Reconstruction of conductivity using the dual-loop method with one injection current in MREIT

Magnetic resonance electrical impedance tomography (MREIT) is to visualize the internal current density and conductivity of an electrically conductive object. Injecting current through surface electrodes, we measure one component of the induced internal magnetic flux density using an MRI scanner. In order to reconstruct the conductivity distribution inside the imaging object, most algorithms in MREIT have required multiple magnetic flux density data by injecting at least two independent currents. In this paper, we propose a direct method to reconstruct the internal isotropic conductivity with one component of magnetic flux density data by injecting one current into the imaging object through a single pair of surface electrodes. Firstly, the proposed method reconstructs a projected current density which is a uniquely determined current from the measured one-component magnetic flux density. Using a relation between voltage potential and current, based on Kirchhoff's voltage law, the proposed method is designed to use a combination of two loops around each pixel from which to derive an implicit matrix system for determination of the internal conductivity. Results from numerical simulations demonstrate that the proposed algorithm stably determines the conductivity distribution in an imaging slice. We compare the reconstructed internal conductivity distribution using the proposed method with that using a conventional method with agarose gel phantom experiments.     

Analytical solutions of electric potential and impedance for a multilayered spherical volume conductor excited by time-harmonic electric current source: application in brain EIT

A model of a multilayered spherical volume conductor with four electrodes is built. In this model, a time-harmonic electric current is injected into the sphere through a pair of drive electrodes, and electric potential is measured by the other pair of measurement electrodes. By solving the boundary value problem of the electromagnetic field, the analytical solutions of electric potential and impedance in the whole conduction region are derived. The theoretical values of electric potential on the surface of the sphere are in good accordance with the experimental results. The analytical solutions are then applied to the simulation of the forward problem of brain electrical impedance tomography (EIT). The results show that, for a real human head, the imaginary part of the electric potential is not small enough to be ignored at above 20 kHz, and there exists an approximate linear relationship between the real and imaginary parts of the electric potential when the electromagnetic parameters of the innermost layer keep unchanged. Increase in the conductivity of the innermost layer leads to a decrease of the magnitude of both real and imaginary parts of the electric potential on the scalp. However, the increase of permittivity makes the magnitude of the imaginary part of the electric potential increase while that of the real part decreases, and vice versa.     

The potential induced in anisotropic tissue by the ultrasonically-induced Lorentz force

In the presence of a magnetic field, an ultrasonic wave propagating through tissue will induce Lorentz forces on the ions, resulting in an electrical current. If the electrical conductivity is anisotropic, this current is tilted toward the fiber direction, causing charge to accumulate between half-wavelengths: positive charge where the current vectors converge and negative where the current vectors diverge. This charge produces an electric field in the direction of propagation that is associated with an electrical potential, and this electric field causes an additional current that is also tilted by the anisotropy. The final result is the total current pointing perpendicular to the direction of propagation and a charging of the tissue every half wavelength. The potential has a greater magnitude than that obtained from colloidal suspensions or ionic solutions (ultrasonic vibration potentials) and may be used as the basis of a technique to image conductivity.     

多通道电阻抗方法胃动力测量机制研究

建立多通道电阻抗信号与胃收缩传导过程的关系,明确生物电阻抗方法检测胃动力的测量机制。应用COMSOL软件建立圆柱容积导体模型,模拟胃环行肌收缩传导过程,进行电磁场正问题仿真计算,获取边界测量电压波形。设计专用实验装置,制作了不同电导率的三层琼脂模型,模拟胃部和胃收缩扰动,完成盐水槽动态模拟实验。仿真研究结果表明,轴向和径向激励模式下,边界测量电压波形清晰显示了胃收缩发生的部位及传导过程,相邻通道间存在明显的相位差。模拟实验结果中,对于电导率为1.35 S/m的被测琼脂模型,轴向激励模式各测量通道出现双波谷的时间差约为9 s;径向激励模式各测量通道出现双波谷的时间差约为6 s,与各测量通道的电极安放位置和间距正好相对应。胃内容物为高电导率和低电导率情况下,边界电压波形的变化趋势相同,方向相反。参数δ,〖AKU-〗和U_max/U_min定量评价结果表明,靠近激励电极的测量通道,电压敏感性和均值较高。多个通道测量的电阻抗信号,能够有效地反映胃内容物电导率的变化、胃不同部位的收缩、以及胃运动传导的时相关系。     

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.     

