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.     

Direct parallel image reconstructions for spiral trajectories using GRAPPA.

The use of spiral trajectories is an efficient way to cover a desired k-space partition in magnetic resonance imaging (MRI). Compared to conventional Cartesian k-space sampling, it allows faster acquisitions and results in a slight reduction of the high gradient demand in fast dynamic scans, such as in functional MRI (fMRI). However, spiral images are more susceptible to off-resonance effects that cause blurring artifacts and distortions of the point-spread function (PSF), and thereby degrade the image quality. Since off-resonance effects scale with the readout duration, the respective artifacts can be reduced by shortening the readout trajectory. Multishot experiments represent one approach to reduce these artifacts in spiral imaging, but result in longer scan times and potentially increased flow and motion artifacts. Parallel imaging methods are another promising approach to improve image quality through an increase in the acquisition speed. However, non-Cartesian parallel image reconstructions are known to be computationally time-consuming, which is prohibitive for clinical applications. In this study a new and fast approach for parallel image reconstructions for spiral imaging based on the generalized autocalibrating partially parallel acquisitions (GRAPPA) methodology is presented. With this approach the computational burden is reduced such that it becomes comparable to that needed in accelerated Cartesian procedures. The respective spiral images with two- to eightfold acceleration clearly benefit from the advantages of parallel imaging, such as enabling parallel MRI single-shot spiral imaging with the off-resonance behavior of multishot acquisitions.     

Consistent non-cartesian off-axis MRI quality: calibrating and removing multiple sources of demodulation phase errors.

The consistency of off-axis MRI with non-Cartesian sequences across a large number of scanners is highly variable. Improper timing alignment of the gradient fields, data acquisition system, and real-time frequency demodulation reference signal, which are necessary for off-axis imaging, is an important source of this variability. In addition, eddy currents and anisotropic gradient delays cause deviations in k-space trajectories that in turn make the demodulation reference signals inaccurate. A method is presented to quickly measure the timing error in the frequency demodulation reference signal and separate it from anisotropic gradient delays. k-Space deviations, as measured with a previous gradient calibration technique, are shown to be a second source of demodulation phase errors that degrade image quality. Using the timing delay and k-space deviations, a retrospective phase correction is applied to each k-space sample before the data are regridded during reconstruction. The timing delays of four MR scanners were measured to be 4.2-7.5 micros below the manufacturer's suggested delay. Significant degradation in 3D radial (3D projection reconstruction (PR)) knee and breast images are retrospectively corrected while a partial prospective correction is applied for spiral imaging. The method allows for more consistent performance of non-Cartesian sequences across multiple scanners without operator intervention.     

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.     

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.     

Spiral imaging: a critical appraisal

In view of recent applications in cardiovascular and functional brain imaging, this work revisits the basic performance characteristics of spiral imaging in direct comparison to echo-planar imaging (EPI) and conventional rapid gradient-echo imaging. Using both computer simulations and experiments on phantoms and human subjects at 2.9 T, the study emphasizes single-shot applications and addresses the design of a suitable trajectory, the choice of a gridding algorithm, and the sensitivity to experimental inadequacies. As a general result, the combination of a spiral trajectory with regridding of the k-space data poses no principle obstacle for high-quality imaging. On the other hand, experimental difficulties such as gradient deviations, resonance offset contributions, and concomitant field effects cause more pronounced and even less acceptable image artifacts than usually obtained for EPI. Moreover, when ignoring parallel imaging strategies that are also applicable to EPI, improvements of image quality via reduced acquisition periods are only achievable by interleaved multishot spirals because partial Fourier sampling and rectangular fields of view (FOVs) cannot be exploited for non-Cartesian trajectories. Taken together, while spiral imaging may find its niche applications, most high-speed imaging needs are more easily served by EPI.     

Applying the uniform resampling (URS) algorithm to a lissajous trajectory: fast image reconstruction with optimal gridding.

Various kinds of nonrectilinear Cartesian k-space trajectories have been studied, such as spiral, circular, and rosette trajectories. Although the nonrectilinear Cartesian sampling techniques generally have the advantage of fast data acquisition, the gridding process prior to 2D-FFT image reconstruction usually requires a number of additional calculations, thus necessitating an increase in the computation time. Further, the reconstructed image often exhibits artifacts resulting from both the k-space sampling pattern and the gridding procedure. To date, it has been demonstrated in only a few studies that the special geometric sampling patterns of certain specific trajectories facilitate fast image reconstruction. In other words, the inherent link among the trajectory, the sampling scheme, and the associated complexity of the regridding/reconstruction process has been investigated to only a limited extent. In this study, it is demonstrated that a Lissajous trajectory has the special geometric characteristics necessary for rapid reconstruction of nonrectilinear Cartesian k-space trajectories with constant sampling time intervals. Because of the applicability of a uniform resampling (URS) algorithm, a high-quality reconstructed image is obtained in a short reconstruction time when compared to other gridding algorithms.     

