k-space undersampling in PROPELLER imaging.

PROPELLER MRI (periodically rotated overlapping parallel lines with enhanced reconstruction) provides images with significantly fewer B(0)-related artifacts than echo-planar imaging (EPI), as well as reduced sensitivity to motion compared to conventional multiple-shot fast spin-echo (FSE). However, the minimum imaging time in PROPELLER is markedly longer than in EPI and 50% longer than in conventional multiple-shot FSE. Often in MRI, imaging time is reduced by undersampling k-space. In the present study, the effects of undersampling on PROPELLER images were evaluated using simulated and in vivo data sets. Undersampling using PROPELLER patterns with reduced number of samples per line, number of lines per blade, or number of blades per acquisition, while maintaining the same k-space field of view (FOV(k)) and uniform sampling at the edges of FOV(k), reduced imaging time but led to severe image artifacts. In contrast, undersampling by means of removing whole blades from a PROPELLER sampling pattern that sufficiently samples k-space produced only minimal image artifacts, mainly manifested as blurring in directions parallel to the blades removed, even when reducing imaging time by as much as 50%. Finally, undersampling using asymmetric blades and taking advantage of Hermitian symmetries to fill-in the missing data significantly reduced imaging time without causing image artifacts.     

Time-resolved undersampled projection reconstruction magnetic resonance imaging of the peripheral vessels using multi-echo acquisition.

The hybrid projection reconstruction (PR) imaging provides high temporal resolution through an undersampled PR acquisition for the in-plane dimensions and Cartesian slice encoding for the through-plane dimension. The undersampling of projection data introduces streak artifact, which may severely compromise image quality. This study reports on a combination of multi-echo acquisition with time-resolved undersampled PR imaging and its application to peripheral magnetic resonance angiography. Multi-echo acquisition improved imaging speed effectively, thereby reducing the undersampling streak artifact and improving the temporal resolution. The gradient distortion was reduced through gradient calibration and accurate k-space trajectory measurement.     

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.     

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.     

Coronary MRA with 3D undersampled projection reconstruction TrueFISP.

Undersampled projection reconstruction (PR) offers improved imaging efficiency allowing a relative tradeoff between signal-to-noise ratio (SNR) or streak artifact and the number of acquired k-space views rather than the tradeoff between resolution or aliasing artifact and the number of acquired k-space lines inherent to Fourier imaging techniques. TrueFISP (true fast imaging with steady state precession) is ideally suited for undersampled PR imaging because of its inherently high SNR. The purpose of this work was to investigate the feasibility of using undersampled three-dimensional (3D) PR TrueFISP for breathhold coronary artery imaging. Phantom studies and a preliminary in vivo comparison demonstrated the improved spatial resolution of PR over Fourier TrueFISP with the same imaging time. In a 24-heartbeat coronary imaging scheme, segmented 3D PR TrueFISP provided a 1.0 x 1.0 mm(2) isotropic in-plane voxel size while acquiring between 93 and 153 views per partition. Streak artifacts were present in some images but were not found to impede coronary artery delineation. In conclusion, 3D undersampled PR TrueFISP provides isotropic in-plane voxel size within a single breathhold and is a promising technique for coronary artery imaging.     

Time-resolved contrast-enhanced carotid imaging using undersampled projection reconstruction acquisition

PURPOSE: To investigate the utility of nonuniform angular spacing of projections in a three-dimensional (3D) hybrid undersampled projection reconstruction (PR) acquisition for contrast-enhanced (CE) time-resolved carotid imaging. MATERIALS AND METHODS: Carotid CE magnetic resonance angiography (CE-MRA) was performed on seven healthy volunteers using a time-resolved hybrid sequence that combined undersampled PR acquisition in-plane and Cartesian slice encoding through-plane. The undersampling streak artifact comes mainly from the superior-inferior (S/I) direction in carotid imaging and is suppressed by nonuniform distribution of the projections. Phantom and volunteer studies were performed to demonstrate its efficacy. RESULTS: The undersampling streak artifact was significantly suppressed through a nonuniform distribution of the projection angles with more projections aligned along the S/I direction. The hybrid PR sequence combined with nonuniform distribution of the projection angles provided time-resolved images of the carotid arteries with high temporal resolution (two seconds per frame) and high spatial resolution (1.0 x 1.0 x 1.5 mm(3)) simultaneously. CONCLUSION: High-resolution dynamic imaging of the carotid arteries is feasible with the use of a hybrid undersampled PR acquisition. Undersampling streak artifact can be suppressed significantly through nonuniform distribution of the projections.     

