B-scan based acoustic source reconstruction for magnetoacoustic tomography with magnetic induction (MAT-MI)

We present in this study, an acoustic source reconstruction method using focused transducer with B-mode imaging for magnetoacoustic tomography with magnetic induction (MAT-MI). MAT-MI is an imaging modality proposed for noninvasive conductivity imaging with high spatial resolution. In MAT-MI, acoustic sources are generated in a conductive object by placing it in a static and a time-varying magnetic field. The acoustic waves from these sources propagate in all directions and are collected with transducers placed around the object. The collected signal is then used to reconstruct the acoustic source distribution and to further estimate the electrical conductivity distribution of the object. A flat piston transducer acting as a point receiver has been used in earlier MAT-MI systems to collect acoustic signals. In this study, we propose to use B-mode scan scheme with a focused transducer that gives a signal gain in its focus region and improves the MAT-MI signal quality. A simulation protocol that can take into account different transducer designs and scan schemes for MAT-MI imaging is developed and used in our evaluation of different MAT-MI system designs. It is shown in our computer simulations that as compared to the earlier approach, the MAT-MI system using B-scan with a focused transducer allows MAT-MI imaging at a closer distance and has improved system sensitivity. In addition, the B-scan imaging technique allows reconstruction of the MAT-MI acoustic sources with a discrete number of scanning locations, which greatly increases the applicability of the MAT-MI approach, especially when a continuous acoustic window is not available in real clinical applications. We have also conducted phantom experiments to evaluate the proposed method, and the reconstructed image shows a good agreement with the target phantom.     

Reconstruction of Vectorial Acoustic Sources in Time-Domain Tomography

A new theory is proposed for the reconstruction of curl-free vector field, whose divergence serves as acoustic source. The theory is applied to reconstruct vector acoustic sources from the scalar acoustic signals measured on a surface enclosing the source area. It is shown that, under certain conditions, the scalar acoustic measurements can be vectorized according to the known measurement geometry and subsequently be used to reconstruct the original vector field. Theoretically, this method extends the application domain of the existing acoustic reciprocity principle from a scalar field to a vector field, indicating that the stimulating vectorial source and the transmitted acoustic pressure vector (acoustic pressure vectorized according to certain measurement geometry) are interchangeable. Computer simulation studies were conducted to evaluate the proposed theory, and the numerical results suggest that reconstruction of a vector field using the proposed theory is not sensitive to variation in the detecting distance. The present theory may be applied to magnetoacoustic tomography with magnetic induction (MAT-MI) for reconstructing current distribution from acoustic measurements. A simulation on MAT-MI shows that, compared to existing methods, the present method can give an accurate estimation on the source current distribution and a better conductivity reconstruction.     

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.     

Local Harmonic $B_z$ Algorithm With Domain Decomposition in MREIT: Computer Simulation Study

Magnetic resonance electrical impedance tomography (MREIT) attempts to provide conductivity images of an electrically conducting object with a high spatial resolution. When we inject current into the object, it produces internal distributions of current density ${bf J}$ and magnetic flux density ${bf B}=(B_x,B_y,B_z)$. By using a magnetic resonance imaging (MRI) scanner, we can measure $B_z$ data where $z$ is the direction of the main magnetic field of the scanner. Conductivity images are reconstructed based on the relation between the injection current and $B_z$ data. The harmonic $B_z$ algorithm was the first constructive MREIT imaging method and it has been quite successful in previous numerical and experimental studies. Its performance is, however, degraded when the imaging object contains low-conductivity regions such as bones and lungs. To overcome this difficulty, we carefully analyzed the structure of a current density distribution near such problematic regions and proposed a new technique, called the local harmonic $B_z$ algorithm. We first reconstruct conductivity values in local regions with a low conductivity contrast, separated from those problematic regions. Then, the method of characteristics is employed to find conductivity values in the problematic regions. One of the most interesting observations of the new algorithm is that it can provide a scaled conductivity image in a local region without knowing conductivity values outside the region. We present the performance of the new algorithm by using computer simulation methods.      

