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.     

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.      

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.     

Estimating Motion From MRI Data

Magnetic resonance imaging (MRI) is an ideal imaging modality to measure blood flow and tissue motion. It provides excellent contrast between soft tissues, and images can be acquired at positions and orientations freely defined by the user. From a temporal sequence of MR images, boundaries and edges of tissues can be tracked by image processing techniques. Additionally, MRI permits the source of the image signal to be manipulated. For example, temporary magnetic tags displaying a pattern of variable brightness may be placed in the object using MR saturation techniques, giving the user a known pattern to detect for motion tracking. The MRI signal is a modulated complex quantity, being derived from a rotating magnetic field in the form of an induced current. Well-defined patterns can also be introduced into the phase of the magnetization, and could be thought of as generalized tags. If the phase of each pixel is preserved during image reconstruction, relative phase shifts can be used to directly encode displacement, velocity and acceleration. New methods for modeling motion fields from MRI have now found application in cardiovascular and other soft tissue imaging. In this review, we shall describe the methods used for encoding, imaging, and modeling motion fields with MRI.     

Multislice Radio-Frequency Current Density Imaging

Radio-frequency current density imaging (RF-CDI) is an imaging technique that noninvasively measures current density distribution at the Larmor frequency utilizing magnetic resonance imaging (MRI). Previously implemented RF-CDI techniques were only able to image a single slice transverse to the static magnetic field ${rm B}_{0}$ . This paper describes the first realization of a multislice RF-CDI sequence on a 1.5 T clinical imager. Multislice RF current density images have been reconstructed for two phantoms. The influence of MRI random noise on the sensitivity of the multislice RF-CDI measurement has also been studied by theoretical analysis, simulation and phantom experiments.      

Conductivity image reconstruction from defective data in MREIT: numerical simulation and animal experiment

Magnetic resonance electrical impedance tomography (MREIT) is designed to produce high resolution conductivity images of an electrically conducting subject by injecting current and measuring the longitudinal component, Bz, of the induced magnetic flux density B = (Bx, By, Bz). In MREIT, accurate measurements of Bz are essential in producing correct conductivity images. However, the measured Bz data may contain fundamental defects in local regions where MR magnitude image data are small. These defective Bz data result in completely wrong conductivity values there and also affect the overall accuracy of reconstructed conductivity images. Hence, these defects should be appropriately recovered in order to carry out any MREIT image reconstruction algorithm. This paper proposes a new method of recovering Bz data in defective regions based on its physical properties and neighboring information of Bz. The technique will be indispensable for conductivity imaging in MREIT from animal or human subjects including defective regions such as lungs, bones, and any gas-filled internal organs.     

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.     

Electromagnetic considerations for RF current density imaging [MRI technique

Radio frequency current density imaging (RF-CDI) is a recent MRI technique that can image a Larmor frequency current density component parallel to B(0). Because the feasibility of the technique was demonstrated only for homogeneous media, the authors' goal here is to clarify the electromagnetic assumptions and field theory to allow imaging RF currents in heterogeneous media. The complete RF field and current density imaging problem is posed. General solutions are given for measuring lab frame magnetic fields from the rotating frame magnetic field measurements. For the general case of elliptically polarized fields, in which current and magnetic field components are not in phase, one can obtain a modified single rotation approximation. Sufficient information exists to image the amplitude and phase of the RF current density parallel to B(0) if the partial derivative in the B(0) direction of the RF magnetic field (amplitude and phase) parallel to B(0) is much smaller than the corresponding current density component. The heterogeneous extension was verified by imaging conduction and displacement currents in a phantom containing saline and pure water compartments. Finally, the issues required to image eddy currents are presented. Eddy currents within a sample will distort both the transmitter coil reference system, and create measurable rotating frame magnetic fields. However, a three-dimensional electro-magnetic analysis will be required to determine how the reference system distortion affects computed eddy current images.     