Regional absolute conductivity reconstruction using projected current density in MREIT

Magnetic resonance electrical impedance tomography (MREIT) is a non-invasive technique for imaging the internal conductivity distribution in tissue within an MRI scanner, utilizing the magnetic flux density, which is introduced when a current is injected into the tissue from external electrodes. This magnetic flux alters the MRI signal, so that appropriate reconstruction can provide a map of the additional z-component of the magnetic field (B(z)) as well as the internal current density distribution that created it. To extract the internal electrical properties of the subject, including the conductivity and/or the current density distribution, MREIT techniques use the relationship between the external injection current and the z-component of the magnetic flux density B = (B(x), B(y), B(z)). The tissue studied typically contains defective regions, regions with a low MRI signal and/or low MRI signal-to-noise-ratio, due to the low density of nuclear magnetic resonance spins, short T(2) or T*(2) relaxation times, as well as regions with very low electrical conductivity, through which very little current traverses. These defective regions provide noisy B(z) data, which can severely degrade the overall reconstructed conductivity distribution. Injecting two independent currents through surface electrodes, this paper proposes a new direct method to reconstruct a regional absolute isotropic conductivity distribution in a region of interest (ROI) while avoiding the defective regions. First, the proposed method reconstructs the contrast of conductivity using the transversal J-substitution algorithm, which blocks the propagation of severe accumulated noise from the defective region to the ROI. Second, the proposed method reconstructs the regional projected current density using the relationships between the internal current density, which stems from a current injection on the surface, and the measured B(z) data. Combining the contrast conductivity distribution in the entire imaging slice and the reconstructed regional projected current density, we propose a direct non-iterative algorithm to reconstruct the absolute conductivity in the ROI. The numerical simulations in the presence of various degrees of noise, as well as a phantom MRI imaging experiment showed that the proposed method reconstructs the regional absolute conductivity in a ROI within a subject including the defective regions. In the simulation experiment, the relative L(2)-mode errors of the reconstructed regional and global conductivities were 0.79 and 0.43, respectively, using a noise level of 50 db in the defective region.     

深部组织热物理参数的测量及其结果分析

本文阐述了用热干扰法测量机体组织热物性参数和灌注率的实现过程：把热敏电阻探头插入所需测量的组织，给热敏电阻供应电能使其温度升高达到预定值，所需电功率的大小与组织的热物性和血液灌注有关，通过建立热敏电阻珠和测量介质的耦合数学模型，得到计算导热率、扩散率和血液灌的表达式。本文首先用这种方法测量液体介质和离体介质的导热率来验证测量系统的准确性，然后用流动的液体模拟活体组织来测量流动介质的导热率和灌注率。实验结果表明：液体实验结果和离体实验结果与文献基本一致，流动液体的实验结果和我们的分析也完全吻合。     

Measurement of bioelectric and acoustic profile of breast tissue using hybrid magnetoacoustic method for cancer detection

This paper proposes a novel hybrid magnetoacoustic measurement (HMM) system aiming at breast cancer detection. HMM combines ultrasound and magnetism for the simultaneous assessment of bioelectric and acoustic profiles of breast tissue. HMM is demonstrated on breast tissue samples, which are exposed to 9.8 MHz ultrasound wave with the presence of a 0.25 Tesla static magnetic field. The interaction between the ultrasound wave and the magnetic field in the breast tissue results in Lorentz Force that produces a magnetoacoustic voltage output, proportional to breast tissue conductivity. Simultaneously, the ultrasound wave is sensed back by the ultrasound receiver for tissue acoustic evaluation. Experiments are performed on gel phantoms and real breast tissue samples harvested from laboratory mice. Ultrasound wave characterization results show that normal breast tissue experiences higher attenuation compared with cancerous tissue. The mean magnetoacoustic voltage results for normal tissue are lower than that for the cancerous tissue group. In conclusion, the combination of acoustic and bioelectric measurements is a promising approach for breast cancer diagnosis.     