Undersampled projection reconstruction applied to MR angiography

Undersampled projection reconstruction (PR) is investigated as an alternative method for MRA (MR angiography). In conventional 3D Fourier transform (FT) MRA, resolution in the phase‐encoding direction is proportional to acquisition time. Since the PR resolution in all directions is determined by the readout resolution, independent of the number of projections (N_p), high resolution can be generated rapidly. However, artifacts increase for reduced N_p. In X‐ray CT, undersampling artifacts from bright objects like bone can dominate other tissue. In MRA, where bright, contrast‐filled vessels dominate, artifacts are often acceptable and the greater resolution per unit time provided by undersampled PR can be realized. The resolution increase is limited by SNR reduction associated with reduced voxel size. The hybrid 3D sequence acquires fractional echo projections in the k_x–k_y plane and phase encodings in k_z. PR resolution and artifact characteristics are demonstrated in a phantom and in contrast‐enhanced volunteer studies. Magn Reson Med 43:91–101, 2000. © 2000 Wiley‐Liss, Inc.     

Myocardial wall tagging with undersampled projection reconstruction.

Azimuthally undersampled projection reconstruction (PR) acquisition is investigated for use in myocardial wall tagging with MR using grid tags to provide increased temporal and spatial resolution. PR can provide the high-resolution images required for tagging with very few projections, at the expense of artifact. Insight is provided into the PR undersampling artifact, in the context of measuring myocardial motion with tags. For Fourier transform imaging, at least 112 phase-encodings must be collected to image tagging grids spaced 7 pixels apart. PR requires about 80 projections, a 1.4-fold reduction in scan time. Magn Reson Med 45:562-567, 2001. Published 2001 Wiley-Liss, Inc.     

Artifact reduction in undersampled projection reconstruction MRI of the peripheral vessels using selective excitation.

The projection reconstruction (PR)-HyperTRICKS (time resolved imaging of contrast kinetics) acquisition integrates the benefits of through-plane Cartesian slice encoding and in-plane undersampled PR. It provides high spatial resolution both in-plane (about 1 mm(2)) and through-plane (1-2 mm), as well as relatively high temporal resolution (about 0.25 frames per second). However, undersampling artifacts that originate from anatomy superior or inferior to a coronal imaging FOV may severely degrade the image quality. In coronal MRA acquisitions, the slice coverage is limited in order to achieve high temporal resolution. In this report we describe an artifact reduction method that uses selective excitation in PR-HyperTRICKS. This technique significantly reduces undersampling streak artifacts while it increases the slice coverage.     

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.     

Single‐shot 3D GRASE with cylindrical k‐space trajectories

Development of GRASE (gradient‐ and spin‐echo) pulse sequences for single‐shot 3D imaging has been motivated by physiologic studies of the brain. The duration of echo‐planar imaging (EPI) subsequences between RF refocusing pulses in the GRASE sequence is determinant of image distortions and susceptibility artifacts. To reduce these artifacts the regular Cartesian trajectory is modified to a circular trajectory in 2D and a cylindrical trajectory in 3D for reduced echo train time. Incorporation of “fly‐back” trajectories lengthened the time of the subsequences and proportionally increased susceptibility artifact but the unipolar readout gradients eliminate all ghost artifacts. The modified cylindrical trajectory reduced susceptibility artifact and distortion artifact while raising the signal‐to‐noise ratio in both phantom and human brain images. Magn Reson Med 60:976–980, 2008. © 2008 Wiley‐Liss, Inc.     

Single breath-hold whole-heart MRA using variable-density spirals at 3T.

Multislice breath-held coronary imaging techniques conventionally lack the coverage of free-breathing 3D acquisitions but use a considerably shorter acquisition window during the cardiac cycle. This produces images with significantly less motion artifact but a lower signal-to-noise ratio (SNR). By using the extra SNR available at 3 T and undersampling k-space without introducing significant aliasing artifacts, we were able to acquire high-resolution fat-suppressed images of the whole heart in 17 heartbeats (a single breath-hold). The basic pulse sequence consists of a spectral-spatial excitation followed by a variable-density spiral readout. This is combined with real-time localization and a real-time prospective shim correction. Images are reconstructed with the use of gridding, and advanced techniques are used to reduce aliasing artifacts.     

Partial RF echo planar imaging with the FAISE method. I. Experimental and theoretical assessment of artifact.

