Double-spin-echo diffusion weighting with a modified eddy current adjustment

Magnetic field inhomogeneities like eddy current-related gradient fields cause geometric distortions in echo-planar imaging (EPI). This in particular affects diffusion-weighted imaging where these distortions vary with the direction of the diffusion weighting and hamper the accurate determination of diffusion parameters. The double-spin-echo preparation often used aims to reduce the cumulative eddy current effect by adjusting the diffusion-weighting gradient pulse durations to the time constant of the dominant eddy current contribution. However, eddy currents with a variety of time constants may be present and cause residual distortions. Here, a modification is proposed where the two bipolar gradient pairs of the preparation are adjusted independently to different time constants. At the expense of a slightly prolonged echo time, residual geometric distortions and correspondingly increased values of the diffusion anisotropy can be reduced as is demonstrated in phantoms and the human brain. Thus, it may help to improve the reliability of diffusion-weighted EPI.     

核磁共振水分子扩散张量成像中基于广义Fibonacci数列的扩散敏感梯度磁场方向分布方案

为了准确得到人体内水分子各向异性扩散信息,在核磁共振扩散张量成像及高角分辨率扩散成像实验中,需要在众多空间均匀分布的方向上依次施加扩散敏感梯度磁场,测量水分子在不同方向上的扩散系数.目前方向分布方案的缺点有方向数目不连续、均匀性有待提高及部分方向数据的损坏会影响整个数据集等.本文以广义Fibonacci数列为基础,提出新的可以产生连续方向数目的扩散敏感梯度磁场方向分布方案,整个方案的方向均匀性较好,数据集内的部分数据仍然具有很好的空间均匀性,而且本方案中相邻两个扩散敏感梯度磁场方向接近相反,可以减小快速变化的高强度梯度磁场产生的涡流对结果的影响.     

Simulating the effects of time-varying magnetic fields with a realistic simulated scanner

Transient magnetic fields induce changes in magnetic resonance (MR) images ranging from small, visually undetectable effects (caused, for instance, by neuronal currents) to more significant ones, such as those created by the gradient fields and eddy currents. Accurately simulating these effects may assist in correcting or optimising MR imaging for many applications (e.g., diffusion imaging, current density imaging, use of magnetic contrast agents, neuronal current imaging, etc.). Here we have extended an existing MR simulator (POSSUM) with a model for changing magnetic fields at a very high-resolution time-scale. This simulator captures a realistic range of scanner and physiological artifacts by modeling the scanner environment, pulse sequence details and subject properties (e.g., brain geometry and air-tissue boundaries).     

An optimized pulse sequence for isotropically weighted diffusion imaging.

Single-shot echo-planar imaging is becoming the most widely used technique for magnetic resonance diffusion imaging, since it enables measurement of diffusion coefficients in human brain without motion artifacts. However, its reliability is limited by geometrical distortions due to eddy currents. In this report, an isotropically weighted echo-planar pulse sequence, optimized to give the maximum signal-to-noise ratio in the computed trace image and designed to produce inherently low distortions, is presented. It is also shown how the residual translational distortion can be easily characterized and removed by postprocessing. A full characterization of the distortion artifact involves a few measurements on a phantom, in order to estimate the distortion as a function of slice orientation, which can then be used to correct any slice orientation. Results of applying the image translation correction to data collected from a patient are presented.     

Finite element analysis of gradient z-coil induced eddy currents in a permanent MRI magnet

In permanent magnetic resonance imaging (MRI) systems, pulsed gradient fields induce strong eddy currents in the conducting structures of the magnet body. The gradient field for image encoding is perturbed by these eddy currents leading to MR image distortions. This paper presents a comprehensive finite element (FE) analysis of the eddy current generation in the magnet conductors. In the proposed FE model, the hysteretic characteristics of ferromagnetic materials are considered and a scalar Preisach hysteresis model is employed. The developed FE model was applied to study gradient z-coil induced eddy currents in a 0.5 T permanent MRI device. The simulation results demonstrate that the approach could be effectively used to investigate eddy current problems involving ferromagnetic materials. With the knowledge gained from this eddy current model, our next step is to design a passive magnet structure and active gradient coils to reduce the eddy current effects.     