Fast 3D imaging using variable-density spiral trajectories with applications to limb perfusion.

Variable-density k-space sampling using a stack-of-spirals trajectory is proposed for ultra fast 3D imaging. Since most of the energy of an image is concentrated near the k-space origin, a variable-density k-space sampling method can be used to reduce the sampling density in the outer portion of k-space. This significantly reduces scan time while introducing only minor aliasing artifacts from the low-energy, high-spatial-frequency components. A stack-of-spirals trajectory allows control over the density variations in both the k(x)-k(y) plane and the k(z) direction while fast k-space coverage is provided by spiral trajectories in the k(x)-k(y) plane. A variable-density stack-of-spirals trajectory consists of variable-density spirals in each k(x)-k(y) plane that are located in varying density in the k(z) direction. Phantom experiments demonstrate that reasonable image quality is preserved with approximately half the scan time. This technique was then applied to first-pass perfusion imaging of the lower extremities which demands very rapid volume coverage. Using a variable-density stack-of-spirals trajectory, 3D images were acquired at a temporal resolution of 2.8 sec over a large volume with a 2.5 x 2.5 x 8 mm(3) spatial resolution. These images were used to resolve the time-course of muscle intensity following contrast injection.     

Improvement of spiral MRI with the measured k-space trajectory

The k-space trajectory of a spiral imaging sequence was measured with a self-encoding technique. The image quality improved dramatically when reconstructed with the measured k-space trajectory. There were substantial artifacts in images reconstructed with the derived k-space trajectory under the assumption of gradient system linearity. The results indicated the non-linearity of the gradient system and the effectiveness of the correction technique.     

MR coronary vessel wall imaging: comparison between radial and spiral k-space sampling

PURPOSE: To compare radial and spiral k-space sampling in navigator-gated ECG-triggered three-dimensional (3D) coronary vessel wall imaging. MATERIALS AND METHODS: The right coronary artery (RCA) vessel walls of eight healthy subjects were imaged using a modified double-inversion prepulse in concert with radial and spiral data acquisition. For data analysis, two investigators blinded to the sequence parameters subjectively assessed image quality in terms of artifacts and vessel wall visualization. Objective measures of the signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and vessel wall definition were also determined. RESULTS: Radial k-space sampling demonstrated fewer artifacts and led to improved visualization of the coronary vessel wall compared to spiral imaging (P < 0.05). This finding was also reflected in a better vessel wall definition using radial data acquisition (P < 0.05). SNR and CNR were found to be higher when spiral k-space sampling was used (n.s.). CONCLUSION: Radial k-space sampling in concert with free-breathing navigator-gated cardiac-triggered MRI of the coronary vessel wall resulted in fewer motion artifacts and improved vessel wall definition compared to spiral k-space sampling. The proposed approach therefore appears to be preferable.     

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.     

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.     

Augmented generalized SENSE reconstruction to correct for rigid body motion.

The correction of motion artifacts continues to be a significant problem in MRI. In the case of uncooperative patients, such as children, or patients who are unable to remain stationary, the accurate determination and correction of motion artifacts becomes a very important prerequisite for achieving good image quality. The application of conventional motion-correction strategies often produces inconsistencies in k-space data. As a result, significant residual artifacts can persist. In this work a formalism is introduced for parallel imaging in the presence of motion. The proposed method can improve overall image quality because it diminishes k-space inconsistencies by exploiting the complementary image encoding capacity of individual receiver coils. Specifically, an augmented version of an iterative SENSE reconstruction is used as a means of synthesizing the missing data in k-space. Motion is determined from low-resolution navigator images that are coregistered by an automatic registration routine. Navigator data can be derived from self-navigating k-space trajectories or in combination with other navigation schemes that estimate patient motion. This correction method is demonstrated by interleaved spiral images collected from volunteers. Conventional spiral scans and scans corrected with proposed techniques are shown, and the results illustrate the capacity of this new correction approach.     

Concomitant gradient field effects in spiral scans.

Maxwell's equations imply that imaging gradients are accompanied by higher order spatially varying fields (concomitant fields) that can cause artifacts in MR imaging. The lowest order concomitant fields depend quadratically on the imaging gradient amplitude and inversely on the static field strength. Time-varying concomitant fields that accompany the readout gradients of spiral scans cause unwanted phase accumulation during the readout, resulting in spatially dependent blurring. Concomitant field phase errors are independent of echo time and, therefore, cannot be detected using Dixon-type field map measurements that are normally used to deblur spiral scan images. Data acquisition methods that reduce concomitant field blurring increase off-resonant spin blurring, and vice versa. Blurring caused by concomitant fields can be removed by variations of image reconstruction methods developed to correct for spatially dependent resonance offsets with nonrectangular k-space trajectories.     

Three-dimensional MRI with an undersampled spherical shells trajectory.

