Undersampling k-space using fast progressive 3D trajectories.

In 3D MRI, sampling k-space with traditional trajectories can be excessively time-consuming. Fast imaging trajectories are used in an attempt to efficiently cover the k-space and reduce the scan time without significantly affecting the image quality. In many applications, further reductions in scan time can be achieved via undersampling of the k-space; however, no clearly optimal method exists. In most 3D trajectories the k-space is divided into regions that are sampled with shots that share a common geometry (e.g., spirals). A different approach is to design trajectories that gradually but uniformly cover the k-space. In the current work, successive shots progressively add sampled regions to the 3D frequency space. By cutting the sequence short, a natural undersampled method is obtained. This can be particularly efficient because in these types of trajectories the contribution of new information by later shots is less significant. In this work the performance of progressive trajectories for different degrees of undersampling is assessed with trajectories based on missile guidance (MG) ideas. The results show that the approach can be efficient in terms of reducing the scan time, and performs better than the stack of spirals (SOS) technique, particularly under nonideal conditions.     

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.     

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.     

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.     

3D time-resolved contrast-enhanced cerebrovascular MR angiography with subsecond frame update times using radial k-space trajectories and highly constrained projection reconstruction

HYPR TRICKS is an acquisition method that combines radial k-space trajectories, sampling k-space at different rates (TRICKS), and a new strategy for image reconstruction that uses highly constrained backprojection reconstruction (HYPR). This approach provides 3D time-resolved contrast-enhanced MR angiograms of the cerebral vessels with subsecond frame update times and submillimeter in-plane spatial resolution. Artifacts are suppressed, and signal-to-noise ratio is well maintained, by using HYPR reconstruction.     

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.     

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.     

Off-centered spiral trajectories.

The quality of spiral images depends on the accuracy of the k-space sampling locations. Although newer gradient systems can provide more accurate gradient waveforms, the sampling positions can be significantly distorted by timing misregistration between data acquisition and gradient systems. Even after the timing of data acquisition is tuned, minor residual errors can still cause shading artifacts which are problematic for quantitative MR applications such as phase-contrast flow quantitation. These timing errors can ideally be corrected by measuring the actual k-space trajectory, but trajectory measurement requires additional data acquisition and scan time. Therefore, off-centered spiral trajectories which are more robust against timing errors are proposed and applied to the phase-contrast method. The new trajectories turn shading artifacts into a slowly varying linear phase in reconstructed images without affecting the magnitude of images.     

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.     

Multispectral imaging with three-dimensional rosette trajectories.

Two-dimensional intersecting k-space trajectories have previously been demonstrated to allow fast multispectral imaging. Repeated sampling of k-space points leads to destructive interference of the signal coming from the off-resonance spectral peaks; on-resonance data reconstruction yields images of the on-resonance peak, with some of the off-resonance energy being spread as noise in the image. A shift of the k-space data by a given off-resonance frequency brings a second frequency of interest on resonance, allowing the reconstruction of a second spectral peak from the same k-space data. Given the higher signal-to-noise per unit time characteristic of a 3D acquisition, we extended the concept of intersecting trajectories to three dimensions. A 3D, rosette-like pulse sequence was designed and implemented on a clinical 1.5T scanner. An iterative density compensation function was developed to weight the 3D intersecting trajectories before Fourier transformation. Three volunteers were scanned using this sequence and separate fat and water images were reconstructed from the same imaging dataset.     

Influence of the k-space trajectory on the dynamic T1-weighted signal in quantitative first-pass cardiac perfusion MRI at 3T.

The dynamic T(1)-weighted signal in first-pass myocardial perfusion MRI can vary as a function of k-space trajectory. The purpose of this study, therefore, was to compare the relative T(1)-weighted signal produced by the linear, centric, and reverse centric k-space trajectories at 3T. The centric k-space trajectory yielded higher arterial input function (AIF) than the linear and reverse centric k-space trajectories (6.21 +/- 0.84 vs. 4.75 +/- 0.75 vs. 4.39 +/- 0.85 mM, respectively; N = 9; P < 0.01), and the reverse centric k-space trajectory yielded higher myocardial signal contrast (as a fraction of equilibrium magnetization) than the linear and centric k-space trajectories (0.17 +/- 0.02 vs. 0.12 +/- 0.02 vs. 0.05 +/- 0.01, respectively; N = 9; P < 0.001). Compared to the linear k-space trajectory, the centric k-space trajectory is relatively optimal for the quantification of AIF, whereas the reverse centric k-space trajectory is relatively optimal for high contrast of myocardial wall enhancement.     

Direct comparison of 3D spiral vs. Cartesian gradient-echo coronary magnetic resonance angiography.

While 3D thin-slab coronary magnetic resonance angiography (MRA) has traditionally been performed using a Cartesian acquisition scheme, spiral k-space data acquisition offers several potential advantages. However, these strategies have not been directly compared in the same subjects using similar methodologies. Thus, in the present study a comparison was made between 3D coronary MRA using Cartesian segmented k-space gradient-echo and spiral k-space data acquisition schemes. In both approaches the same spatial resolution was used and data were acquired during free breathing using navigator gating and prospective slice tracking. Magnetization preparation (T(2) preparation and fat suppression) was applied to increase the contrast. For spiral imaging two different examinations were performed, using one or two spiral interleaves, during each R-R interval. Spiral acquisitions were found to be superior to the Cartesian scheme with respect to the signal-to-noise ratio (SNR) and contrast-to-noise-ratio (CNR) (both P < 0.001) and image quality. The single spiral per R-R interval acquisition had the same total scan duration as the Cartesian acquisition, but the single spiral had the best image quality and a 2.6-fold increase in SNR. The double-interleaf spiral approach showed a 50% reduction in scanning time, a 1.8-fold increase in SNR, and similar image quality when compared to the standard Cartesian approach. Spiral 3D coronary MRA appears to be preferable to the Cartesian scheme. The increase in SNR may be "traded" for either shorter scanning times using multiple consecutive spiral interleaves, or for enhanced spatial resolution.     