On the use of water phantom images to calibrate and correct eddy current induced artefacts in MR diffusion tensor imaging

The accurate determination of absolute measures of diffusion anisotropy in vivo using single-shot, echo-planar imaging techniques requires the acquisition of a set of high signal-to-noise ratio, diffusion-weighted images that are free from eddy current induced image distortions. Such geometric distortions can be characterized and corrected in brain imaging data using magnification (M), translation (T), and shear (S) distortion parameters derived from separate water phantom calibration experiments. Here we examine the practicalities of using separate phantom calibration data to correct high b-value diffusion tensor imaging data by investigating the stability of these distortion parameters, and hence the eddy currents, with time. It is found that M, T, and S vary only slowly with time (i.e., on the order of weeks), so that calibration scans need not be performed after every patient examination. This not only minimises the scan time required to collect the calibration data, but also the computational time needed to characterize these eddy current induced distortions. Examples of how measurements of diffusion anisotropy are improved using this post-processing scheme are also presented.     

Correction of spatial distortion in magnetic resonance angiography for radiosurgical treatment planning of cerebral arteriovenous malformations.

A treatment planning system based on magnetic resonance (MR) angiographic imaging data for the radiosurgery of inoperable cerebral arteriovenous malformations is reported. MR angiography was performed using a three-dimensional (3D) velocity-compensated fast imaging with steady-state precession (FISP) sequence. Depending on the individual MR system, inhomogeneities and nonlinearities induced by eddy currents during the pulse sequence can distort the images and produce spurious displacements of the stereotactic coordinates in both the x-y plane and the z axis. If necessary, these errors in position can be assessed by means of two phantoms placed within the stereotactic guidance system--a "2D-phantom" displaying "pincushion" distortion in the image, and a "3D-phantom" displaying displacement, warp, and tilt of the image plane itself. The pincushion distortion can be "corrected" (reducing displacements from 2-3 mm to 1 mm) by calculations based on modeling the distortion as a fourth order 2D polynomial. Displacement, warp, and tilt of the image plane may be corrected by adjustment of the gradient shimming currents. After correction, the accuracy of the geometric information is limited only by the pixel resolution of the image (= 1 mm). Precise definition of the target volume could be performed by the therapist either directly in the MR images or in calculated projection MR angiograms obtained by a maximum intensity projection algorithm. MR angiography provides a sensitive, noninvasive 3D method for defining target volume and critical structures, and for calculating precise dose distributions for radiosurgery of cerebral arteriovenous malformations.     

A hybrid strategy for correcting geometric distortion in echo-planar images

A hybrid strategy for geometric distortion correction of echo-planar images is demonstrated. This procedure utilizes standard field mapping for signal displacement correction and the so-called reverse gradient acquisition for signal intensity correction. (The term reverse gradient refers to an acquisition of two sets of echo-planar images with phase encoding gradients of opposite polarity.) The hybrid strategy is applied to human brain echo-planar images acquired with and without diffusion-weighting. A comparison of the hybrid distortion corrected images to those corrected with standard field mapping only demonstrates much better performance of the hybrid method. A variant of the hybrid method is also demonstrated which requires the acquisition of only one pair of opposite polarity images within a set of images.     

Estimation of mutual information objective function based on Fourier shift theorem: an application to eddy current distortion correction in diffusion tensor imaging

Diffusion tensor imaging requires correction of eddy current distortion in diffusion-weighted images. An effective retrospective correction approach is to transform a diffusion-weighted image to maximize the mutual information (MI) between the transformed diffusion-weighted image and the corresponding T2-weighted image. In the literature, either linear interpolation or partial volume interpolation is applied to estimate the MI objective function. However, these interpolation methods induce artifacts to the MI objective function, thus compromising correction results. In this work, the MI objective function is estimated based on interpolation using Fourier shift theorem. This method eliminates the artifacts incurred with the aforementioned interpolation methods. The algorithm is further improved by approximating pixel values using their nearest neighbors in the up-sampled spatial domain, resulting in dramatically increased computational efficiency without compromising the correction results. The effects of varying the number of quantization levels and using Parzen window filtering to smooth the MI objective function are also investigated to obtain optimized algorithm parameters. The diffusion tensor image quality after applying the proposed distortion correction method is significantly improved visually.     