三维磁感应磁声成像的新算法研究

 磁感应磁声成像技术(MAT-MI)作为一种新型无创的电阻抗成像技术,融合了磁感应技术和超声断层扫描技术,提供了高分辨率的成像结果.本研究提出了一种用于MAT-MI计算电导率分布的新型算法,解决电导率重建过程中的奇异值问题,同时又缩短了重建所需时间,并通过计算机仿真构建的三维环状线圈和乳腺模型,验证了算法的稳定性和可靠性.     

Magnetic resonance driven electrical impedance tomography: a simulation study

Magnetic resonance electrical impedance tomography (MREIT) is a method for reconstructing a three-dimensional image of the conductivity distribution in a target volume using magnetic resonance (MR). In MREIT, currents are applied to the volume through surface electrodes and their effects on the MR induced magnetic fields are analyzed to produce the conductance image. However, current injection through surface electrodes poses technical problems such as the limitation on the safely applicable currents. In this paper, we present a new method called magnetic resonance driven electrical impedance tomography (MRDEIT), where the magnetic resonance in each voxel is used as the applied magnetic field source, and the resultant electromagnetic field is measured through surface electrodes or radio-frequency (RF) detectors placed near the surface. Because the applied magnetic field is at the RF frequency and eddy currents are the integral components in the method, a vector wave equation for the electric field is used as the basis of the analysis instead of a quasi-static approximation. Using computer simulations, it is shown that complex permittivity images can be reconstructed using MRDEIT, but that improvements in signal detection are necessary for detecting moderate complex permittivity changes.     

The effect of electrical anisotropy during magnetoacoustic tomography with magnetic induction

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a technique for imaging electrical conductivity in tissue. A time-varying magnetic field induces currents that interact with a static magnetic field to produce a Lorentz force, initiating ultrasonic waves. The goal of this communication is to examine the effect of anisotropy during MAT-MI.     

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.     

Image reconstruction in magnetic resonance conductivity tensor imaging (MRCTI)

Almost all magnetic resonance electrical impedance tomography (MREIT) reconstruction algorithms proposed to date assume isotropic conductivity in order to simplify the image reconstruction. However, it is well known that most of biological tissues have anisotropic conductivity values. In this study, four novel anisotropic conductivity reconstruction algorithms are proposed to reconstruct high resolution conductivity tensor images. Performances of these four algorithms and a previously proposed algorithm are evaluated in several aspects and compared.     

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.     

A New Method for Electric Impedance Imaging Using an Eddy Current With a Tetrapolar Circuit

A new contactless technique for electrical impedance imaging, using an eddy current managed along with the tetrapolar circuit method, is proposed. The eddy current produced by a magnetic field is superimposed on a constant current that is normally used in the tetrapolar circuit method, and thus is used to control the current distribution in the body. By changing the current distribution, a set of voltage differences is measured with a pair of electrodes. This set of voltage differences is used in the image reconstruction of the resistivity distribution. The least square error minimization method is used in the reconstruction algorithm. The principle of this method is explained theoretically. A backprojection algorithm was used to get 2-D images. Based on this principle, a measurement system was developed and model experiments were conducted with a saline-filled phantom. The estimated shape of each model in the reconstructed image was similar to that of the corresponding model. From the results of these experiments, it is confirmed that the proposed method is applicable to the realization of electrical conductivity imaging.     

一种磁感应成像中生物组织涡流信号的新型测量方法

磁感应成像(MIT)是对所测生物组织电导率进行图像重建的一种新型技术,生物组织所产生的涡流信号过于微弱制约着MIT检测装置的设计精度和重建图像的分辨率.该文基于涡流信号的特点,提出一种最大化减少主磁场信号的涡流检测方法,即对线圈传感器进行改进有效抵消主磁场信号从而增大涡流场.针对所提出的MIT测量模型,通过仿真实验,确...     

