Fat/water separation using a concentric rings trajectory

The concentric rings two‐dimensional (2D) k‐space trajectory enables flexible trade‐offs between image contrast, signal‐to‐noise ratio (SNR), spatial resolution, and scan time. However, to realize these benefits for in vivo imaging applications, a robust method is desired to deal with fat signal in the acquired data. Multipoint Dixon techniques have been shown to achieve uniform fat suppression with high SNR‐efficiency for Cartesian imaging, but application of these methods for non‐Cartesian imaging is complicated by the fact that fat off‐resonance creates significant blurring artifacts in the reconstruction. In this work, two fat–water separation algorithms are developed for the concentric rings. A retracing design is used to sample rings near the center of k‐space through multiple revolutions to characterize the fat–water phase evolution difference at multiple time points. This acquisition design is first used for multipoint Dixon reconstruction, and then extended to a spectroscopic approach to account for the trajectory's full evolution through 3D k‐t space. As the trajectory is resolved in time, off‐resonance effects cause shifts in frequency instead of spatial blurring in 2D k‐space. The spectral information can be used to assess field variation and perform robust fat–water separation. In vivo experimental results demonstrate the effectiveness of both algorithms. Magn Reson Med, 2009. © 2008 Wiley‐Liss, Inc.     

Density compensation functions for spiral MRI

In interleaved spiral MRI, an object's Fourier transform is sampled along a set of curved trajectories in the spatial frequency domain (k-space). An image of the object is then reconstructed, usually by interpolating the sampled Fourier data onto a Cartesian grid and applying the fast Fourier transform (FFT) algorithm. To obtain accurate results, it is necessary to account for the nonuniform density with which k-space is sampled. An analytic density compensation function (DCF) for spiral MRI, based on the Jacobian determinant for the transformation between Cartesian coordinates and the spiral sampling parameters of time and interleaf rotation angle, is derived in this paper, and the reconstruction accuracy achieved using this function is compared with that obtained using several previously published expressions. Various non-ideal conditions, including intersecting trajectories, are considered. The new DCF eliminated intensity cupping that was encountered in images reconstructed with other functions, and significantly reduced the level of artifact observed when unevenly spaced sampling trajectories, such as those achieved with trapezoidal gradient waveforms, were employed. Modified forms of this function were found to provide similar improvements when intersecting trajectories made the spiral-Cartesian transformation noninvertible, and when the shape of the spiral trajectory varied between interleaves.     

Interleaved spiral‐in/out with application to functional MRI (fMRI)

The conventional spiral‐in/out trajectory samples k‐space sufficiently in the spiral‐in path and sufficiently in the spiral‐out path to enable creation of separate images. We propose an “interleaved spiral‐in/out” trajectory comprising a spiral‐in path that gathers one half of the k‐space data, and a complimentary spiral‐out path that gathers the other half. The readout duration is thereby reduced by approximately half, offering two distinct advantages: reduction of signal dropout due to susceptibility‐induced field gradients (at the expense of signal‐to‐noise ratio [SNR]), and the ability to achieve higher spatial resolution when the readout duration is identical to the conventional method. Two reconstruction methods are described; both involve temporal filtering to remove aliasing artifacts. Empirically, interleaved spiral‐in/out images are free from false activation resulting from signal pileup around the air/tissue interface, which is common in the conventional spiral‐out method. Comparisons with conventional methods using a hyperoxia stimulus reveal greater frontal‐orbital activation volumes but a slight reduction of overall activation in other brain regions. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Non‐Cartesian parallel imaging reconstruction

Non‐Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non‐Cartesian trajectories can enable more efficient coverage of k‐space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be used to reconstruct images from undersampled Cartesian data, non‐Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the nonhomogeneous sensitivities of multi‐coil phased arrays. This review will begin with an overview of non‐Cartesian k‐space trajectories and their sampling properties, followed by an in‐depth discussion of several selected non‐Cartesian parallel imaging algorithms. Three representative non‐Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non‐Cartesian generalized autocalibrating partially parallel acquisition (GRAPPA), and Iterative Self‐Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non‐Cartesian parallel imaging will be covered. J. Magn. Reson. Imaging 2014;40:1022–1040 . © 2014 Wiley Periodicals, Inc.     

