Reduced aliasing artifacts using variable-density k-space sampling trajectories.

A variable-density k-space sampling method is proposed to reduce aliasing artifacts in MR images. Because most of the energy of an image is concentrated around the k-space center, aliasing artifacts will contain mostly low-frequency components if the k-space is uniformly undersampled. On the other hand, because the outer k-space region contains little energy, undersampling that region will not contribute severe aliasing artifacts. Therefore, a variable-density trajectory may sufficiently sample the central k-space region to reduce low-frequency aliasing artifacts and may undersample the outer k-space region to reduce scan time and to increase resolution. In this paper, the variable-density sampling method was implemented for both spiral imaging and two-dimensional Fourier transform (2DFT) imaging. Simulations, phantom images and in vivo cardiac images show that this method can significantly reduce the total energy of aliasing artifacts. In general, this method can be applied to all types of k-space sampling trajectories.     

High-resolution diffusion-weighted imaging with interleaved variable-density spiral acquisitions

PURPOSE: To develop a multishot magnetic resonance imaging (MRI) pulse sequence and reconstruction algorithm for diffusion-weighted imaging (DWI) in the brain with submillimeter in-plane resolution. MATERIALS AND METHODS: A self-navigated multishot acquisition technique based on variable-density spiral k-space trajectory design was implemented on clinical MRI scanners. The image reconstruction algorithm takes advantage of the oversampling of the center k-space and uses the densely sampled central portion of the k-space data for both imaging reconstruction and motion correction. The developed DWI technique was tested in an agar gel phantom and three healthy volunteers. RESULTS: Motions result in phase and k-space shifts in the DWI data acquired using multishot spiral acquisitions. With the two-dimensional self-navigator correction, diffusion-weighted images with a resolution of 0.9 x 0.9 x 3 mm3 were successfully obtained using different interleaves ranging from 8-32. The measured apparent diffusion coefficient (ADC) in the homogenous gel phantom was (1.66 +/- 0.09) x 10(-3) mm2/second, which was the same as measured with single-shot methods. The intersubject average ADC from the brain parenchyma of normal adults was (0.91 +/- 0.01) x 10(-3) mm2/second, which was in a good agreement with the reported literature values. CONCLUSION: The self-navigated multishot variable-density spiral acquisition provides a time-efficient approach to acquire high-resolution diffusion-weighted images on a clinical scanner. The reconstruction algorithm based on motion correction in the k-space data is robust, and measured ADC values are accurate and reproducible.     

Undersampled elliptical centric view-order for improved spatial resolution in contrast-enhanced MR angiography.

Although contrast-enhanced MR angiography (CE-MRA) has been successfully developed into a routine clinical imaging technique, there is still need for improved spatial resolution in a given acquisition time. Undersampled projection reconstruction (PR) techniques maintain spatial resolution with reduced scan times, and the elliptical centric (EC) view order provides high quality arterial phase images without venous contamination. In this work, we present a hybrid elliptical centric-projection reconstruction (EC-PR) technique to provide spatial resolution improvement over standard EC in a given time. The k-space sampling was performed by undersampling the periphery of the k(Y)-k(Z) phase encoding plane of an EC view order in a PR like manner. The sampled views were maintained on a rectilinear grid, and thus reconstructed by standard 3DFT. The non-sampled views were compensated either by zero-filling or performing a 2D homodyne reconstruction. Compared to a fully sampled k-space, the EC-PR sequence acquired in the same scan time provides a resolution improvement of about two, as shown by point spread function analysis and phantom experiments. The hypothesis that EC-PR provides improved resolution while retaining diagnostically adequate SNR was tested in 11 CE-MRA studies of the popliteal and carotid arteries and shown to be true (P < 0.03).     

Reduced spatial side lobes in chemical-shift imaging.

Density-weighted k-space sampling with spiral trajectories is used to reduce spatial side lobes in chemical-shift imaging (CSI). In this method, more time is spent collecting data at the center of k space and less time at the edges of k space in order to make the sampling density proportional to a given apodization function, subject to constraints imposed by gradient performance and Nyquist sampling. The efficient k-space coverage of spiral-based trajectories enables good control over the sampling density within practical in vivo scan times. The density-weighted acquisition is compared to a conventional, nonweighted spiral sampling without the application of a window function. For a fixed voxel size and imaging time, the noise variance is observed to be the same for both cases, while spatial side lobes are greatly reduced with the variable-density sampling. This method is demonstrated on a normal volunteer by imaging of brain metabolites at 1.5 T with both single slice CSI and volumetric CSI. Magn Reson Med 42:314-323, 1999.     