In Vivo High-ResolutionConductivity Imaging of the Human Leg Using MREIT: The First Human Experiment

We present the first in vivo cross-sectional conductivity image of the human leg with 1.7 mm pixel size using the magnetic resonance electrical impedance tomography (MREIT) technique. After a review of its experimental protocol by an Institutional Review Board (IRB), we performed MREIT imaging experiments of four human subjects using a 3 T MRI scanner. Adopting thin and flexible carbon–hydrogel electrodes with a large surface area and good contact, we could inject as much as 9 mA current in a form of 15 ms pulse into the leg without producing a painful sensation and motion artifact. Sequentially injecting two imaging currents in two different directions, we collected induced magnetic flux density data inside the leg. Scaled conductivity images reconstructed by using the single-step harmonic $B_{z}$ algorithm well distinguished different parts of the subcutaneous adipose tissue, muscle, crural fascia, intermuscular septum and bone inside the leg. We could observe spurious noise spikes in the outer layer of the bone primarily due to the MR signal void phenomenon there. Around the fat, the chemical shift of about two pixels occurred obscuring the boundary of the fat region. Future work should include a fat correction method incorporated in the MREIT pulse sequence and improvements in radio-frequency coils and image reconstruction algorithms. Further human imaging experiments are planned and being conducted to produce conductivity images from different parts of the human body.      

MRI artifact cancellation due to rigid motion in the imaging plane

A post-processing technique has been developed to suppress the magnetic resonance imaging (MRI) artifact arising from object planar rigid motion. In two-dimensional Fourier transform (2-DFT) MRI, rotational and translational motions of the target during magnetic resonance magnetic resonance (MR) scan respectively impose nonuniform sampling and a phase error an the collected MRI signal. The artifact correction method introduced considers the following three conditions: (1) for planar rigid motion with known parameters, a reconstruction algorithm based on bilinear interpolation and the super-position method is employed to remove the MRI artifact, (2) for planar rigid motion with known rotation angle and unknown translational motion (including an unknown rotation center), first, a super-position bilinear interpolation algorithm is used to eliminate artifact due to rotation about the center of the imaging plane, following which a phase correction algorithm is applied to reduce the remaining phase error of the MRI signal, and (3) to estimate unknown parameters of a rigid motion, a minimum energy method is proposed which utilizes the fact that planar rigid motion increases the measured energy of an ideal MR image outside the boundary of the imaging object; by using this property all unknown parameters of a typical rigid motion are accurately estimated in the presence of noise. To confirm the feasibility of employing the proposed method in a clinical setting, the technique was used to reduce unknown rigid motion artifact arising from the head movements of two volunteers.     

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.     

Minimizing interference from magnetic resonance imagers duringelectrocardiography

Magnetic resonance imaging (MRI) allows a physician to obtain images of internal organs noninvasively. Imaging a moving organ such as the heart requires a trigger so that successive scans can be synchronized. In the case of cardiac imaging this trigger is the electrocardiogram (ECG). When a patient is in an MRI scanner he/she is subjected to both static and dynamic magnetic fields which can cause interference In the ECG. The dynamic fields consist of 8- to 64-MHz radio frequency (RF) pulses and low-frequency magnetic gradient pulses with frequency components below 100 Hz. Conventional bandpass filters are only moderately effective because the passband allows magnetic gradient-induced interference to be superimposed on the ECG, causing distortion of the signal. This paper describes a technique which can be used to remove induced MRI gradient interference from an ECG recorded on a patient inside the bore of a MRI scanner. Induced signal from an external loop is subtracted from the ECG to minimize the low-frequency interference. The gradient induced low-frequency interference was reduced to approximately 20% of its magnitude when using conventional ECG amplifiers     

Nonrigid Registration of Joint Histograms for Intensity Standardization in Magnetic Resonance Imaging

A major disadvantage of magnetic resonance imaging (MRI) compared to other imaging modalities like computed tomography is the fact that its intensities are not standardized. Our contribution is a novel method for MRI signal intensity standardization of arbitrary MRI scans, so as to create a pulse sequence dependent standard intensity scale. The proposed method is the first approach that uses the properties of all acquired images jointly (e.g., T1- and T2-weighted images). The image properties are stored in multidimensional joint histograms. In order to normalize the probability density function (pdf) of a newly acquired data set, a nonrigid image registration is performed between a reference and the joint histogram of the acquired images. From this matching a nonparametric transformation is obtained, which describes a mapping between the corresponding intensity spaces and subsequently adapts the image properties of the newly acquired series to a given standard. As the proposed intensity standardization is based on the probability density functions of the data sets only, it is independent of spatial coherence or prior segmentations of the reference and current images. Furthermore, it is not designed for a particular application, body region or acquisition protocol. The evaluation was done using two different settings. First, MRI head images were used, hence the approach can be compared to state-of-the-art methods. Second, whole body MRI scans were used. For this modality no other normalization algorithm is known in literature. The Jeffrey divergence of the pdfs of the whole body scans was reduced by 45%. All used data sets were acquired during clinical routine and thus included pathologies.      