Improved diffusion-weighting efficiency of pulsed gradient stimulated echo MR measurements with background gradient cross-term suppression

Accurate diffusion measurements with pulsed gradient NMR are hampered by cross-terms of the diffusion-weighting and background gradients. For experiments based on a stimulated echo pulse sequence, that is preferred for samples with a T2 short compared to the diffusion time, a diffusion-weighting scheme has been presented that avoids these cross-terms in each of the en- and decoding periods separately. However, this approach suffers from a reduced diffusion-weighting efficiency because the two gradients applied in each of the periods have effectively opposite polarities leading to a partial cancellation. An extension of this scheme is presented that involves an additional gradient pulse in each period and delivers an improved diffusion-weighting efficiency without sacrificing the cross-term compensation. Analytical expressions for the gradient pulse lengths and amplitudes are given for arbitrary timing parameters. MR measurements with artificial (switched) background gradients were performed to test the cross-term compensation capability of the proposed extension. The results show that considerably higher q and b values can be achieved with the extension without changing the timing parameters. The MR measurements yielded identical diffusion coefficients without, with the same, and with different background gradients in the en- and decoding periods demonstrating the cross-term compensation of the presented approach.     

Eddy current simulation in thick cylinders of finite length induced by coils of arbitrary geometry

Eddy currents are inevitably induced when time-varying magnetic field gradients interact with the metallic structures of a magnetic resonance imaging (MRI) scanner. The secondary magnetic field produced by this induced current degrades the spatial and temporal performance of the primary field generated by the gradient coils. Although this undesired effect can be minimized by using actively and/or passively shielded gradient coils and current pre-emphasis techniques, a residual eddy current still remains in the MRI scanner structure. Accurate simulation of these eddy currents is important in the successful design of gradient coils and magnet cryostat vessels. Efficient methods for simulating eddy currents are currently restricted to cylindrical-symmetry. The approach presented in this paper divides thick conducting cylinders into thin layers (thinner than the skin depth) and expresses the current density on each as a Fourier series. The coupling between each mode of the Fourier series with every other is modeled with an inductive network method. In this way, the eddy currents induced in realistic cryostat surfaces by coils of arbitrary geometry can be simulated. The new method was validated by simulating a canonical problem and comparing the results against a commercially available software package. An accurate skin depth of 2.76 mm was calculated in 6 min with the new method. The currents induced by an actively shielded x-gradient coil were simulated assuming a finite length cylindrical cryostat consisting of three different conducting materials. Details of the temporal-spatial induced current diffusion process were simulated through all cryostat layers, which could not be efficiently simulated with any other method. With this data, all quantities that depend on the current density, such as the secondary magnetic field, are simply evaluated.     

Crossing fibers, diffractions and nonhomogeneous magnetic field: correction of artifacts by bipolar gradient pulses

In recent years, diffusion tensor imaging (DTI) and its variants have been used to describe fiber orientations and q-space diffusion MR was proposed as a means to obtain structural information on a micron scale. Therefore, there is an increasing need for complex phantoms with predictable microcharacteristics to challenge different indices extracted from the different diffusion MR techniques used. The present study examines the effect of diffusion pulse sequence on the signal decay and diffraction patterns observed in q-space diffusion MR performed on micron-scale phantoms of different geometries and homogeneities. We evaluated the effect of the pulse gradient stimulated-echo, the longitudinal eddy current delay (LED) and the bipolar LED (BPLED) pulse sequences. Interestingly, in the less homogeneous samples, the expected diffraction patterns were observed only when diffusion was measured with the BPLED sequence. We demonstrated the correction ability of bipolar diffusion gradients and showed that more accurate physical parameters are obtained when such a diffusion gradient scheme is used. These results suggest that bipolar gradient pulses may result in more accurate data if incorporated into conventional diffusion-weighted imaging and DTI.     

