Real-time imaging with radial GRAPPA: Implementation on a heterogeneous architecture for low-latency reconstructions

Combination of non-Cartesian trajectories with parallel MRI permits to attain unmatched acceleration rates when compared to traditional Cartesian MRI during real-time imaging. However, computationally demanding reconstructions of such imaging techniques, such as k-space domain radial generalized auto-calibrating partially parallel acquisitions (radial GRAPPA) and image domain conjugate gradient sensitivity encoding (CG-SENSE), lead to longer reconstruction times and unacceptable latency for online real-time MRI on conventional computational hardware. Though CG-SENSE has been shown to work with low-latency using a general purpose graphics processing unit (GPU), to the best of our knowledge, no such effort has been made for radial GRAPPA. Radial GRAPPA reconstruction, which is robust even with highly undersampled acquisitions, is not iterative, requiring only significant computation during initial calibration while achieving good image quality for low-latency imaging applications. In this work, we present a very fast, low-latency, reconstruction framework based on a heterogeneous system using multi-core CPUs and GPUs. We demonstrate an implementation of radial GRAPPA that permits reconstruction times on par with or faster than acquisition of highly accelerated datasets in both cardiac and dynamic musculoskeletal imaging scenarios. Acquisition and reconstruction times are reported.

Single echo MRI

Purpose

Previous nonlinear gradient research has focused on trajectories that reconstruct images with a minimum number of echoes. Here we describe sequences where the nonlinear gradients vary in time to acquire the image in a single readout. The readout is designed to be very smooth so that it can be compressed to minimal time without violating peripheral nerve stimulation limits, yielding an image from a single 4 ms echo.

Theory and Methods

This sequence was inspired by considering the code of each voxel, i.e. the phase accumulation that a voxel follows through the readout, an approach connected to traditional encoding theory. We present simulations for the initial sequence, a low slew rate analog, and higher resolution reconstructions.

Results

Extremely fast acquisitions are achievable, though as one would expect, SNR is reduced relative to the slower Cartesian sampling schemes because of the high gradient strengths.

Conclusions

The prospect that nonlinear gradients can acquire images in a single <10 ms echo makes this a novel and interesting approach to image encoding.

Calibrationless parallel magnetic resonance imaging: a joint sparsity model

State-of-the-art parallel MRI techniques either explicitly or implicitly require certain parameters to be estimated, e.g., the sensitivity map for SENSE, SMASH and interpolation weights for GRAPPA, SPIRiT. Thus all these techniques are sensitive to the calibration (parameter estimation) stage. In this work, we have proposed a parallel MRI technique that does not require any calibration but yields reconstruction results that are at par with (or even better than) state-of-the-art methods in parallel MRI. Our proposed method required solving non-convex analysis and synthesis prior joint-sparsity problems. This work also derives the algorithms for solving them. Experimental validation was carried out on two datasets-eight channel brain and eight channel Shepp-Logan phantom. Two sampling methods were used-Variable Density Random sampling and non-Cartesian Radial sampling. For the brain data, acceleration factor of 4 was used and for the other an acceleration factor of 6 was used. The reconstruction results were quantitatively evaluated based on the Normalised Mean Squared Error between the reconstructed image and the originals. The qualitative evaluation was based on the actual reconstructed images. We compared our work with four state-of-the-art parallel imaging techniques; two calibrated methods-CS SENSE and l1SPIRiT and two calibration free techniques-Distributed CS and SAKE. Our method yields better reconstruction results than all of them.