Electrical conductivity imaging using gradient B, decomposition algorithm in magnetic resonance electrical impedance tomography (MREIT)

In magnetic resonance electrical impedance tomography (MREIT), we try to visualize cross-sectional conductivity (or resistivity) images of a subject. We inject electrical currents into the subject through surface electrodes and measure the z component Bz of the induced internal magnetic flux density using an MRI scanner. Here, z is the direction of the main magnetic field of the MRI scanner. We formulate the conductivity image reconstruction problem in MREIT from a careful analysis of the relationship between the injection current and the induced magnetic flux density Bz. Based on the novel mathematical formulation, we propose the gradient Bz decomposition algorithm to reconstruct conductivity images. This new algorithm needs to differentiate Bz only once in contrast to the previously developed harmonic Bz algorithm where the numerical computation of (inverted delta)2Bz is required. The new algorithm, therefore, has the important advantage of much improved noise tolerance. Numerical simulations with added random noise of realistic amounts show the feasibility of the algorithm in practical applications and also its robustness against measurement noise.     

Harmonic decomposition in PDE-based denoising technique for magnetic resonance electrical impedance tomography

Recent progress in magnetic resonance electrical impedance tomography (MREIT) research via simulation and biological tissue phantom studies have shown that conductivity images with higher spatial resolution and accuracy are achievable. In order to apply MREIT to human subjects, one of the important remaining problems to be solved is to reduce the amount of the injection current such that it meets the electrical safety regulations. However, by limiting the amount of the injection current according to the safety regulations, the measured MR data such as the z-component of magnetic flux density Bz in MREIT tend to have low SNR and get usually degraded in their accuracy due to the nonideal data acquisition system of an MR scanner. Furthermore, numerical differentiations of the measured Bz required by the conductivity image reconstruction algorithms tend to further deteriorate the quality and accuracy of the reconstructed conductivity images. In this paper, we propose a denoising technique that incorporates a harmonic decomposition. The harmonic decomposition is especially suitable for MREIT due to the physical characteristics of Bz. It effectively removes systematic and random noises, while preserving important key features in the MR measurements, so that improved conductivity images can be obtained. The simulation and experimental results demonstrate that the proposed denoising technique is effective for MREIT, producing significantly improved quality of conductivity images. The denoising technique will be a valuable tool in MREIT to reduce the amount of the injection current when it is combined with an improved MREIT pulse sequence.     

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.     

Fast nonlinear image reconstruction for scanning impedance imaging

Scanning (electrical) impedance imaging (SII) is a novel high-resolution imaging modality that has the potential of imaging the electrical properties of thin biological tissues. In this paper, we apply the reciprocity principle to the modeling of the SII system and develop a fast nonlinear inverse method for image reconstruction. The method is fast because it uses convolution to eliminate the requirement of a numerical solver for the 3-D electrostatic field in the SII system. Numerical results show that our approach can accurately reveal the exact conductivity distribution from the measured current map for different 2-D simulation phantoms. Experiments were also performed using our SII system for a piece of butterfly wing and breast cancer cells. Two-dimensional current images were measured and corresponding quantitative conductivity images were restored using our approach. The reconstructed images are quantitative and reveal details not present in the measured images.     

Absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method

Magnetic induction tomography (MIT) attempts to image the electrical and magnetic characteristics of a target using impedance measurement data from pairs of excitation and detection coils. This inverse eddy current problem is nonlinear and also severely ill posed so regularization is required for a stable solution. A regularized Gauss-Newton algorithm has been implemented as a nonlinear, iterative inverse solver. In this algorithm, one needs to solve the forward problem and recalculate the Jacobian matrix for each iteration. The forward problem has been solved using an edge based finite element method for magnetic vector potential A and electrical scalar potential V, a so called A, A - V formulation. A theoretical study of the general inverse eddy current problem and a derivation, paying special attention to the boundary conditions, of an adjoint field formula for the Jacobian is given. This efficient formula calculates the change in measured induced voltage due to a small perturbation of the conductivity in a region. This has the advantage that it involves only the inner product of the electric fields when two different coils are excited, and these are convenient computationally. This paper also shows that the sensitivity maps change significantly when the conductivity distribution changes, demonstrating the necessity for a nonlinear reconstruction algorithm. The performance of the inverse solver has been examined and results presented from simulated data with added noise.     