一种永磁磁共振中磁体涡流场的测量方法

磁共振成像（Magntic Resonance Imaging,MRI）技术是一种先进的医疗影像技术.在MRI系统中,通过梯度线圈电流快速切换方向,对待测区域施加梯度磁场,产生的梯度磁场会在其周围的金属体内激发出变化的涡旋电场,进而导致金属体内闭合的回路中产生对原来的梯度电流起抑制作用的感生电流,也就是我们所说的涡流.本文介绍了一种测量磁体涡流场的方法,结合电磁感应定律,设计了一种磁体涡流场测量装置,通过硬件采集以及软件处理的方法,将理想梯度场与实际磁场进行相减并将波形实时呈现,实验结果表明该方法可实现对磁体涡流场的测量.     

Quantitative analysis of spatial distortions of diffusion techniques at 3T

Diffusion has been widely adopted in the clinical setting to study the microstructural tissue changes in conjunction with anatomic imaging and metabolic imaging to offer insights on the status of the tissue injury or lesion. However, geometric distortions caused by magnetic susceptibility effects, eddy currents and gradient imperfections greatly affect the clinical utility of the diffusion images. Several diffusion methods have been proposed in the recent years to obtain diffusion parameters with increased accuracy. In most cases, the comparisons to the clinical standard echo-planar imaging (EPI) diffusion are done visually without quantitative measurements. In this study, we present three simple, complementary quantitative methods of nonrigid image registration and shape analyses for evaluating spatial distortions on magnetic resonance images with application in comparing single-shot fast spin-echo (SSFSE) and EPI based diffusion measurements. These methods have confirmed the SSFSE based diffusion method is less distorted than the EPI based one, which is generally accepted through visual inspection.     

Performance of single spin-echo and doubly refocused diffusion-weighted sequences in the presence of eddy current fields with multiple components

Echo-planar diffusion-weighted images can display significant geometric distortions due to eddy current fields. Several preparation schemes have been proposed, which can null eddy currents with a single time constant. The aim of this work was to compare the performance of three such pulse sequences in the presence of multiple components and investigate whether affine registration is capable of correcting for the resulting distortions. A magnetic resonance imaging simulator was used to eliminate potential confounding factors. The doubly refocused sequences showed substantially reduced effects. Applying affine registration to the single spin-echo images leads to reduced residuals, but not to the level observed for the doubly refocused sequences. Modified versions of the standard single spin-echo and doubly refocused sequences performed better than their original counterparts. Affine registration is not sufficient to correct for strong eddy current effects, which should therefore be minimized at source. When the use of a doubly refocused sequence is not possible, a modified single spin-echo sequence should be considered.     

Single point measurements of magnetic field gradient waveform

Pulsed magnetic field gradients are fundamental to spatial encoding and diffusion weighting in magnetic resonance. The ideal pulsed magnetic field gradient should have negligible rise and fall times, however, there are physical limits to how fast the magnetic field gradient may change with time. Finite gradient switching times, and transient, secondary, induced magnetic field gradients (eddy currents) alter the ideal gradient waveform and may introduce a variety of undesirable image artifacts. We have developed a new method to measure the complete magnetic field gradient waveform. The measurement employs a heavily doped test sample with short MR relaxation times (T(1), T(2), and T(2)(*)<100 micros) and a series of closely spaced broadband radiofrequency excitations, combined with single point data acquisition. This technique, a measure of evolving signal phase, directly determines the magnetic field gradient waveform experienced by the test sample. The measurement is sensitive to low level transient magnetic fields produced by eddy currents and other short and long time constant non-ideal gradient waveform behaviors. Data analysis is particularly facile permitting a very ready experimental check of gradient performance.     