The shells trajectory is a 3D data acquisition method with improved efficiency compared to Cartesian sampling. It is a true center-out trajectory that does not repeatedly resample the center of k-space, and also offers advantages for motion correction. This work demonstrates that k-space undersampling can be combined with the shells trajectory to further accelerate the acquisition. The undersampling was implemented by removing selected interleaves from shells with larger radii. Because only the outer portion of k-space was undersampled, the artifacts introduced were of low energy and high spatial frequency. The undersampling rate was determined by a Kaiser window with a variable shape parameter beta. Various undersampling schemes with different beta values were examined. Phantom and volunteer studies demonstrate that when up to a twofold acceleration is achieved, only minor artifacts are introduced by undersampling the shells trajectory. For a fixed acquisition time, the improved efficiency can be used to increase spatial resolution.     

Reconstruction of undersampled non-Cartesian data sets using pseudo-Cartesian GRAPPA in conjunction with GROG.

Most k-space-based parallel imaging reconstruction techniques, such as Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA), necessitate the acquisition of regularly sampled Cartesian k-space data to reconstruct a nonaliased image efficiently. However, non-Cartesian sampling schemes offer some inherent advantages to the user due to their better coverage of the center of k-space and faster acquisition times. On the other hand, these sampling schemes have the disadvantage that the points acquired generally do not lie on a grid and have complex k-space sampling patterns. Thus, the extension of Cartesian GRAPPA to non-Cartesian sequences is nontrivial. This study introduces a simple, novel method for performing Cartesian GRAPPA reconstructions on undersampled non-Cartesian k-space data gridded using GROG (GRAPPA Operator Gridding) to arrive at a nonaliased image. Because the undersampled non-Cartesian data cannot be reconstructed using a single GRAPPA kernel, several Cartesian patterns are selected for the reconstruction. This flexibility in terms of both the appearance and number of patterns allows this pseudo-Cartesian GRAPPA to be used with undersampled data sets acquired with any non-Cartesian trajectory. The successful implementation of the reconstruction algorithm using several different trajectories, including radial, rosette, spiral, one-dimensional non-Cartesian, and zig-zag trajectories, is demonstrated.     

Spiral-in/out BOLD fMRI for increased SNR and reduced susceptibility artifacts.

BOLD fMRI is hampered by dropout of signal in the orbitofrontal and parietal brain regions due to magnetic field gradients near air-tissue interfaces. This work reports the use of spiral-in trajectories that begin at the edge of k-space and end at the origin, and spiral in/out trajectories in which a spiral-in readout is followed by a conventional spiral-out trajectory. The spiral-in trajectory reduces the dropout and increases the BOLD contrast. The spiral-in and spiral-out images can be combined in several ways to simultaneously achieve increased signal-to-noise ratio (SNR) and reduced dropout artifacts. Activation experiments employing an olfaction task demonstrate significantly increased activation volumes due to reduced dropout, and overall increased SNR in all regions.     

Bunched phase encoding (BPE): a new fast data acquisition method in MRI.

A new fast data acquisition method, "Bunched Phase Encoding" (BPE), is presented. In conventional rectilinear data acquisition, only a readout gradient (and no phase encoding gradient) is applied when k-space data are acquired. Reduction of the number of phase encoding lines by increasing the phase encoding step size often leads to aliasing artifacts. Papoulis's generalized sampling theory asserts that in some cases aliasing artifact-free signals can be reconstructed even if the Nyquist criterion is violated in some regions of the Fourier domain. In this study, Papoulis's theoretical construct is exploited to reduce the number of acquired phase encoding lines. To achieve this, k-space data are sampled along a "zigzag" trajectory during each readout; samples are acquired at a sampling frequency higher than that of the normal rectilinear acquisition. The total number of TR cycles and, hence, the total scan time can be reduced. The resultant signal-to-noise ratio (SNR) often varies across the reconstructed image when using the BPE technique, and the image SNR depends on the reconstruction method. This work is comparable to a gradient based version of parallel imaging. Evidence suggests it may serve as the basis for new opportunities for fast data acquisition in MRI.     

Optimization of spiral‐based pulse sequences for first‐pass myocardial perfusion imaging

Although spiral trajectories have multiple attractive features such as their isotropic resolution, acquisition efficiency, and robustness to motion, there has been limited application of these techniques to first‐pass perfusion imaging because of potential off‐resonance and inconsistent data artifacts. Spiral trajectories may also be less sensitive to dark‐rim artifacts that are caused, at least in part, by cardiac motion. By careful consideration of the spiral trajectory readout duration, flip angle strategy, and image reconstruction strategy, spiral artifacts can be abated to create high‐quality first‐pass myocardial perfusion images with high signal‐to‐noise ratio. The goal of this article was to design interleaved spiral pulse sequences for first‐pass myocardial perfusion imaging and to evaluate them clinically for image quality and the presence of dark‐rim, blurring, and dropout artifacts. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.