Conductivity imaging with low level current injection using transversal J-substitution algorithm in MREIT

An aim of magnetic resonance electrical impedance tomography (MREIT) is to visualize the internal current density and conductivity of the electrically imaged object by injecting current through electrodes attached to it. Due to a limited amount of injection current, one of the most important factors in MREIT is how to control the noise contained in the measured magnetic flux density data. This paper describes a new iterative algorithm called the transversal J-substitution algorithm which is robust to measured noise. As a result, the proposed transversal J-substitution algorithm considerably improves the quality of the reconstructed conductivity image under a low injection current. The relation between the reconstructed contrast of conductivity and the measured noise in the magnetic flux density is analyzed. We show that the contrast of first update of the conductivity with a homogeneous initial guess using the proposed algorithm has sufficient distinguishability to detect the anomaly. Results from numerical simulations demonstrate that the transversal J-substitution algorithm is robust to the noise. For practical implementations of MREIT, we tested real experiments in an agarose gel phantom using low current injection with amplitudes 1 mA and 5 mA to reconstruct the interior conductivity distribution.     

Reproductive integrity of mammalian cells exposed to power frequency electromagnetic fields

Human lymphocytes and Chinese hamster ovary (CHO) fibroblasts were analyzed for cytogenetic and cytotoxic endpoints to determine whether exposure to power frequency (60 Hz) electromagnetic fields (EMF) interferes with normal cell growth and reproduction. An exposure chamber was built to apply variable electric current densities of 3, 30, 300, and 3,000 microA/cm2, simultaneously with a fixed magnetic field of 2.2 G to proliferating cells. The current densities were chosen to bracket those that may be induced in the human body by fields measured beneath high voltage (765 kV) power transmission lines. The electric current was applied through the media of a cell culture chamber positioned between two stainless steel electrodes but separated from direct contact with the culture media by a salt bridge composed of a 1% agarose gel. The magnetic field was generated using two pairs of Helmholtz coils driven 73 degrees out of phase producing an elliptically polarized magnetic field 36 degrees out of phase with the electric field. The EMFs were measured and mapped inside the cell culture chamber to insure their uniformity. CHO cells were exposed continuously for 24-96 hr (depending on experiment) and human lymphocytes were exposed continuously for 72 hr. The EMFs were monitored throughout the entire treatment period using a multichannel chart recorder to verify continuous application of the desired fields. Sister-chromatid exchange and micronuclei were monitored to evaluate the potential for genotoxicity. In addition, standard growth curves, clonogenicity, and cell cycle kinetics were analyzed to evaluate possible cytotoxic effects. The experimental data consistently showed that the growth rate and reproductive integrity of both cell types was unaffected by exposure to the electromagnetic fields.     

基于头部组织不同电导率特性的阻抗成像正问题仿真研究

目的 通过建立5层有限元真实头模型,研究了各层组织非均质和颅骨、脑白质各向异性电特性对电阻抗成像问题中电磁场分布的影响.方法 对头部各组织建立4种电导率分布模型:均质分布、非均质分布以及颅骨和脑白质各向异性电导率模型;通过正问题数值求解得到不同模型下的磁场分布和电场分布,并通过定量的统计分析研究非均质和各向异性电导率特...     

Image reconstruction of anisotropic conductivity tensor distribution in MREIT: computer simulation study

We describe a novel method of reconstructing images of an anisotropic conductivity tensor distribution inside an electrically conducting subject in magnetic resonance electrical impedance tomography (MREIT). MREIT is a recent medical imaging technique combining electrical impedance tomography (EIT) and magnetic resonance imaging (MRI) to produce conductivity images with improved spatial resolution and accuracy. In MREIT, we inject electrical current into the subject through surface electrodes and measure the z-component Bz of the induced magnetic flux density using an MRI scanner. Here, we assume that z is the direction of the main magnetic field of the MRI scanner. Considering the fact that most biological tissues are known to have anisotropic conductivity values, the primary goal of MREIT should be the imaging of an anisotropic conductivity tensor distribution. However, up to now, all MREIT techniques have assumed an isotropic conductivity distribution in the image reconstruction problem to simplify the underlying mathematical theory. In this paper, we firstly formulate a new image reconstruction method of an anisotropic conductivity tensor distribution. We use the relationship between multiple injection currents and the corresponding induced Bz data. Simulation results show that the algorithm can successfully reconstruct images of anisotropic conductivity tensor distributions. While the results show the feasibility of the method, they also suggest a more careful design of data collection methods and data processing techniques compared with isotropic conductivity imaging.     