Model-based Acceleration of Parameter mapping (MAP) for saturation prepared radially acquired data

A reconstruction technique called Model-based Acceleration of Parameter mapping (MAP) is presented allowing for quantification of longitudinal relaxation time and proton density from radial single-shot measurements after saturation recovery magnetization preparation. Using a mono-exponential model in image space, an iterative fitting algorithm is used to reconstruct one well resolved and consistent image for each of the projections acquired during the saturation recovery relaxation process. The functionality of the algorithm is examined in numerical simulations, phantom experiments, and in-vivo studies. MAP reconstructions of single-shot acquisitions feature the same image quality and resolution as fully sampled reference images in phantom and in-vivo studies. The longitudinal relaxation times obtained from the MAP reconstructions are in very good agreement with the reference values in numerical simulations as well as phantom and in-vivo measurements. Compared to available contrast manipulation techniques, no averaging of projections acquired at different time points of the relaxation process is required in MAP imaging. The proposed technique offers new ways of extracting quantitative information from single-shot measurements acquired after magnetization preparation. The reconstruction simultaneously yields images with high spatiotemporal resolution fully consistent with the acquired data as well as maps of the effective longitudinal relaxation parameter and the relative proton density.

Compressed sensing reconstruction for whole-heart imaging with 3D radial trajectories: a graphics processing unit implementation

A disadvantage of three-dimensional (3D) isotropic acquisition in whole-heart coronary MRI is the prolonged data acquisition time. Isotropic 3D radial trajectories allow undersampling of k-space data in all three spatial dimensions, enabling accelerated acquisition of the volumetric data. Compressed sensing (CS) reconstruction can provide further acceleration in the acquisition by removing the incoherent artifacts due to undersampling and improving the image quality. However, the heavy computational overhead of the CS reconstruction has been a limiting factor for its application. In this article, a parallelized implementation of an iterative CS reconstruction method for 3D radial acquisitions using a commercial graphics processing unit is presented. The execution time of the graphics processing unit-implemented CS reconstruction was compared with that of the C++ implementation, and the efficacy of the undersampled 3D radial acquisition with CS reconstruction was investigated in both phantom and whole-heart coronary data sets. Subsequently, the efficacy of CS in suppressing streaking artifacts in 3D whole-heart coronary MRI with 3D radial imaging and its convergence properties were studied. The CS reconstruction provides improved image quality (in terms of vessel sharpness and suppression of noise-like artifacts) compared with the conventional 3D gridding algorithm, and the graphics processing unit implementation greatly reduces the execution time of CS reconstruction yielding 34-54 times speed-up compared with C++ implementation.

The Role of Nonlinear Gradients in Parallel Imaging: A k-Space Based Analysis

Sequences that encode the spatial information of an object using nonlinear gradient fields are a new frontier in MRI, with potential to provide lower peripheral nerve stimulation, windowed fields of view, tailored spatially-varying resolution, curved slices that mirror physiological geometry, and, most importantly, very fast parallel imaging with multichannel coils. The acceleration for multichannel images is generally explained by the fact that curvilinear gradient isocontours better complement the azimuthal spatial encoding provided by typical receiver arrays. However, the details of this complementarity have been more difficult to specify. We present a simple and intuitive framework for describing the mechanics of image formation with nonlinear gradients, and we use this framework to review some the main classes of nonlinear encoding schemes.

K-t sparse GROWL: sequential combination of partially parallel imaging and compressed sensing in k-t space using flexible virtual coil

Because dynamic MR images are often sparse in x-f domain, k-t space compressed sensing (k-t CS) has been proposed for highly accelerated dynamic MRI. When a multichannel coil is used for acquisition, the combination of partially parallel imaging and k-t CS can improve the accuracy of reconstruction. In this work, an efficient combination method is presented, which is called k-t sparse Generalized GRAPPA fOr Wider readout Line. One fundamental aspect of this work is to apply partially parallel imaging and k-t CS sequentially. A partially parallel imaging technique using a Generalized GRAPPA fOr Wider readout Line operator is adopted before k-t CS reconstruction to decrease the reduction factor in a computationally efficient way while preserving temporal resolution. Channel combination and relative sensitivity maps are used in the flexible virtual coil scheme to alleviate the k-t CS computational load with increasing number of channels. Using k-t FOCUSS as a specific example of k-t CS, the experiments with Cartesian and radial data sets demonstrate that k-t sparse Generalized GRAPPA fOr Wider readout Line can produce results with two times lower root-mean-square error than conventional channel-by-channel k-t CS while consuming up to seven times less computational cost.