Single-shot fast spin-echo diffusion tensor imaging of the brain and spine with head and phased array coils at 1.5 T and 3.0 T

In this study, we investigated the use of a single-shot fast spin-echo-based sequence to perform diffusion tensor imaging (DTI) with improved anatomic fidelity through the entire brain and the cervical spine. Traditionally, diffusion tensor images have been acquired by single-shot echo-planar imaging (EPI) methods in which large distortions result from magnetic susceptibility effects, especially near air-tissue interfaces. These distortions can be problematic, especially in anterior and inferior portions of the brain, and they also can severely limit applications in the spine. At higher magnetic fields these magnetic susceptibility artifacts are increased. The single-shot fast spin-echo (SSFSE) method used in this study utilizes radiofrequency rephasing in the transverse plane and thus provides diffusion images with negligible distortion even at 3 Tesla. In addition, the SSFSE sequence does not require multiple fast-receivers, which are not available on many magnetic resonance (MR) systems. Phased array coils were used to increase the signal-to-noise ratio of the images, offering a major inherent advantage in diffusion tensor imaging of the spine and brain. The mean diffusion measurements obtained with the SSFSE acquisition were not statistically different (p > 0.05) from EPI-based acquisitions. Compared to routine T(2)-weighted MR images, the DTI-EPI sequence showed up to 20% in elongation of the brain in the anterior-posterior direction on a sagittal image due to magnetic susceptibility distortions, whereas in the DTI-SSFSE, the image distortions were negligible. The diffusion tensor SSFSE method was also able to assess diffusion abnormalities in a brain stem hemorrhage, unaffected by the spatial distortions that limited conventional EPI acquisition.     

On the use of the FLAIR technique to improve the correction of eddy current induced artefacts in MR diffusion tensor imaging

Eddy current induced geometric distortions can only be accurately corrected in brain diffusion-weighted echo-planar (DW-EP) images for b-values less than approximately 300 s mm(-2) using the iterative cross-correlation (ICC) algorithm. This is due to the difference in signal intensity of the cerebrospinal fluid (CSF) compartment in the diffusion-weighted and baseline T(2)-weighted echo-planar (T2W-EP) images. At larger values of b, image misalignment artefacts can, however, be removed by directly correlating CSF-suppressed T2W-EP images with non-CSF-suppressed and CSF-suppressed DW-EP images. Separate phantom experiments can also be performed to provide eddy current calibration data. Here the ability of these methods to remove eddy current induced artefacts from DW-EP images collected in volunteer diffusion tensor imaging (DTI) experiments is investigated. Monte Carlo simulations show that in order for the ICC algorithm to produce accurate estimates of the eddy current induced distortions at b-values greater than 1000 s mm(-2), the degree of CSF suppression should be greater than approximately 80%. This condition is typically met for FLAIR inversion times between 0.5 and 0.8 of the spin-lattice relaxation time of CSF. In volunteer studies the most complete image realignment was provided by direct correlation of CSF-suppressed T2W-EP and DW-EP images acquired in the FLAIR DTI experiment. These results indicate that although calibration data obtained from brain or phantom images can significantly reduce eddy current induced distortions, the optimum image realignment achievable using post-processing methods is likely to be that obtained by direct image warping techniques.     

Magnetic fields mapping with the phase reference method

A simple method for imaging the magnetic field produced by arbitrary current distribtions is presented. The method is based on the use of a phase reference image and can be easily adapted to any standard magnetic resonance imaging scanner. Examples are given to application to gradient coil characterization and quantitative field measurements.     

Coherent cross-polarization theory for a spin-12 coupled to a general object

This work describes a segmented radial turbo-spin-echo technique (DW-rTSE) for high-resolution multislice diffusion-weighted imaging and quantitative ADC mapping. Diffusion-weighted images with an in-plane resolution of 700 microm and almost free of bulk motion can be obtained in vivo without cardiac gating. However, eddy currents and pulsatile brain motion cause severe artifacts when strong diffusion weighting is applied. This work explains in detail the artifacts in projection reconstruction (PR) imaging arising from eddy currents and describes an effective eddy current compensation based on the adjustment of gradient timing. Application of the diffusion gradients in all three orthogonal directions is possible without degradation of the images due to eddy current artifacts, allowing studies of the diffusional anisotropy. Finally, a self-navigation approach is proposed to reduce residual nonrigid body motion artifacts. Five healthy volunteers were examined to show the feasibility of this method.