Regularized iterative reconstruction for undersampled BLADE and its applications in three‐point Dixon water–fat separation

In MRI, the suppression of fat signal is very important for many applications. Multipoint Dixon based water–fat separation methods are commonly used due to its robustness to B₀ homogeneity compared with other fat suppression methods, such as spectral fat saturation. The traditional Cartesian k‐space trajectory based multipoint Dixon technique is sensitive to motion, such as pulsatile blood flow, resulting in artifacts that compromise image quality. This work presents a three‐point Dixon water–fat separation method using undersampled BLADE (aka PROPELLER) for motion robustness and speed. A regularized iterative reconstruction method is then proposed for reducing the streaking artifacts coming from undersampling. In this study, the performance of the regularized iterative reconstruction method is first tested by simulations and on MR phantoms. The performance of the proposed technique is then evaluated in vivo by comparing it with conventional fat suppression methods on the human brain and knee. Experiments show that the presented method delivers reliable water–fat separation results. The reconstruction method suppresses streaking artifacts typical for undersampled BLADE acquisition schemes without missing fine structures in the image. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

An efficient gridding reconstruction method for multishot non‐Cartesian imaging with correction of off‐resonance artifacts

An efficient iterative gridding reconstruction method with correction of off‐resonance artifacts was developed, which is especially tailored for multiple‐shot non‐Cartesian imaging. The novelty of the method lies in that the transformation matrix for gridding (T) was constructed as the convolution of two sparse matrices, among which the former is determined by the sampling interval and the spatial distribution of the off‐resonance frequencies and the latter by the sampling trajectory and the target grid in the Cartesian space. The resulting T matrix is also sparse and can be solved efficiently with the iterative conjugate gradient algorithm. It was shown that, with the proposed method, the reconstruction speed in multiple‐shot non‐Cartesian imaging can be improved significantly while retaining high reconstruction fidelity. More important, the method proposed allows tradeoff between the accuracy and the computation time of reconstruction, making customization of the use of such a method in different applications possible. The performance of the proposed method was demonstrated by numerical simulation and multiple‐shot spiral imaging on rat brain at 4.7 T. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Characterizing and correcting gradient errors in non‐cartesian imaging: Are gradient errors linear time‐invariant (LTI)?

Non‐Cartesian and rapid imaging sequences are more sensitive to scanner imperfections such as gradient delays and eddy currents. These imperfections vary between scanners and over time and can be a significant impediment to successful implementation and eventual adoption of non‐Cartesian techniques by scanner manufacturers. Differences between the k‐space trajectory desired and the trajectory actually acquired lead to misregistration and reduction in image quality. While early calibration methods required considerable scan time, more recent methods can work more quickly by making certain approximations. We examine a rapid gradient calibration procedure applied to multiecho three‐dimensional projection reconstruction (3DPR) acquisitions in which the calibration runs as part of every scan. After measuring the trajectories traversed for excitations on each of the orthogonal gradient axes, trajectories for the oblique projections actually acquired during the scan are synthesized as linear combinations of these measurements. The ability to do rapid calibration depends on the assumption that gradient errors are linear and time‐invariant (LTI). This work examines the validity of these assumptions and shows that the assumption of linearity is reasonable, but that gradient errors can vary over short time periods (due to changes in gradient coil temperature) and thus it is important to use calibration data matched to the scan data. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Contrast‐kinetics‐resolved whole‐heart coronary MRA using 3DPR

Slow contrast infusion was recently proposed for contrast‐enhanced whole‐heart coronary MR angiography. Current protocols use Cartesian k‐space sampling with empiric acquisition delays, potentially resulting in suboptimal coronary artery delineation and image artifacts if there is a timing error. This study aimed to investigate the feasibility of using time‐resolved three‐dimensional projection reconstruction for whole‐heart coronary MR angiography. With this method, data acquisition was started simultaneously with contrast injection. Sequential time frames were reconstructed by employing a sliding window scheme with temporal tornado filtering. Additionally, a self‐timing method was developed to monitor contrast enhancement during a scan and automatically determine the peak enhancement time around which optimal temporal frames were reconstructed. Our preliminary results on six healthy volunteers showed that by using time‐resolved three‐dimensional projection reconstruction, the contrast kinetics of the coronary artery system throughout a scan could be retrospectively resolved and assessed. In addition, the blood signal dynamics predicted using self‐timing was closely correlated to the true dynamics in time‐resolved reconstruction. This approach is useful for optimizing delineation of each coronary artery and minimizing image artifacts for contrast‐enhanced whole‐heart MRA. Magn Reson Med 63:970–978, 2010. © 2010 Wiley‐Liss, Inc.     