A radial self-calibrated (RASCAL) generalized autocalibrating partially parallel acquisition (GRAPPA) method using weight interpolation

A generalized autocalibrating partially parallel acquisition (GRAPPA) method for radial k-space sampling is presented that calculates GRAPPA weights without synthesized or acquired calibration data. Instead, GRAPPA weights are fitted to the undersampled data as if they were the calibration data. Because the relative k-space shifts associated with these GRAPPA weights vary for a radial trajectory, new GRAPPA weights can be resampled for arbitrary shifts through interpolation, which are then used to generate missing projections between the acquired projections. The method is demonstrated in phantoms and in abdominal and brain imaging. Image quality is similar to radial GRAPPA using fully sampled calibration data, and improved relative to a previously described self-calibrated radial GRAPPA technique.

Spiral phyllotaxis: the natural way to construct a 3D radial trajectory in MRI

While radial 3D acquisition has been discussed in cardiac MRI for its excellent results with radial undersampling, the self-navigating properties of the trajectory need yet to be exploited. Hence, the radial trajectory has to be interleaved such that the first readout of every interleave starts at the top of the sphere, which represents the shell covering all readouts. If this is done sub-optimally, the image quality might be degraded by eddy current effects, and advanced density compensation is needed. In this work, an innovative 3D radial trajectory based on a natural spiral phyllotaxis pattern is introduced, which features optimized interleaving properties: (1) overall uniform readout distribution is preserved, which facilitates simple density compensation, and (2) if the number of interleaves is a Fibonacci number, the interleaves self-arrange such that eddy current effects are significantly reduced. These features were theoretically assessed in comparison with two variants of an interleaved Archimedean spiral pattern. Furthermore, the novel pattern was compared with one of the Archimedean spiral patterns, with identical density compensation, in phantom experiments. Navigator-gated whole-heart coronary imaging was performed in six healthy volunteers. High reduction of eddy current artifacts and overall improvement in image quality were achieved with the novel trajectory.

Fast MR image reconstruction for partially parallel imaging with arbitrary k-space trajectories

Both acquisition and reconstruction speed are crucial for magnetic resonance (MR) imaging in clinical applications. In this paper, we present a fast reconstruction algorithm for SENSE in partially parallel MR imaging with arbitrary k-space trajectories. The proposed method is a combination of variable splitting, the classical penalty technique and the optimal gradient method. Variable splitting and the penalty technique reformulate the SENSE model with sparsity regularization as an unconstrained minimization problem, which can be solved by alternating two simple minimizations: One is the total variation and wavelet based denoising that can be quickly solved by several recent numerical methods, whereas the other one involves a linear inversion which is solved by the optimal first order gradient method in our algorithm to significantly improve the performance. Comparisons with several recent parallel imaging algorithms indicate that the proposed method significantly improves the computation efficiency and achieves state-of-the-art reconstruction quality.

A rapid and robust numerical algorithm for sensitivity encoding with sparsity constraints: self-feeding sparse SENSE

The method of enforcing sparsity during magnetic resonance imaging reconstruction has been successfully applied to partially parallel imaging (PPI) techniques to reduce noise and artifact levels and hence to achieve even higher acceleration factors. However, there are two major problems in the existing sparsity-constrained PPI techniques: speed and robustness. By introducing an auxiliary variable and decomposing the original minimization problem into two subproblems that are much easier to solve, a fast and robust numerical algorithm for sparsity-constrained PPI technique is developed in this work. The specific implementation for a conventional Cartesian trajectory data set is named self-feeding Sparse Sensitivity Encoding (SENSE). The computational cost for the proposed method is two conventional SENSE reconstructions plus one spatially adaptive image denoising procedure. With reconstruction time approximately doubled, images with a much lower root mean square error (RMSE) can be achieved at high acceleration factors. Using a standard eight-channel head coil, a net acceleration factor of 5 along one dimension can be achieved with low RMSE. Furthermore, the algorithm is insensitive to the choice of parameters. This work improves the clinical applicability of SENSE at high acceleration factors.

