Measurement of ion diffusion using magnetic resonance electrical impedance tomography

In magnetic resonance electrical impedance tomography (MREIT), currents are applied to an object, the resulting magnetic flux density measured using MRI and the conductivity distribution reconstructed using these MRI data. In this study, we assess the ability of MREIT to monitor changes in the conductivity distribution of an agarose gel phantom, using injected current pulses of 900 microA. The phantom initially contained a distinct region of high sodium chloride concentration which diffused into the background over time. MREIT data were collected over a 12 h span, and conductivity images were reconstructed using the iterative sensitivity matrix method with Tikhonov regularization. The results indicate that MREIT was able to monitor the changing conductivity and concentration distributions resulting from the diffusion of ions within the agarose gel phantom.     

磁共振电阻抗成像方法的研究进展

磁共振电阻抗成像方法是传统电阻抗成像和磁共振成像的结合，是一种新的电阻抗成像方法。按照电阻抗测量激励器与接收器的不同，可将其划分为接触式和非接触式两种。应用磁共振电阻抗成像方法可以获得高分辨率、高精度的电阻抗图像，对临床辅助诊断具有重要意义。对磁共振电阻抗成像方法的两种形式及其发展前景给予综述。     

Equipotential projection-based magnetic resonance electrical impedance tomography and experimental realization

In this study, a direct, fast image reconstruction algorithm, based on the fact that equipotential lines are perpendicular to current lines in a volume conductor, is proposed for magnetic resonance electrical impedance tomography (MR-EIT). The proposed technique is evaluated both on simulated and measured data for conductor and insulator objects.     

一维感应式磁共振电阻抗成像重建方法研究

对一维感应式的磁共振电阻抗成像技术进行原理性研究.针对同心圆盘模型推导了正问题的计算方法及逆问题的重建原理公式,通过仿真分析验证重建方法的正确性,并考察了该方法的抗噪性能.将为进一步研究感应式磁共振电阻抗成像技术的原理及实践提供理论基础.     

Experimental results for 2D magnetic resonance electrical impedance tomography (MR-EIT) using magnetic flux density in one direction

Magnetic resonance electrical impedance tomography (MR-EIT) is an emerging imaging technique that reconstructs conductivity images using magnetic flux density measurements acquired employing MRI together with conventional EIT measurements. In this study, experimental MR-EIT images from phantoms with conducting and insulator objects are presented. The technique is implemented using the 0.15 T Middle East Technical University MRI system. The dc current method used in magnetic resonance current density imaging is adopted. A reconstruction algorithm based on the sensitivity matrix relation between conductivity and only one component of magnetic flux distribution is used. Therefore, the requirement for object rotation is eliminated. Once the relative conductivity distribution is found, it is scaled using the peripheral voltage measurements to obtain the absolute conductivity distribution. Images of several insulator and conductor objects in saline filled phantoms are reconstructed. The L2 norm of relative error in conductivity values is found to be 13%, 17% and 14% for three different conductivity distributions.     

Phase artefact reduction in magnetic resonance electrical impedance tomography (MREIT)

Cross-sectional conductivity imaging in magnetic resonance electrical impedance tomography (MREIT) requires the measurement of internal magnetic flux density using an MRI scanner. Current injection MRI techniques have been used to induce magnetic flux density distributions that appear in phase parts of the obtained MR signals. Since any phase error, as well as noise, deteriorates the quality of reconstructed conductivity images, we must minimize them during the data acquisition process. In this paper, we describe a new method to correct unavoidable phase errors to reduce artefacts in reconstructed conductivity images. From numerical simulations and phantom experiments, we found that the zeroth- and first-order phase errors can be effectively minimized to produce better conductivity images. The promising results suggest that this technique should be employed together with improved MREIT pulse sequences in future studies of high-resolution conductivity imaging.     

Three-dimensional forward solver and its performance analysis for magnetic resonance electrical impedance tomography (MREIT) using recessed electrodes

In magnetic resonance electrical impedance tomography (MREIT), we try to reconstruct a cross-sectional resistivity (or conductivity) image of a subject. When we inject a current through surface electrodes, it generates a magnetic field. Using a magnetic resonance imaging (MRI) scanner, we can obtain the induced magnetic flux density from MR phase images of the subject. We use recessed electrodes to avoid undesirable artefacts near electrodes in measuring magnetic flux densities. An MREIT image reconstruction algorithm produces cross-sectional resistivity images utilizing the measured internal magnetic flux density in addition to boundary voltage data. In order to develop such an image reconstruction algorithm, we need a three-dimensional forward solver. Given injection currents as boundary conditions, the forward solver described in this paper computes voltage and current density distributions using the finite element method (FEM). Then, it calculates the magnetic flux density within the subject using the Biot-Savart law and FEM. The performance of the forward solver is analysed and found to be enough for use in MREIT for resistivity image reconstructions and also experimental designs and validations. The forward solver may find other applications where one needs to compute voltage, current density and magnetic flux density distributions all within a volume conductor.     