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.     

A model-based four-dimensional left ventricular surface detector

The authors have developed a general model-based surface detector for finding the four-dimensional (three spatial dimensions plus time) endocardial and epicardial left ventricular boundaries. The model encoded left ventricular (LV) shape, smoothness, and connectivity into the compatibility coefficients of a relaxation labeling algorithm. This surface detection method was applied to gated single photon emission computed tomography (SPECT) perfusion images, tomographic radionuclide ventriculograms, and cardiac rotation magnetic resonance images. Its accuracy was investigated using actual patient data. Global left ventricular volumes correlated well, with a maximum correlation coefficient of 0.98 for magnetic resonance imaging (MRI) endocardial surfaces and a minimum of 0.88 for SPECT epicardial surfaces. The average absolute errors of edge detection were 6.4, 5.6. and 4.6 mm for tomographic radionuclide ventriculograms, gated perfusion SPECT, and magnetic resonance images, respectively.     

Ghost cancellation algorithms for MRI images

Ghost cancellation algorithms for restoring magnetic resonance imaging (MRI) images in medical applications are described. The approach is to model the effect of the time delays and the asymmetry of the sinusoidal readout gradient for even and odd lines with two phase functions relating the actual object density to even and odd parts of the observed image. A priori information about the phase functions is exploited in order to estimate the true object density. Examples of applying this ghost cancellation approach to liver and heart images is presented.     

A time-harmonic inverse methodology for the design of RF coils inMRI

An inverse methodology is described to assist in the design of radio-frequency (RF) coils for magnetic resonance imaging (MRI) applications. The time-harmonic electromagnetic Green's functions are used to calculate current on the coil and shield cylinders that will generate a specified internal magnetic field. Stream function techniques and the method of moments are then used to implement this theoretical current density into an RF coil. A novel asymmetric coil operating for a 4.5 T MRI machine was designed and constructed using this methodology and the results are presented.     

基于DAWGAN-GP的磁共振图像重构方法研究

本文提出了一种基于改进Wasserstein生成式对抗网络（De-aliasing Wasserstein Generative Adversarial Network with Gradient Penalty,DAWGAN-GP）的磁共振图像重构算法,该方法利用Wasserstein生成式对抗网络代替传统的生成式对抗网络,并结合梯度惩罚的方法提高训练速度,解决WGAN收敛缓慢问题.此外,为了有更好的重构效果,我们将感知损失,像素损失和频域损失引入至损失函数中进行网络训练.实验结果表明,对比现有的基于深度学习的磁共振图像重构算法,基于DAWGAN-GP的磁共振图像重构方法具有更好的重构效果,可获得更高的峰值信噪比（Peak Signal to Noise Ratio,PSNR）和更好的结构相似性（Structural Similarity Index Measure,SSIM）.     

Interframe coding of magnetic resonance images

Presents a new interframe coding method for medical images, in particular magnetic resonance (MR) images. Until now, attempts in using interframe redundancies for coding MR images have been unsuccessful. The authors believe that the main reason for this is twofold: unsuitable interframe estimation models and the thermal noise inherent in magnetic resonance imaging (MRI). The interframe model used here is a continuous affine mapping based on (and optimized by) deforming triangles. The inherent noise of MRI is dealt with by using a median filter within the estimation loop. The residue frames are quantized with a zero-tree wavelet coder, which includes arithmetic entropy coding. This particular method of quantization allows for progressive transmission, which aside from avoiding buffer control problems is very attractive in medical imaging applications.     

Deformation-based mapping of volume change from serial brain MRI in the presence of local tissue contrast change

This paper is motivated by the analysis of serial structural magnetic resonance imaging (MRI) data of the brain to map patterns of local tissue volume loss or gain over time, using registration-based deformation tensor morphometry. Specifically, we address the important confound of local tissue contrast changes which can be induced by neurodegenerative or neurodevelopmental processes. These not only modify apparent tissue volume, but also modify tissue integrity and its resulting MRI contrast parameters. In order to address this confound we derive an approach to the voxel-wise optimization of regional mutual information (RMI) and use this to drive a viscous fluid deformation model between images in a symmetric registration process. A quantitative evaluation of the method when compared to earlier approaches is included using both synthetic data and clinical imaging data. Results show a significant reduction in errors when tissue contrast changes locally between acquisitions. Finally, examples of applying the technique to map different patterns of atrophy rate in different neurodegenerative conditions is included.