Improved hepatic arterial phase MRI with 3‐second temporal resolution

Purpose:

To assess 3‐s temporal resolution for arterial phase bolus timing on dynamic liver MRI.

Materials and Methods:

One hundred consecutive patients undergoing fluoro‐triggered dynamic gadoxetate enhanced liver MRI with standard Cartesian k‐space LAVA (Liver Acquisition with Volume Acceleration) were compared with 61 consecutive patients imaged using spiral k‐space LAVA reconstructed at 3‐s temporal resolution with sliding window reconstruction. For qualitative analysis, bolus timing, hepatic artery branch order visualized, and overall image quality were evaluated. For quantitative analysis, contrast to noise ratio between aorta and liver parenchyma, aorta and portal vein, and signal intensity ratio between aorta and liver parenchyma were calculated.

Results:

MR fluoroscopy triggered single phase standard LAVA produced optimal arterial phase timing in 35% patients, compared with 88% with Spiral LAVA (P < 0.0001). Spiral LAVA had superior bolus timing scoring 2.0, compared with 1.0 with standard LAVA (P < 0.0001). Overall image quality and hepatic artery branch order visualization scoring were superior on spiral LAVA, compared with standard LAVA (P < 0.001). The aorta to liver parenchyma signal intensity ratio was also superior on spiral LAVA, compared with standard LAVA (2.8 vs. 2.2; P < 0.001).

Conclusion:

Dynamic liver MRI bolus timing improves using 3‐s temporal resolution. J. Magn. Reson. Imaging 2013;37:1129–1136. © 2013 Wiley Periodicals, Inc.     

Radial k‐t FOCUSS for high‐resolution cardiac cine MRI

A compressed sensing dynamic MR technique called k‐t FOCUSS (k‐t FOCal Underdetermined System Solver) has been recently proposed. It outperforms the conventional k‐t BLAST/SENSE (Broad‐use Linear Acquisition Speed‐up Technique/SENSitivity Encoding) technique by exploiting the sparsity of x‐f signals. This paper applies this idea to radial trajectories for high‐resolution cardiac cine imaging. Radial trajectories are more suitable for high‐resolution dynamic MRI than Cartesian trajectories since there is smaller tradeoff between spatial resolution and number of views if streaking artifacts due to limited views can be resolved. As shown for Cartesian trajectories, k‐t FOCUSS algorithm efficiently removes artifacts while preserving high temporal resolution. k‐t FOCUSS algorithm applied to radial trajectories is expected to enhance dynamic MRI quality. Rather than using an explicit gridding method, which transforms radial k‐space sampling data to Cartesian grid prior to applying k‐t FOCUSS algorithms, we use implicit gridding during FOCUSS iterations to prevent k‐space sampling errors from being propagated. In addition, motion estimation and motion compensation after the first FOCUSS iteration were used to further sparsify the residual image. By applying an additional k‐t FOCUSS step to the residual image, improved resolution was achieved. In vivo experimental results show that this new method can provide high spatiotemporal resolution even from a very limited radial data set. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

Using the GRAPPA operator and the generalized sampling theorem to reconstruct undersampled non‐Cartesian data

As expected from the generalized sampling theorem of Papoulis, the use of a bunched sampling acquisition scheme in conjunction with a conjugate gradient (CG) reconstruction algorithm can decrease scan time by reducing the number of phase‐encoding lines needed to generate an unaliased image at a given resolution. However, the acquisition of such bunched data requires both modified pulse sequences and high gradient performance. A novel method of generating the “bunched” data using self‐calibrating GRAPPA operator gridding (GROG), a parallel imaging method that shifts data points by small distances in k‐space (with Δk usually less than 1.0, depending on the receiver coil) using the GRAPPA operator, is presented here. With the CG reconstruction method, these additional “bunched” points can then be used to reconstruct an image with reduced artifacts from undersampled data. This method is referred to as GROG‐facilitated bunched phase encoding (BPE), or GROG‐BPE. To better understand how the patterns of bunched points, maximal blip size, and number of bunched points affect the reconstruction quality, a number of simulations were performed using the GROG‐BPE approach. Finally, to demonstrate that this method can be combined with a variety of trajectories, examples of images with reduced artifacts reconstructed from undersampled in vivo radial, spiral, and rosette data are shown. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Free‐breathing cine MRI