Contrast-enhanced whole-heart coronary magnetic resonance angiography at 3 T with radial EPI

Whole-heart coronary magnetic resonance angiography is a promising method for detecting coronary artery disease. However, the imaging time is relatively long (typically 10-15 min). The goal of this study was to implement a radial echo planar imaging sequence for contrast-enhanced whole-heart coronary magnetic resonance angiography, with the aim of combining the scan efficiency of echo planar imaging with the motion insensitivity of radial k-space sampling. A self-calibrating phase correction technique was used to correct for off-resonance effects, trajectory measurement was used to correct for k-space trajectory errors, and variable density sampling was used in the partition direction to reduce streaking artifacts. Seven healthy volunteers and two patients were scanned with the proposed radial echo planar imaging sequence, and the images were compared with a traditional gradient echo and X-ray angiography techniques, respectively. Whole-heart images with the radial EPI technique were acquired with a resolution of 1.0 × 1.0 × 2.0 mm(3) in a scan time of 5 min. In healthy volunteers, the average image quality scores and visualized vessel lengths of the RCA and LAD were similar for the radial EPI and gradient echo techniques (P value > 0.05 for all). Anecdotal patient studies showed excellent agreement of the radial EPI technique with X-ray angiography.

Improvements in multislice parallel imaging using radial CAIPIRINHA

Multislice parallel imaging involves the simultaneous sampling of multiple parallel slices which are subsequently separated using parallel imaging reconstruction. The CAIPIRINHA technique improves this reconstruction by manipulating the phase of the RF excitation pulses to shift the aliasing pattern such that there is less aliasing energy to be reconstructed. In this work, it is shown that combining the phase manipulation used in CAIPIRINHA with a non-Cartesian (radial) sampling scheme further decreases the aliasing energy for the parallel imaging algorithm to reconstruct, thereby further increasing the degree to which a multi-channel receiver array can be utilized for parallel imaging acceleration. In radial CAIPIRINHA, individual bands (slices) in a multislice excitation are modulated with view-dependent phase, causing a destructive interference of entire slices. This destructive interference leads to a reduction in aliasing compared to the coherent shifts one observes when using this same technique with a Cartesian trajectory. Recovery of each individual slice is possible because the applied phase pattern is known, and a conjugate-gradient reconstruction algorithm minimizes the contributions from other slices. Results are presented with a standard 12-channel head coil with acceleration factors up to 14, where radial CAIPIRINHA produces an improved reconstruction when compared with Cartesian CAIPIRINHA.

Combination of compressed sensing and parallel imaging for highly accelerated first-pass cardiac perfusion MRI

First-pass cardiac perfusion MRI is a natural candidate for compressed sensing acceleration since its representation in the combined temporal Fourier and spatial domain is sparse and the required incoherence can be effectively accomplished by k-t random undersampling. However, the required number of samples in practice (three to five times the number of sparse coefficients) limits the acceleration for compressed sensing alone. Parallel imaging may also be used to accelerate cardiac perfusion MRI, with acceleration factors ultimately limited by noise amplification. In this work, compressed sensing and parallel imaging are combined by merging the k-t SPARSE technique with sensitivity encoding (SENSE) reconstruction to substantially increase the acceleration rate for perfusion imaging. We also present a new theoretical framework for understanding the combination of k-t SPARSE with SENSE based on distributed compressed sensing theory. This framework, which identifies parallel imaging as a distributed multisensor implementation of compressed sensing, enables an estimate of feasible acceleration for the combined approach. We demonstrate feasibility of 8-fold acceleration in vivo with whole-heart coverage and high spatial and temporal resolution using standard coil arrays. The method is relatively insensitive to respiratory motion artifacts and presents similar temporal fidelity and image quality when compared to Generalized autocalibrating partially parallel acquisitions (GRAPPA) with 2-fold acceleration.