High-resolution DTI of a localized volume using 3D single-shot diffusion-weighted STimulated echo-planar imaging (3D ss-DWSTEPI).

Diffusion tensor MRI (DTI) using conventional single-shot (SS) 2D diffusion-weighted (DW)-EPI is subject to severe susceptibility artifacts. Multishot DW imaging (DWI) techniques can reduce these distortions, but they generally suffer from artifacts caused by motion-induced phase errors. Parallel imaging can also reduce the distortions if the sensitivity profiles of the receiver coils allow a sufficiently high reduction factor for the desired field of view (FOV). A novel 3D DTI technique, termed 3D single-shot STimulated EPI (3D ss-STEPI), was developed to acquire high-resolution DW images of a localized region. The new technique completes k-space acquisition of a limited 3D volume after a single diffusion preparation. Because the DW magnetization is stored in the longitudinal direction until readout, it undergoes T(1) rather than T(2) decay. Inner volume imaging (IVI) is used to limit the imaging volume. This reduces the time required for EPI readout of each complete k(x)-k(y) plane, and hence reduces T(2)(*) decay during the readout and T(1) decay between the readout of each k(z). 3D ss-STEPI images appear to be free of severe susceptibility and motion artifacts. 3D ss-STEPI allows high-resolution DTI of limited volumes of interest, such as localized brain regions, cervical spinal cord, optic nerve, and other extracranial organs.     

A modified projection reconstruction trajectory for reduction of undersampling artifacts

PURPOSE: To reduce undersampling artifacts for a given number of repetitions of the projection reconstruction (PR) sequence by modifying its k-space trajectory to sample more mid-frequencies while reducing the sampling coverage of the peripheral spatial frequencies. MATERIALS AND METHODS: The single k-space spoke measured per repetition in the standard PR was modified so that one complete and two partial spokes were measured per repetition but with decreased k-space extent. The point spread functions (PSFs) and undersampling artifacts of the modified PR were compared with those of the standard PR for various numbers of projections. Phantom and in vivo images were used to assess the relative performance. RESULTS: PSF analysis indicated that the modified PR method provided reduced undersampling artifacts with somewhat reduced spatial resolution. The phantom and in vivo images corroborated this. CONCLUSION: The modified PR trajectory provides reduced undersampling artifact vs. the standard PR, particularly when the number of projections is limited and the artifact level is high.     

Deconvolution-interpolation gridding (DING): accurate reconstruction for arbitrary k-space trajectories.

A simple iterative algorithm, termed deconvolution-interpolation gridding (DING), is presented to address the problem of reconstructing images from arbitrarily-sampled k-space. The new algorithm solves a sparse system of linear equations that is equivalent to a deconvolution of the k-space with a small window. The deconvolution operation results in increased reconstruction accuracy without grid subsampling, at some cost to computational load. By avoiding grid oversampling, the new solution saves memory, which is critical for 3D trajectories. The DING algorithm does not require the calculation of a sampling density compensation function, which is often problematic. DING's sparse linear system is inverted efficiently using the conjugate gradient (CG) method. The reconstruction of the gridding system matrix is simple and fast, and no regularization is needed. This feature renders DING suitable for situations where the k-space trajectory is changed often or is not known a priori, such as when patient motion occurs during the scan. DING was compared with conventional gridding and an iterative reconstruction method in computer simulations and in vivo spiral MRI experiments. The results demonstrate a stable performance and reduced root mean square (RMS) error for DING in different k-space trajectories.     

Simulation study of scan timing in three-dimensional contrast-enhanced MR angiography

In our study of three-dimensional contrast-enhanced MR angiography, we performed a computer simulation to quantitatively investigate vessel visibility according to scan timing. To construct the simulated MR images, we varied the position (scan timing) and range (enhancement-duration) of k-space data assumed to be acquired during contrast enhancement. In the present study, either the sequential or centric phase-encoding order in k(y) and k(z) on k-space was assumed to be used. When scan timing was shifted from the optimal timing, the visibility of thick vessels decreased, and the signal intensity in thin vessels was higher than that in thick vessels. We found that the appropriate setting of scan timing was an important factor in the visibility of thick vessels. Meanwhile, we also noted that extending the enhancement-duration (or shortening the scan time) could increase the visibility of thin vessels. Our results and the simple technique used for simulation are considered to be useful for the study of three-dimensional contrast-enhanced MR angiography.     

