference phase of the demodulator. Two possible methods, maximization of the demodulator output and minimization of reciprocity error have been assessed, applied to each electrode combination individually, or to all combinations as a whole. Using an EIT system with a single impedance measuring circuit and multiplexer to address the 16 electrodes, the methods were tested on resistor-capacitor networks, saline-filled tanks and humans during variation of the saline concentration of a constant fluid volume in the stomach. Optimization of each channel individually gave less error, particularly on humans, and maximization of the output of the demodulator was more robust. This method is, therefore, recommended to optimize systems and reduce systematic errors with similar EIT systems.     

Temperature dependence of tissue impedivity in electrical impedance tomography of cryosurgery

The temperature-dependent impedivity of rat liver, transverse abdominal muscle and full skin was determined in vitro as a function of frequency across the temperature range 5 degrees C to 37 degrees C and from 100 Hz to 10 kHz. This study was motivated by an increasing interest in using electrical impedance tomography (EIT) for imaging of cryosurgery and a lack of applicable data in the hypothermic range. Using a controlled-temperature impedance analyzer, it was found that as the temperature is reduced the resulting increase in tissue impedivity is more pronounced at low frequencies and that the beta dispersion, resulting from cell membrane polarization, shifts to lower frequencies. With these new data a simple case study of EIT of liver cryosurgery was examined, using a finite-element model incorporating the Pennes bio-heat equation, to determine the impact of this behavior on imaging accuracy. Overestimation of the ice-front position was found to occur if the EIT system ignored the effects of the low-temperature zone surrounding the frozen tissue. This error decreases with increasing blood perfusion and with higher measurement frequencies.     

Finite element modeling of electrode-skin contact impedance inelectrical impedance tomography

In electrical impedance tomography (EIT), the measured voltages are sensitive to electrode-skin contact impedance because the contact impedance and the current density through it are both high. Large electrodes were used to provide a more uniform current distribution and reduce the contact impedance. A large electrode differs from a point electrode in that it has shunting and edge effects that cannot be modeled by a single resistor. The finite-element method (FEM) was used to study the electric field distributions underneath an electrode, and three models were developed: a FEM model, a simplified FEM model, and a weighted load model. The FEM models considered both shunting and edge effects and closely matched the experimental measurements. It is concluded that FEM models of electrodes can be used to improve the performance of an electrical impedance tomography reconstruction algorithm     

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.     

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.     

Estimation of anomaly location and size using electrical impedance tomography

We developed a new algorithm that estimates locations and sizes of anomalies in electrically conducting medium based on electrical impedance tomography (EIT) technique. When only the boundary current and voltage measurements are available, it is not practically feasible to reconstruct accurate high-resolution cross-sectional conductivity or resistivity images of a subject. In this paper, we focus our attention on the estimation of locations and sizes of anomalies with different conductivity values compared with the background tissues. We showed the performance of the algorithm from experimental results using a 32-channel EIT system and saline phantom. With about 1.73% measurement error in boundary current-voltage data, we found that the minimal size (area) of the detectable anomaly is about 0.72% of the size (area) of the phantom. Potential applications include the monitoring of impedance related physiological events and bubble detection in two-phase flow. Since this new algorithm requires neither any forward solver nor time-consuming minimization process, it is fast enough for various real-time applications in medicine and nondestructive testing.     

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     

Cryosurgical monitoring using bioimpedance measurements--a feasibility study for electrical impedance tomography

The effectiveness of cryosurgery in treating tumors is highly dependent on knowledge of freezing extent, and therefore relies heavily on real-time imaging techniques for monitoring. Electrical impedance tomography (EIT), which utilizes tissue impedance variation to construct an image, is very well suited to cryosurgery since frozen tissue impedance is much higher than that of unfrozen tissue. In this study, we explore cryosurgical monitoring as a previously uninvestigated application for EIT. The feasibility of bio-impedance measurements to detect ice front propagation is demonstrated by freezing planar tissue samples one-dimensionally while measuring impedance along a linear array. The experimental results compare favorably to a simple finite element model designed to provide an electrical field visualization tool.     

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。     

EIT forward problem parallel simulation environment with anisotropic tissue and realistic electrode models

Electrical impedance tomography (EIT) is an imaging technology based on impedance measurements. To retrieve meaningful insights from these measurements, EIT relies on detailed knowledge of the underlying electrical properties of the body. This is obtained from numerical models of current flows therein. The nonhomogeneous and anisotropic electric properties of human tissues make accurate modeling and simulation very challenging, leading to a tradeoff between physical accuracy and technical feasibility, which at present severely limits the capabilities of EIT. This work presents a complete algorithmic flow for an accurate EIT modeling environment featuring high anatomical fidelity with a spatial resolution equal to that provided by an MRI and a novel realistic complete electrode model implementation. At the same time, we demonstrate that current graphics processing unit (GPU)-based platforms provide enough computational power that a domain discretized with five million voxels can be numerically modeled in about 30 s.     

J-substitution algorithm in magnetic resonance electrical impedance tomography (MREIT): phantom experiments for static resistivity images

Recently, a new static resistivity image reconstruction algorithm is proposed utilizing internal current density data obtained by magnetic resonance current density imaging technique. This new imaging method is called magnetic resonance electrical impedance tomography (MREIT). The derivation and performance of J-substitution algorithm in MREIT have been reported as a new accurate and high-resolution static impedance imaging technique via computer simulation methods. In this paper, we present experimental procedures, denoising techniques, and image reconstructions using a 0.3-tesla (T) experimental MREIT system and saline phantoms. MREIT using J-substitution algorithm effectively utilizes the internal current density information resolving the problem inherent in a conventional EIT, that is, the low sensitivity of boundary measurements to any changes of internal tissue resistivity values. Resistivity images of saline phantoms show an accuracy of 6.8%-47.2% and spatial resolution of 64 x 64. Both of them can be significantly improved by using an MRI system with a better signal-to-noise ratio.     

Propagation of measurement noise through backprojection reconstruction in electrical impedance tomography

A framework to analyze the propagation of measurement noise through backprojection reconstruction algorithms in electrical impedance tomography (EIT) is presented. Two measurement noise sources were considered: noise in the current drivers and in the voltage detectors. The influence of the acquisition system architecture (serial/semi-parallel) is also discussed. Three variants of backprojection reconstruction are studied: basic (unweighted), weighted and exponential backprojection. The results of error propagation theory have been compared with those obtained from simulated and experimental data. This comparison shows that the approach provides a good estimate of the reconstruction error variance. It is argued that the reconstruction error in EIT images obtained via backprojection can be approximately modeled as a spatially nonstationary Gaussian distribution. This methodology allows us to develop a spatial characterization of the reconstruction error in EIT images.     

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.     

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.     

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.      

Time-harmonic impedance tomography using the T-matrix method

A time-harmonic formulation for the electrical impedance tomography (EIT) inverse problem accounting for electrodynamic effects is derived. This work abandons the standard electrostatic impedance model for a full-wave T-matrix model. The advantage of this method is an accurate physical model that includes finite frequency effects, such as diffusion phenomena, and electrode contact impedance effects. This model offers the potential for increased resolution and larger invertible contrast objects than other methods when used on experimental data, because it may represent a more realistic physical model. Also, an accurate gradient matrix is used in the Newton iterative method so the image reconstruction converges in a few iterations. These advantages are realized with no increase in the computational complexity of this algorithm, compared to the static finite element model. A calibration technique is suggested for measurement systems, to test the validity of a theoretical model that includes electrode contact impedance effects.     

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.     

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