PROPELLER for motion-robust imaging of in vivo mouse abdomen at 9.4 T

In vivo high-field MRI in the abdomen of small animals is technically challenging because of the small voxel sizes, short T(2) and physiological motion. In standard Cartesian sampling, respiratory and gastrointestinal motion can lead to ghosting artefacts. Although respiratory triggering and navigator echoes can either avoid or compensate for motion, they can lead to variable TRs, require invasive intubation and ventilation, or extend TEs. A self-navigated fast spin echo (FSE)-based periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) acquisition was implemented at 9.4 T to enable high-resolution in vivo MRI of mouse abdomen without the use of additional navigators or triggering. T(2)-weighted FSE-PROPELLER data were compared with single-shot FSE and multi-shot FSE data with and without triggering. Single-shot methods, although rapid and robust to motion, demonstrated strong blurring. Multi-shot FSE data showed better resolution, but suffered from marked blurring in the phase-encoding direction and motion in between shots, leading to ghosting artefacts. When respiratory triggering was used, motion artefacts were largely avoided. However, TRs and acquisition times were lengthened by up to approximately 20%. The PROPELLER data showed a 25% and 61% improvement in signal-to-noise ratio and contrast-to-noise ratio, respectively, compared with multi-shot FSE data, together with a 35% reduction in artefact power. A qualitative comparison between acquisition methods using diffusion-weighted imaging was performed. The results were similar, with the exception that respiratory triggering was unable to exclude major motion artefacts as a result of the sensitisation to motion by the diffusion gradients. The PROPELLER data were of consistently higher quality. Considerations specific to the use of PROPELLER at high field are discussed, including the selection of practical blade widths and the effects on contrast, resolution and artefacts.

Accelerating time-resolved MRA with multiecho acquisition

A new four-dimensional magnetic resonance angiography (MRA) technique called contrast-enhanced angiography with multiecho and radial k-space is introduced, which accelerates the acquisition using multiecho while maintaining a high spatial resolution and increasing the signal-to-noise ratio (SNR). An acceleration factor of approximately 2 is achieved without parallel imaging or undersampling by multiecho (i.e., echo-planar imaging) acquisition. SNR is gained from (1) longer pulse repetition times, which allow more time for T(1) regrowth; (2) decreased specific absorption rate, which allows use of flip angles that maximize contrast at high field; and (3) minimized effects of a transient contrast bolus signal with a shorter temporal footprint. Simulations, phantom studies, and in vivo scans were performed. Contrast-enhanced angiography with multiecho and radial k-space can be combined with parallel imaging techniques such as Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) to provide additional 2-fold acceleration in addition to higher SNR to trade off for parallel imaging. This technique can be useful in diagnosing vascular lesions where accurate dynamic information is necessary.

RT-GROG: parallelized self-calibrating GROG for real-time MRI

A real-time implementation of self-calibrating Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) operator gridding for radial acquisitions is presented. Self-calibrating GRAPPA operator gridding is a parallel-imaging-based, parameter-free gridding algorithm, where coil sensitivity profiles are used to calculate gridding weights. Self-calibrating GRAPPA operator gridding's weight-set calculation and image reconstruction steps are decoupled into two distinct processes, implemented in C++ and parallelized. This decoupling allows the weights to be updated adaptively in the background while image reconstruction threads use the most recent gridding weights to grid and reconstruct images. All possible combinations of two-dimensional gridding weights G(x)(m)G(y)(n) are evaluated for m,n = {-0.5, -0.4, ..., 0, 0.1, ..., 0.5} and stored in a look-up table. Consequently, the per-sample two-dimensional weights calculation during gridding is eliminated from the reconstruction process and replaced by a simple look-up table access. In practice, up to 34x faster reconstruction than conventional (parallelized) self-calibrating GRAPPA operator gridding is achieved. On a 32-coil dataset of size 128 x 64, reconstruction performance is 14.5 frames per second (fps), while the data acquisition is 6.6 fps.