Retrospective motion compensation using variable-density spiral trajectories

PURPOSE: To develop a method of retrospectively correcting for motion artifacts using a variable-density spiral (VDS) trajectory. MATERIALS AND METHODS: Each VDS interleaf was designed to adequately sample the same center region of k-space. This central overlapping region can then be used to measure rigid body motion between the acquisition of each VDS interleaf. By applying appropriate phase shifts and rotations of the k-space data, rigid body motion artifacts can be removed, resulting in images with less motion corruption. RESULTS: Both phantom and volunteer experiments are shown, demonstrating the technique's ability to further reduce artifacts in images acquired with an already motion-resistant acquisition trajectory. Registration accuracy is highly dependent on the trajectory design parameters. This space was explored to find an optimal design of VDS trajectories for motion compensation. CONCLUSION: Using appropriately designed VDS trajectories, residual motion artifacts can be significantly reduced by retrospectively correcting for in-plane rigid body motion. An overlapping region of approximately 8% of the central region of k-space and approximately 70 interleaves were found to be near-optimal parameters for retrospective correction using VDS trajectories.     

MRI using a concentric rings trajectory.

The concentric rings two-dimensional (2D) k-space trajectory provides an alternative way to sample polar data. By collecting 2D k-space data in a series of rings, many unique properties are observed. The concentric rings are inherently centric-ordered, provide a smooth weighting in k-space, and enable shorter total scan times. Due to these properties, the concentric rings are well-suited as a readout trajectory for magnetization-prepared studies. When non-Cartesian trajectories are used for MRI, off-resonance effects can cause blurring and degrade the image quality. For the concentric rings, off-resonance blur can be corrected by retracing rings near the center of k-space to obtain a field map with no extra excitations, and then employing multifrequency reconstruction. Simulations show that the concentric rings exhibit minimal effects due to T(2) (*) modulation, enable shorter scan times for a Nyquist-sampled dataset than projection-reconstruction imaging or Cartesian 2D Fourier transform (2DFT) imaging, and have more spatially distributed flow and motion properties than Cartesian sampling. Experimental results show that off-resonance blurring can be successfully corrected to obtain high-resolution images. Results also show that concentric rings effectively capture the intended contrast in a magnetization-prepared sequence.     

Novel interleaved spiral imaging motion correction technique using orbital navigators.

Although spiral imaging seldom produces apparent artifacts related to flow, it remains sensitive to rapid object motion. In this article, a new correction method is presented for rapid rigid body motion in interleaved spiral imaging. With this technique, an identical circular navigator k-space trajectory is linked to each spiral trajectory. Data inconsistency due to both rotation and translation among spiral interleaves can be corrected by evaluating the magnitudes and phases of the data contained in the navigator "ring." Further, it is difficult to create a frequency field map for off-resonance correction when an object moves during a scan, because there is motion-dependent misregistration between the two images acquired with different TEs. However, this difficulty can be overcome by combining the motion-correction method with a recently proposed technique (off-resonance correction using variable-density spirals (ORC-VDS)), thereby enabling both motion compensation and off-resonance correction with no additional scanning.     

3D z-shim method for reduction of susceptibility effects in BOLD fMRI.

Susceptibility-induced magnetic field gradients (SFGs) perpendicular to the slice plane often result in signal dropout in blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) experiments. Two-dimensional (2D) z-shim methods reduce these effects by acquiring multiple images with different slice refocusing gradient areas. In this work a 3D z-shim method is introduced as a more efficient alternative. The technique augments the k-space data for a conventional 3D phase encoding acquisition with N additional lines that extend the k(z) coverage sufficiently to sample k-space fully in regions with SFGs. Multiple subsets of these data are reconstructed using a sliding window that provides N +1 z-shim images. Fewer total acquisitions are required than with the 2D method for the same coverage, and finer z-shim steps are obtained. The technique is demonstrated with a motor task using intentionally introduced SFGs and compared with the 2D method. The results confirm increased BOLD SNR and activation with the new method in good agreement with theory. Magn Reson Med 42:290-299, 1999.     