Vertical electric field stimulated neural cell functionality on porous amorphous carbon electrodes

We demonstrate the efficacy of amorphous macroporous carbon substrates as electrodes to support neuronal cell proliferation and differentiation in electric field mediated culture conditions. The electric field was applied perpendicular to carbon substrate electrode, while growing mouse neuroblastoma (N2a) cells in vitro. The placement of the second electrode outside of the cell culture medium allows the investigation of cell response to electric field without the concurrent complexities of submerged electrodes such as potentially toxic electrode reactions, electro-kinetic flows and charge transfer (electrical current) in the cell medium. The macroporous carbon electrodes are uniquely characterized by a higher specific charge storage capacity (0.2 mC/cm²) and low impedance (3.3 kΩ at 1 kHz). The optimal window of electric field stimulation for better cell viability and neurite outgrowth is established. When a uniform or a gradient electric field was applied perpendicular to the amorphous carbon substrate, it was found that the N2a cell viability and neurite length were higher at low electric field strengths (≤2.5 V/cm) compared to that measured without an applied field (0 V/cm). While the cell viability was assessed by two complementary biochemical assays (MTT and LDH), the differentiation was studied by indirect immunostaining. Overall, the results of the present study unambiguously establish the uniform/gradient vertical electric field based culture protocol to either enhance or to restrict neurite outgrowth respectively at lower or higher field strengths, when neuroblastoma cells are cultured on porous glassy carbon electrodes having a desired combination of electrochemical properties.     

Measurement of electric fields due to time-varying magnetic field gradients using dipole probes

The operation of dipole probes in measuring electric fields in conductive media exposed to temporally varying magnetic fields is discussed. The potential measured by the probe can be thought of as originating from two contributions to the electric field, namely the gradient of the scalar electric potential and the temporal derivative of the magnetic vector potential. Using this analysis, it is shown that the exact form of the wire paths employed when using electric field probes to measure the effects of temporally varying magnetic fields is very important and this prediction is verified via simple experiments carried out using different probe geometries in a cylindrical sample exposed to a temporally varying, uniform magnetic field. Extending this work, a dipole probe has been used to measure the electric field induced in a cylindrical sample by gradient coils as used in magnetic resonance imaging (MRI). Analytic solutions for the electric field in an infinite cylinder are verified by comparison with experimental measurements. Deviations from the analytic solutions of the electric field for the x-gradient coil due to the finite length of the sample cylinder are also demonstrated.     

Model of electrical conductivity of skeletal muscle based on tissue structure

Recent experiments carried out in our laboratory with the four-electrode method showed that the electrical conductivity of skeletal muscle tissue depends on the frequency of the injected current and the distance between the current electrodes. A model is proposed in order to study these effects. The model takes into account the structure of the tissue on the scale of individual fibres. It discerns three main components with respect to electrical properties: (a) extracellular medium with electrical conductivity σ_e; (b) intracellular medium with electrical conductivity σ_i; (c) muscle fibre membrane with impedance Z_m. The model results show an apparent frequency dependence of the electrical conductivity of skeletal muscle tissue, as well as the way the conductivity is affected by the length the current is conducted.     

A primary current distribution model of a novel micro-electroporation channel configuration

Traditional macro and micro-electroporation devices utilize facing electrodes, which generate electric fields inversely proportional to their separation distance. Although the separation distances in micro-electroporation devices are significantly smaller than those in macro-electroporation devices, they are limited by cell size. Because of this, significant potential differences are required to induce electroporation. These potential differences are often large enough to cause water electrolysis, resulting in electrode depletion and bubble formation, both of which adversely affect the electroporation process. Here, we present a theoretical study of a novel micro-electroporation channel composed of an electrolyte flowing over a series of adjacent electrodes separated by infinitesimally small insulators. Application of a small, non-electrolysis inducing potential difference between the adjacent electrodes results in radially-varying electric fields that emanate from these insulators, causing cells flowing through the channel to experience a pulsed electric field. This eliminates the need for a pulse generator, making a minimal power source (such as a battery) the only electrical equipment that is needed. A non-dimensional primary current distribution model of the novel micro-electroporation channel shows that decreasing the channel height results in an exponential increase in the electric field magnitude, and that cells experience exponentially greater electric field magnitudes the closer they are to the channel walls. Finally, dimensional primary current distribution models of two potential applications, water sterilization and cell transfection, demonstrate the practical feasibility of the novel micro-electroporation channel.     