Basic principles of magnetic resonance imaging

With rapid progress in MR imaging techniques, it has now become one of the important clinical imaging techniques. In this paper, the basic principles of NMR and MR imaging techniques are briefly described. Furthermore, the technical background of principal MR imaging techniques such as the spin-echo, gradient-echo, fast spin-echo and ultra-fast MR imaging technique is reviewed. The principles of proton density-, T1- and T2-weighted contrast images are also described. Finally, the technical background of functional MR imaging is briefly reviewed and the typical fMR image obtained by activation of motor cortex with finger tapping is presented.     

A new magnetic resonance electrical impedance tomography (MREIT) algorithm: the RSM-MREIT algorithm with applications to estimation of human head conductivity

We have developed a new magnetic resonance electrical impedance tomography (MREIT) algorithm, the RSM-MREIT algorithm, for noninvasive imaging of the electrical conductivity distribution using only one component of magnetic flux density. The proposed RSM-MREIT algorithm uses the response surface methodology (RSM) algorithm for optimizing the conductivity distribution through minimizing the errors between the measured and calculated magnetic flux densities. A series of computer simulations has been conducted to assess the performance of the proposed RSM-MREIT algorithm to estimate electrical conductivity values of the scalp, the skull and the brain tissue, in a three-shell piecewise homogeneous head model. Computer simulation studies were conducted in both a spherical and realistic-geometry head model with a single variable (the brain-to-skull conductivity ratio) and three variables (the conductivity of the brain, the skull, and the scalp). The relative error between the target and estimated head conductivity values was less than 12% for both the single-variable and three-variable simulations. These promising simulation results demonstrate the feasibility of the proposed RSM-MREIT algorithm in estimating electrical conductivity values in a piecewise homogeneous head model of the human head, and suggest that the RSM-MREIT algorithm merits further investigation.     

电流密度成像及其在生物电阻抗成像中的应用

本文首先介绍了生物电阻抗成像(electrical impedance tomography,EIT)的数学模型、系统设计、算法分类及其存在的问题。然后介绍了由加拿大Toronto大学的Joy、Scott等人提出的电流密度成像(current density imaging,CDI)的基本原理及发展现状,提出将CDI应用到EIT可以得到精确度与分辨率都较高的阻抗图像及实现的基本思路。最后讨论了将CDI应用到EIT的发展前景及需要解决的问题。     

Design of an electrical impedance tomography phantom using active elements

The architecture of a novel phantom for electrical impedance tomography (EIT) is proposed. The design employs active elements, which include multiplying digital to analogue converters (MDAC), so that the impedance distribution in the phantom may be varied dynamically using computer control. The phantom is designed to assist in the validation of an EIT system under test. A number of published layouts for passive phantoms are analysed, and the requirements for an active element are specified for the most applicable of these. The use of active elements throughout a phantom imposes significant costs because of the need for each active element to operate independently. This proposal limits the cost and complexity by employing active elements in a restricted region of the phantom. Currently available technology, principally due to the limited analogue bandwidth of the MDAC, precludes the construction of a fully capable phantom from active elements. However, a design is specified that would enable its future development to cover the frequency range from 10kHz to 1 MHz.     

一种基于频谱约束的多频动态电阻抗断层成像算法

本文旨在提出一种基于频谱约束的多频动态电阻抗断层成像(EIT)算法。在已知成像域内各组分电导率频谱的情况下,通过重构独立于频率的参数——体积分数变化,同时利用多个激励频率下的测量电压差重构一帧时差图像,从而大大增加测量数据量以改善逆问题的病态性。数值仿真实验显示,该算法较传统阻尼最小二乘算法具有更小的图像伪影,且在低信噪比情形下具有更小的位置误差和形变误差。本研究有望为动态EIT提供一种有效利用多频信息的方法,并为在已知各组分电导率频谱情况下的动态EIT发展提供一个新思路。     

Cell tracking using magnetic resonance imaging

Cell tracking by in vivo magnetic resonance imaging (MRI) requires strategies of labelling the cells with MRI contrast agents. The principal routes to achieve efficient cell labelling for neurological applications are discussed with methodological advantages and caveats. Beyond temporo-spatial localization of labelled cells, the investigation of functional cell status is of great interest to allow studies of functional cell dynamics. The two major approaches to reach this goal, use of responsive contrast agents and generation of transgenic cell lines, are discussed.     