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.     

Improved venous suppression and spatial resolution with SENSE in elliptical centric 3D contrast-enhanced MR angiography.

The elliptical centric (EC) view order samples a 3DFT acquisition from the center of k-space outward, and when applied to contrast-enhanced MR angiography (CE-MRA) provides intrinsic venous suppression. This is because the veins enhance several seconds after the scan is initiated, and are thus encoded solely by noncentral k-space frequencies. A separate method, sensitivity encoding (SENSE), accelerates the k-space sampling rate by reducing the phase FOV or, equivalently, by increasing the k-space sampling interval, and has been used to increase spatiotemporal resolution. We hypothesized that by combining SENSE with EC, sampling of central k-space would be accelerated and the k-space radius at which the veins first showed contrast enhancement would be increased over a reference scan, thus providing improved venous suppression and spatial resolution without additional scan time. This hypothesis was studied with the use of phantom and carotid CE-MRA experiments, and the results demonstrated an approximate 25% reduction in venous signal when SENSE was used.     

Fast three-dimensional k-space trajectory design using missile guidance ideas.

Three-dimensional (3D) k-space trajectories are needed to acquire volumetric images in MRI. While scan time is determined by the trajectory efficiency, image quality and distortions depend on the shape of the trajectories. There are several 3D trajectory strategies for sampling the k-space using rectilinear or curve schemes. Since there is no evidence about their optimality in terms of image quality and acquisition time, a new design method based on missile guidance ideas is explored. Since air-to-air missile guidance shares similar goals and constraints with the problem of k-space trajectory design, a control approach for missiles is used to design a 3D trajectory. The k-space is divided into small cubes, and each one is treated as a target to be sampled. The main goal is to cover the entire space as quickly and efficiently as possible, with good performance under different conditions. This novel design method is compared to other trajectories using simulated and real data. As an example, a trajectory that requires 0.11 times the number of shots needed by the cylindrical 3DFT acquisition was designed. This trajectory requires more shots (1.66 times) than the stack of spirals, but behaves better under nonideal conditions, such as off-resonance and motion.     

Spiral scanning with anisotropic field of view

Spiral scanning has been used to achieve much shorter scan times than conventional techniques for a wide range of applications. The major drawback with spiral scans is blurring from off-resonant spins, which is proportional to the readout time. Blurring limits maximal spatial resolution and minimal scan time potentially achievable with spiral scanning. Anisotropic field of view is used in conventional scanning to improve image quality by matching /c-space trajectory to object characteristics. Anisotropic field of view improves spatial resolution in spiral scanning without increasing scan time or blurring. The resolution improvement results from increased maximal k-space radius allowed by the lower field of view. A field of view reduction by a factor of 2 in one direction provides up to 60% resolution improvement in that direction. Reduced SNR also results from non-uniform /c-space sampling.     

Design and analysis of a practical 3D cones trajectory.

The 3D Cones k-space trajectory has many desirable properties for rapid and ultra-short echo time magnetic resonance imaging. An algorithm is presented that generates the 3D Cones gradient waveforms given a desired field of view and resolution. The algorithm enables a favorable trade-off between increases in readout time and decreases in the total number of required readouts. The resulting trajectory is very signal-to-noise ratio (SNR) efficient and has excellent aliasing properties. A rapid high-resolution ultra-short echo time imaging sequence is used to compare the 3D Cones trajectory to 3D projection reconstruction (3DPR) sampling schemes. For equivalent scan times, the 3D Cones trajectory has better SNR performance and fewer aliasing artifacts as compared to the 3DPR trajectory.     

Design of a logarithmic k-space spiral trajectory.

Spiral acquisitions are used in fast cardiac imaging because they traverse k-space efficiently and minimize flow artifacts. A variable pitch logarithmic spiral trajectory is designed to critically sample the low-frequency region in k-space and gradually undersample the high-frequency region. An approximate analytical expression for the trajectory provides a fast means to calculate the gradient waveforms and the sampled data points. A numerical method is introduced based on the trajectory curvature and the rate of change in the gradient magnitude with time for the composite Archimedean-logarithmic trajectory. The pulse sequence is implemented and images are acquired on phantoms and human hearts. The images show improved image resolution and some improvement in image quality as a result of increased extent in k-space and reduction in aliasing artifacts, respectively.