Standard MRI cine exams for the study of cardiac function are segmented over several heartbeats and thus require a breath‐hold to minimize breathing motion artifacts, which is a current limitation of this approach. The purpose of this study was to develop a method for the measurement and correction of respiratory motion that is compatible with cine imaging. Real‐time images were used to measure the respiratory motion of heart, to allow translations, rotations, and shears to be measured and corrected in the k‐space domain prior to a final gated‐segmented reconstruction, using the same data for both purposes. A method for data rejection to address the effects of through‐plane motion and complex deformations is described (respiratory gating). A radial k‐space trajectory was used in this study to allow direct reconstruction of undersampled real‐time images, although the techniques presented are applicable with Cartesian k‐space trajectories. Corrected and uncorrected free‐breathing gated‐segmented images acquired over 18 sec were compared to the current standard breath‐hold Cartesian images using both quantitative sharpness profiles (mm^?1) and clinical scoring (1 to 5 scale, 3: clinically acceptable). Free‐breathing, free‐breathing corrected, and breath‐hold images had average sharpness values of 0.23 ± 0.04, 0.38 ± 0.04, and 0.44 ± 0.04 mm^?1 measured at the blood–endocardium interface, and clinical scores of 2.2 ± 0.5, 4.2 ± 0.4, and 4.7 ± 0.5, respectively. Magn Reson Med 60:709–717, 2008. © 2008 Wiley‐Liss, Inc.     

Fast,simple gradient delay estimation for spiral MRI

Timing delays between data acquisition and gradient transmission result in image degradation. This is especially true in spiral MRI, where delays can alter data in a nonuniform manner, generating significant artifact in the reconstructed data. The many methods that exist to mitigate these delays or measure the k‐space coordinates require long measurement times, complicated analysis, specialized phantoms or hardware, or significant changes to the sequence of interest. A fast and simple method is proposed to measure delays on each gradient channel. It requires only minimal modification to an existing spiral sequence and can be used to measure independent delays on three gradient channels and any scan subject within six sequence repetition times. The effectiveness and accuracy of this method are analyzed. Magn Reson Med 63:1683–1690, 2010. © 2010 Wiley‐Liss, Inc.     

Optimization of k‐space trajectories for compressed sensing by Bayesian experimental design

The optimization of k‐space sampling for nonlinear sparse MRI reconstruction is phrased as a Bayesian experimental design problem. Bayesian inference is approximated by a novel relaxation to standard signal processing primitives, resulting in an efficient optimization algorithm for Cartesian and spiral trajectories. On clinical resolution brain image data from a Siemens 3T scanner, automatically optimized trajectories lead to significantly improved images, compared to standard low‐pass, equispaced, or variable density randomized designs. Insights into the nonlinear design optimization problem for MRI are given. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

Variable‐density spiral‐in/out functional magnetic resonance imaging

A variable‐density spiral k‐space trajectory is introduced for brain functional magnetic resonance imaging. The proposed spiral trajectory consists of an Archimedean spiral from the k‐space origin to an arbitrary fraction r of the maximum k‐space radius, extending beyond this point with a variable‐density spiral in which the sampling density decreases as the k‐space radius increases. It, therefore, permits a reduction in readout time at the expense of undersampling only the high spatial frequencies, in which the energy in T₂*‐weighted brain images is low. The trajectory was implemented in a two‐dimensional spiral‐in/out sequence, and single‐shot high‐resolution (1.72 × 1.72 mm² in‐plane) functional magnetic resonance imaging data were acquired from human volunteers. Compared with a two‐shot fully Archimedean spiral sequence with the same spatial coverage and total scan time, the variable‐density sequence yielded greater activation magnitudes with improved temporal efficiency and minor artifacts. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.     

SPIRiT: Iterative self‐consistent parallel imaging reconstruction from arbitrary k‐space

A new approach to autocalibrating, coil‐by‐coil parallel imaging reconstruction, is presented. It is a generalized reconstruction framework based on self‐consistency. The reconstruction problem is formulated as an optimization that yields the most consistent solution with the calibration and acquisition data. The approach is general and can accurately reconstruct images from arbitrary k‐space sampling patterns. The formulation can flexibly incorporate additional image priors such as off‐resonance correction and regularization terms that appear in compressed sensing. Several iterative strategies to solve the posed reconstruction problem in both image and k‐space domain are presented. These are based on a projection over convex sets and conjugate gradient algorithms. Phantom and in vivo studies demonstrate efficient reconstructions from undersampled Cartesian and spiral trajectories. Reconstructions that include off‐resonance correction and nonlinear ?₁‐wavelet regularization are also demonstrated. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