Detection of breast abnormalities using a prototype resonance electrical impedance spectroscopy system: a preliminary study

Electrical impedance spectroscopy has been investigated with but limited success as an adjunct procedure to mammography and as a possible pre-screening tool to stratify risk for having or developing breast cancer in younger women. In this study, the authors explored a new resonance frequency based [resonance electrical impedance spectroscopy (REIS)] approach to identify breasts that may have highly suspicious abnormalities that had been recommended for biopsies. The authors assembled a prototype REIS system generating multifrequency electrical sweeps ranging from 100 to 4100 kHz every 12 s. Using only two probes, one in contact with the nipple and the other with the outer breast skin surface 60 mm away, a paired transmission signal detection system is generated. The authors recruited 150 women between 30 and 50 years old to participate in this study. REIS measurements were performed on both breasts. Of these women 58 had been scheduled for a breast biopsy and 13 had been recalled for additional imaging procedures due to suspicious findings. The remaining 79 women had negative screening examinations. Eight REIS output signals at and around the resonance frequency were computed for each breast and the subtracted signals between the left and right breasts were used in a simple jackknifing method to select an optimal feature set to be inputted into a multi-feature based artificial neural network (ANN) that aims to predict whether a woman's breast had been determined as abnormal (warranting a biopsy) or not. The classification performance was evaluated using a leave-one-case-out method and receiver operating characteristics (ROC) analysis. The study shows that REIS examination is easy to perform, short in duration, and acceptable to all participants in terms of comfort level and there is no indication of sensation of an electrical current during the measurements. Six REIS difference features were selected as input signals to the ANN. The area under the ROC curve (A(z)) was 0.707 +/- 0.033 for classifying between biopsy cases and non-biopsy (including recalled and screening negative) and the performance (A(z)) increased to 0.746 +/- 0.033 after excluding recalled but negative cases. At 95% specificity, the sensitivity levels were approximately 20.5% and 30.4% in the two data sets tested. The results suggest that differences in REIS signals between two breasts measured in and around the tissue resonance frequency can be used to identify at least some of the women with suspicious abnormalities warranting biopsy with high specificity.     

影响生物电阻抗断层成像质量的因素

由于成像质量较差,限制了生物电阻抗断层成像技术的临床应用,本文在介绍生物电阻抗断层成像研究概况的基础上,指出了影响成像质量的主要问题是成像过程中的病态性问题,并讨论了形成病态性的主要因素是：（1）驱动测量模式,（2）重构模型;（3）图像重构算法。     

Multi-frequency static imaging in electrical impedance tomography: Part 1 instrumentation requirements

Static images of the human body using electrical impedance tomography techniques can be obtained by measuring at two or more different frequencies. The frequencies used depend on the application, and their selection depends on the frequency behaviour of the impedance for the target tissue. An analysis using available data and theoretical models for tissue impedance yields the expected impedance and boundary voltage changes, therefore setting the measurement instrument specifications. The instrument errors produced by different sources are analysed, and, from this analysis it is possible to determine the feasibility of building the instrument, the limit values for some parameters (or components) and indications on the most suitable design of critical parts. This analysis also shows what kinds of error can be expected in the reconstructed images. It is concluded that it is possible to build an instrument with limited errors, allowing static images to be obtained. An instrument has been built that meets some of the design requirements and fails in others because of technological problems. In vivo images obtained with this instrument will be presented in Part 2 of this work.     

A dual-frequency electrical impedance tomography system

An electrical impedance tomography (EIT) system has been constructed, operating at two frequencies, 40.96 and 81.92 kHz, for investigating the practicability of the dual-frequency imaging method discussed theoretically in a previous paper. For testing the system, a phantom with a frequency-dependent electrical conductivity was designed. The properties of the phantom can be adjusted to match the frequency dependence observed in a given type of tissue. Dual-frequency images were obtained from a phantom simulating liver and also from 200 g of porcine liver in a saline tank. Prior to image reconstruction, it was necessary to apply a correction to the data to cancel the effects of stray capacitance within the electronics.