Error analysis of nonconstant admittivity for MR-based electric property imaging

Magnetic resonance electrical property tomography (MREPT) is a new imaging modality to visualize a distribution of admittivity γ = σ+iωε inside the human body where σ and ε denote electrical conductivity and permittivity, respectively. Using B1 maps acquired by an magnetic resonance imaging scanner, it produces cross-sectional images of σ and ε at the Larmor frequency. Since current MREPT methods rely on an assumption of a locally homogeneous admittivity, there occurs a reconstruction error where this assumption fails. Rigorously analyzing the reconstruction error in MREPT, we showed that the error is fundamental and may cause technical difficulties in interpreting MREPT images of a general inhomogeneous object. We performed numerical simulations and phantom experiments to quantitatively support the error analysis. We compared the MREPT image reconstruction problem with that of magnetic resonance electrical impedance tomography (MREIT) to highlight distinct features of both methods to probe the same object in terms of its high- and low-frequency conductivity distributions, respectively. MREPT images showed large errors along boundaries where admittivity values changed whereas MREIT images showed no such boundary effects. Noting that MREIT makes use of the term neglected in MREPT, a novel MREPT admittivity image reconstruction method is proposed to deal with the boundary effects, which requires further investigation on the complex directional derivative in the real Euclidian space [Formula: see text].     

Anatomically constrained electrical impedance tomography forthree-dimensional anisotropic bodies

As shown previously for two-dimensional geometries, anisotropy effects should not be ignored in electrical impedance tomography (EIT) and structural information is important for the reconstruction of anisotropic conductivities. Here, we describe the static reconstruction of an anisotropic conductivity distribution for the more realistic three-dimensional (3-D) case. Boundaries between different conductivity regions are anatomically constrained using magnetic resonance imaging (MRI) data. The values of the conductivities are then determined using gradient-type-algorithms in a nonlinear-indirect approach. At each iteration, the forward problem is solved by the finite element method. The approach is used to reconstruct the 3-D conductivity profile of a canine torso. Both computational performance and simulated reconstruction results are presented together with a detailed study on the sensitivity of the prediction error with respect to different parameters. In particular, the use of an intracavity catheter to better extract interior conductivities is demonstrated     

An FDTD model for calculation of gradient-induced eddy currents in MRI system

In most magnetic resonance imaging (MRI) systems, pulsed magnetic gradient fields induce eddy currents in the conducting structures of the superconducting magnet. The eddy currents induced in structures within the cryostat are particularly problematic as they are characterized by long time constants by virtue of the low resistivity of the conductors. This paper presents a three-dimensional (3-D) finite-difference time-domain (FDTD) scheme in cylindrical coordinates for eddy-current calculation in conductors. This model is intended to be part of a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The singularity apparent in the governing equations is removed by using a series expansion method and the conductor-air boundary condition is handled using a variant of the surface impedance concept. The numerical difficulty due to the "asymmetry" of Maxwell equations for low-frequency eddy-current problems is circumvented by taking advantage of the known penetration behavior of the eddy-current fields. A perfectly matched layer absorbing boundary condition in 3-D cylindrical coordinates is also incorporated. The numerical method has been verified against analytical solutions for simple cases. Finally, the algorithm is illustrated by modeling a pulsed field gradient coil system within an MRI magnet system. The results demonstrate that the proposed FDTD scheme can be used to calculate large-scale eddy-current problems in materials with high conductivity at low frequencies.