Analysis of recoverable current from one component of magnetic flux density in MREIT and MRCDI

Magnetic resonance current density imaging (MRCDI) provides a current density image by measuring the induced magnetic flux density within the subject with a magnetic resonance imaging (MRI) scanner. Magnetic resonance electrical impedance tomography (MREIT) has been focused on extracting some useful information of the current density and conductivity distribution in the subject Omega using measured B(z), one component of the magnetic flux density B. In this paper, we analyze the map Tau from current density vector field J to one component of magnetic flux density B(z) without any assumption on the conductivity. The map Tau provides an orthogonal decomposition J = J(P) + J(N) of the current J where J(N) belongs to the null space of the map Tau. We explicitly describe the projected current density J(P) from measured B(z). Based on the decomposition, we prove that B(z) data due to one injection current guarantee a unique determination of the isotropic conductivity under assumptions that the current is two-dimensional and the conductivity value on the surface is known. For a two-dimensional dominating current case, the projected current density J(P) provides a good approximation of the true current J without accumulating noise effects. Numerical simulations show that J(P) from measured B(z) is quite similar to the target J. Biological tissue phantom experiments compare J(P) with the reconstructed J via the reconstructed isotropic conductivity using the harmonic B(z) algorithm.     

Anisotropic conductivity imaging with MREIT using equipotential projection algorithm

Magnetic resonance electrical impedance tomography (MREIT) combines magnetic flux or current density measurements obtained by magnetic resonance imaging (MRI) and surface potential measurements to reconstruct images of true conductivity with high spatial resolution. Most of the biological tissues have anisotropic conductivity; therefore, anisotropy should be taken into account in conductivity image reconstruction. Almost all of the MREIT reconstruction algorithms proposed to date assume isotropic conductivity distribution. In this study, a novel MREIT image reconstruction algorithm is proposed to image anisotropic conductivity. Relative anisotropic conductivity values are reconstructed iteratively, using only current density measurements without any potential measurement. In order to obtain true conductivity values, only either one potential or conductivity measurement is sufficient to determine a scaling factor. The proposed technique is evaluated on simulated data for isotropic and anisotropic conductivity distributions, with and without measurement noise. Simulation results show that the images of both anisotropic and isotropic conductivity distributions can be reconstructed successfully.     

Use of conductive gels for electric field homogenization increases the antitumor efficacy of electroporation therapies

Electroporation is used in tissue for gene therapy, drug therapy and minimally invasive tissue ablation. The electrical field that develops during the application of the high voltage pulses needs to be precisely controlled. In the region to be treated, it is desirable to generate a homogeneous electric field magnitude between two specific thresholds whereas in other regions the field magnitude should be as low as possible. In the case of irregularly shaped tissue structures, such as bulky tumors, electric field homogeneity is almost impossible to be achieved with current electrode arrangements. We propose the use of conductive gels, matched to the conductivity of the tissues, to fill dead spaces between plate electrodes gripping the tissue so that the electric field distribution becomes less heterogeneous. Here it is shown that this technique indeed improves the antitumor efficacy of electrochemotherapy in sarcomas implanted in mice. Furthermore, we analyze, through finite element method simulations, how relevant the conductivity mismatches are. We found that conductivity mismatching errors are surprisingly well tolerated by the technique. Gels with conductivities ranging from 5 mS cm(-1) to 10 mS cm(-1) will be a proper solution for most cases.     

Contactless dielectrophoresis: a new technique for cell manipulation

Dielectrophoresis (DEP) has become a promising technique to separate and identify cells and microparticles suspended in a medium based on their size or electrical properties. Presented herein is a new technique to provide the non-uniform electric field required for DEP that does not require electrodes to contact the sample fluid. In our method, electrodes are capacitively-coupled to a fluidic channel through dielectric barriers; the application of a high-frequency electric field to these electrodes then induces an electric field in the channel. This technique combines the cell manipulation abilities of traditional DEP with the ease of fabrication found in insulator-based technologies. A microfluidic device was fabricated based on this principle to determine the feasibility of cell manipulations through contactless DEP (cDEP). We were able to demonstrate cell responses unique to the DEP effect in three separate cell lines. These results illustrate the potential for this technique to identify cells through their electrical properties without fear of contamination from electrodes.