The fast acquisition interleaved spin-echo (FAISE) method is a partial RF echo-planar technique which utilizes a specific phase-encode reordering algorithm to manipulate image contrast (Melki et al., J. Magn. Reson. Imaging 1:319, 1991). The technique can generate "spin-echo" like images up to 16 times faster than conventional spin-echo methods. However, the presence of T2 decay throughout the variable k-space trajectories used to manipulate T2 contrast ensures the presence of image artifacts, especially along the phase-encode direction. In this work, we experimentally and theoretically examine the type and extent of artifacts associated with the FAISE technique. We demonstrate the existence of well-defined minima of phase-encode ghost noise for selected k-space trajectories, examine the extent of blurring and edge enhancement artifacts, demonstrate the influence of matrix size and number of echoes per train on phase-encode artifact, and show how proper choice of FAISE sequence parameters can lead to proton density brain images which are practically indistinguishable from conventional spin-echo proton density images. A comparison of contrast between FAISE and standard spin-echo methods is presented in a companion article referred to as II.     

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).     

Rapid fat-suppressed isotropic steady-state free precession imaging using true 3D multiple-half-echo projection reconstruction.

Three-dimensional projection reconstruction (3D PR)-based techniques are advantageous for steady-state free precession (SSFP) imaging for several reasons, including the capability to achieve short repetition times (TRs). In this paper, a multi-half-echo technique is presented that dramatically improves the data-sampling efficiency of 3D PR sequences while it retains this short-TR capability. The k-space trajectory deviations are measured quickly and corrected on a per-sample point basis. A two-pass RF cycling technique is then applied to the dual-half-echo implementation to generate fat/water-separated images. The resultant improvement in the signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) was demonstrated in volunteer studies. Volumetric images with excellent spatial resolution, coverage, and contrast were obtained with high speed. The non-contrast-enhanced SSFP studies show that this technique has promising potential for MR angiography (MRA).     

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.     

Sparse MRI: The application of compressed sensing for rapid MR imaging.

The sparsity which is implicit in MR images is exploited to significantly undersample k-space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain-for example, in terms of spatial finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressed-sensing, images with a sparse representation can be recovered from randomly undersampled k-space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noise-like interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudo-random variable-density undersampling of phase-encodes. The reconstruction is performed by minimizing the l(1) norm of a transformed image, subject to data fidelity constraints. Examples demonstrate improved spatial resolution and accelerated acquisition for multislice fast spin-echo brain imaging and 3D contrast enhanced angiography.     

Rapid T2 estimation with phase-cycled variable nutation steady-state free precession.

Variable nutation SSFP (DESPOT2) permits rapid, high-resolution determination of the transverse (T2) relaxation constant. A limitation of DESPOT2, however, is the presence of T2 voids due to off-resonance banding artifacts associated with SSFP images. These artifacts typically occur in images acquired with long repetition times (TR) in the presence of B0 inhomogeneities, or near areas of magnetic susceptibility difference, such that the transverse magnetization experiences a net phase shift during the TR interval. This places constraints on the maximum spatial resolution that can be achieved without artifact. Here, a novel implementation of DESPOT2 is presented incorporating RF phase-cycling which acts to shift the spatial location of the bands, allowing reconstruction of a single, reduced artifact-image. The method is demonstrated in vivo with the acquisition of a 0.34 mm3 isotropic resolution T2 map of the brain with high precision and accuracy and significantly reduced artifact.     

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.     

Off-resonance artifacts correction with convolution in k-space (ORACLE)

Off-resonance artifacts hinder the wider applicability of echo-planar imaging and non-Cartesian MRI methods such as radial and spiral. In this work, a general and rapid method is proposed for off-resonance artifacts correction based on data convolution in k-space. The acquired k-space is divided into multiple segments based on their acquisition times. Off-resonance-induced artifact within each segment is removed by applying a convolution kernel, which is the Fourier transform of an off-resonance correcting spatial phase modulation term. The field map is determined from the inverse Fourier transform of a basis kernel, which is calibrated from data fitting in k-space. The technique was demonstrated in phantom and in vivo studies for radial, spiral and echo-planar imaging datasets. For radial acquisitions, the proposed method allows the self-calibration of the field map from the imaging data, when an alternating view-angle ordering scheme is used. An additional advantage for off-resonance artifacts correction based on data convolution in k-space is the reusability of convolution kernels to images acquired with the same sequence but different contrasts.