MR gradient response modeling to ensure excitation coherence

Gradient system response has a significant effect on the shape and dispersion of complex k-space trajectories, as used in echo-planar magnetic resonance imaging and designed excitation. The authors have developed a method that characterizes the gradient response directly by placing k-space “landmarks” in the raw data. The method produces a clear delineation of the k-space trajectory, while providing information about related factors such as magnetic field homogeneity and temporal coherence of the radio-frequency (RF) and gradient waveforms. By using parameters derived from data collected under varying conditions, gradient response is modeled as a linear system consisting of a response delay function with a frequency-dependent slope. The results allow corrections that can be applied to the RF waveform or to the k-space trajectory. Application of this correction to designed excitation with the sinusoidal k-space trajectory is demonstrated and discussed.     

Improved 2D time-of-flight angiography using a radial-line k-space acquisition

For flow imaging applications, radial-line k-space acquisition methods offer advantages over conventional 2DFT methods. Specifically, radial-line acquisition methods mitigate artifacts resulting from pulsatile flow while offering a potential reduction in scan times. In this paper, radial-line and 2DFT acquisitions are compared in a two-dimensional time-of-flight angiography sequence. The twisting radial-line (TwiRL) trajectory, a variant of 2D projection reconstruction, is used to represent the family of radial-line trajectories. In both phantom and in vivo studies, the TwiRL images demonstrate improved vessel depiction including a more uniform signal intensity and better delineation of the vasculature in comparison with images obtained via the 2DFT method.     

3D hyperpolarized He-3 MRI of ventilation using a multi-echo projection acquisition.

A method is presented for high-resolution 3D imaging of the whole lung using inhaled hyperpolarized (HP) He-3 MR with multiple half-echo radial trajectories that can accelerate imaging through undersampling. A multiple half-echo radial trajectory can be used to reduce the level of artifact for undersampled 3D projection reconstruction (PR) imaging by increasing the amount of data acquired per unit time for HP He-3 lung imaging. The point spread functions (PSFs) for breath-held He-3 MRI using multiple half-echo trajectories were evaluated using simulations to predict the effects of T(2)* and gas diffusion on image quality. Results from PSF simulations were consistent with imaging results in volunteer studies showing improved image quality with increasing number of echoes using up to 8 half-echoes. The 8-half-echo acquisition is shown to accommodate lost breath-holds as short as 6 sec using a retrospective reconstruction at reduced resolution and also to allow reduced breath-hold time compared with an equivalent Cartesian trajectory. Furthermore, preliminary results from a 3D dynamic inhalation-exhalation maneuver are demonstrated using the 8-half-echo trajectory. Results demonstrate the first high-resolution 3D PR imaging of ventilation and respiratory dynamics in humans using HP He-3 MR.     

Inversion recovery radial MRI with interleaved projection sets.

The radial trajectory has found applications in cardiac imaging because of its resilience to undersampling and motion artifacts. Recent work has shown that interleaved and weighted radial imaging can produce images with multiple contrasts from a single data set. This feature was investigated for inversion recovery imaging of scar using a radial technique. The 2D radial imaging method was modified to acquire quadruply interleaved projection sets within each acquisition window of the cardiac cycle. These data were reconstructed using k-space weightings that used a smaller segment of the acquisition window for the central k-space data, the determinant of image contrast. This method generates four images with different T1 weightings. The novel approach was compared with noninterleaved radial imaging, interleaved radial without weightings, and Cartesian imaging in simulations, phantoms, and seven subjects with clinical myocardial infarction. The results show that during a typical acquisition window after an inversion pulse, magnetization changes rapidly. The interleaved acquisition provided better image quality than the noninterleaved radial acquisition. Interleaving with weighting provided better quality when the inversion time (TI) was shorter than optimal; otherwise, interleaving without weighting was superior. These methods enable a radial trajectory to be employed in conjunction with preparation pulses for viability imaging.     

Fast “real time” imaging with different k-space update strategies for interventional procedures

Interventional procedures under MR guidance require the images to be acquired with a fast acquisition strategy, a rapid reconstruction algorithm for “real-time” imaging (ie, high temporal resolution), acquisition of at least three adjacent slices to track a tool reliably, and high tissue contrast to ensure safe positioning of interventional devices. Often times, the field strength for interventional MR-imaging units is limited by the open magnet design. This complicates the trade-off between scan time and image quality, particularly when applied during low field interventional MRI procedures. To minimize the impact of some of these tradeoffs, a combination of keyhole techniques or modified k-space trajectories, in conjunction with a fluoroscopic (ie, continuous acquisition) mode and a real time reconstruction, permits rapid imaging in a low field system using standard (speed optimized) reconstruction hardware and standard gradient electronics. The purpose of this study was to design and describe different keyhole strategies that can be used in a real time mode to increase the image frame rate by a factor of up to 16. By updating the entire raw data space with our strategies, even small changes of the object could be recognized. Our results using these new strategies on two commercially available open magnet MR-imaging units (Siemens Magnetom Open 0.2T resistive magnet, Toshiba Access 0.064T permanent magnet) and a 1.5T superconductive solenoidal magnet design imager (Siemens SP) are presented to show the potential of these acquisition strategies in interventional MRI. Furthermore, these strategies may also be helpful for several other medical applications requiring high temporal resolution like contrast-enhanced breast imaging or functional brain imaging.     

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.