The influence of radial undersampling schemes on compressed sensing reconstruction in breast MRI

Fast imaging applications in magnetic resonance imaging (MRI) frequently involve undersampling of k‐space data to achieve the desired temporal resolution. However, high temporal resolution images generated from undersampled data suffer from aliasing artifacts. In radial k‐space sampling, this manifests as undesirable streaks that obscure image detail. Compressed sensing reconstruction has been shown to reduce such streak artifacts, based on the assumption of image sparsity. Here, compressed sensing is implemented with three different radial sampling schemes (golden‐angle, bit‐reversed, and random sampling), which are compared over a range of spatiotemporal resolutions. The sampling methods are implemented in static scenarios where different undersampling patterns could be compared. Results from point spread function studies, simulations, phantom and in vivo experiments show that the choice of radial sampling pattern influences the quality of the final image reconstructed by the compressed sensing algorithm. While evenly undersampled radial trajectories are best for specific temporal resolutions, golden‐angle radial sampling results in the least overall error when various temporal resolutions are considered. Reduced temporal fluctuations from aliasing artifacts in golden‐angle sampling translates to improved compressed sensing reconstructions overall. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.     

Higher order reconstruction for MRI in the presence of spatiotemporal field perturbations

Despite continuous hardware advances, MRI is frequently subject to field perturbations that are of higher than first order in space and thus violate the traditional k‐space picture of spatial encoding. Sources of higher order perturbations include eddy currents, concomitant fields, thermal drifts, and imperfections of higher order shim systems. In conventional MRI with Fourier reconstruction, they give rise to geometric distortions, blurring, artifacts, and error in quantitative data. This work describes an alternative approach in which the entire field evolution, including higher order effects, is accounted for by viewing image reconstruction as a generic inverse problem. The relevant field evolutions are measured with a third‐order NMR field camera. Algebraic reconstruction is then formulated such as to jointly minimize artifacts and noise in the resulting image. It is solved by an iterative conjugate‐gradient algorithm that uses explicit matrix‐vector multiplication to accommodate arbitrary net encoding. The feasibility and benefits of this approach are demonstrated by examples of diffusion imaging. In a phantom study, it is shown that higher order reconstruction largely overcomes variable image distortions that diffusion gradients induce in EPI data. In vivo experiments then demonstrate that the resulting geometric consistency permits straightforward tensor analysis without coregistration. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

k-t ISD: dynamic cardiac MR imaging using compressed sensing with iterative support detection

Compressed sensing (CS) has been used in dynamic cardiac MRI to reduce the data acquisition time. The sparseness of the dynamic image series in the spatial‐ and temporal‐frequency (x‐f) domain has been exploited in existing works. In this article, we propose a new k‐t iterative support detection (k‐t ISD) method to improve the CS reconstruction for dynamic cardiac MRI by incorporating additional information on the support of the dynamic image in x‐f space based on the theory of CS with partially known support. The proposed method uses an iterative procedure for alternating between image reconstruction and support detection in x‐f space. At each iteration, a truncated ?₁ minimization is applied to obtain the reconstructed image in x‐f space using the support information from the previous iteration. Subsequently, by thresholding the reconstruction, we update the support information to be used in the next iteration. Experimental results demonstrate that the proposed k‐t ISD method improves the reconstruction quality of dynamic cardiac MRI over the basic CS method in which support information is not exploited. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.     

Two‐dimensional radial acquisition technique with density adaption in sodium MRI

Conventional 2D radial projections suffer from losses in signal‐to‐noise ratio efficiency because of the nonuniform k‐space sampling. In this study, a 2D projection reconstruction method with variable gradient amplitudes is presented to cover the k‐space uniformly. The gradient is designed to keep the average sampling density constant. By this, signal‐to‐noise ratio is increased, and the linear form of the radial trajectory is kept. The simple gradient design and low hardware requirements in respect of slew rate allow an easy implementation at MR scanners. Measurements with the density‐adapted 2D radial trajectory were compared with the conventional projection reconstruction method. It is demonstrated that the density‐adapted 2D radial trajectory technique provides higher signal‐to‐noise ratio (up to 28% in brain tissue), less blurring, and fewer artifacts in the presence of magnetic field inhomogeneities than imaging with the conventional 2D radial trajectory scheme. The presented sequence is well‐suited for electrocardiographically gated sodium heart MRI and other applications with short relaxation times. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.