Motion correction using an enhanced floating navigator and GRAPPA operations

A method for motion correction in multicoil imaging applications, involving both data collection and reconstruction, is presented. The floating navigator method, which acquires a readout line off center in the phase-encoding direction, is expanded to detect translation/rotation and inconsistent motion. This is done by comparing floating navigator data with a reference k-space region surrounding the floating navigator line, using a correlation measure. The technique of generalized autocalibrating partially parallel acquisition is further developed to correct for a fully sampled, motion-corrupted dataset. The flexibility of generalized autocalibrating partially parallel acquisition kernels is exploited by extrapolating readout lines to fill in missing "pie slices" of k-space caused by rotational motion and regenerating full k-space data from multiple interleaved datasets, facilitating subsequent rigid-body motion correction or proper weighting of inconsistent data (e.g., with through-plane and nonrigid motion). Phantom and in vivo imaging experiments with turbo spin-echo sequence demonstrate the correction of severe motion artifacts.

Auto-calibrated parallel imaging reconstruction for arbitrary trajectories using k-space sparse matrices (kSPA)

Image acquisition of magnetic resonance imaging (MRI) can be accelerated by using multiple receiving coils simultaneously. The problem of reconstructing an unaliased image from partially sampled k-space data can be formulated as a large system of sparse linear equations. The k-space sparse matrix (kSPA) algorithm proposes to solve the system of equations by finding a sparse approximate inverse. This algorithm has been shown to accelerate the image reconstruction for a large number of coils. The original kSPA algorithm requires knowledge of coil sensitivities. Here, we propose and demonstrate an auto-calibrated kSPA algorithm that does not require the explicit computation of the coil sensitivity maps. We have also shown that calibration data, in principle, can be acquired at any region of k-space. This property applies to arbitrary sampling trajectories and all reconstruction algorithms based on k-space. In practice, because of its higher SNR, calibration data acquired at the center of k-space performed more favorably. Such auto-calibration can be advantageous in cases where an accurate sensitivity map is difficult to obtain.

Image reconstructions with the rotating RF coil

Recent studies have shown that rotating a single RF transceive coil (RRFC) provides a uniform coverage of the object and brings a number of hardware advantages (i.e. requires only one RF channel, averts coil-coil coupling interactions and facilitates large-scale multi-nuclear imaging). Motion of the RF coil sensitivity profile however violates the standard Fourier Transform definition of a time-invariant signal, and the images reconstructed in this conventional manner can be degraded by ghosting artifacts. To overcome this problem, this paper presents Time Division Multiplexed-Sensitivity Encoding (TDM-SENSE), as a new image reconstruction scheme that exploits the rotation of the RF coil sensitivity profile to facilitate ghost-free image reconstructions and reductions in image acquisition time. A transceive RRFC system for head imaging at 2 Tesla was constructed and applied in a number of in vivo experiments. In this initial study, alias-free head images were obtained in half the usual scan time. It is hoped that new sequences and methods will be developed by taking advantage of coil motion.

General formulation for quantitative G-factor calculation in GRAPPA reconstructions

In this work a theoretical description for practical quantitative estimation of the noise enhancement in generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstructions, equivalent to the geometry (g)-factor in sensitivity encoding for fast MRI (SENSE) reconstructions, is described. The GRAPPA g-factor is derived directly from the GRAPPA reconstruction weights. The procedure presented here also allows the calculation of quantitative g-factor maps for both the uncombined and combined accelerated GRAPPA images. This enables, for example, a fast comparison between the performances of various GRAPPA reconstruction kernels or SENSE reconstructions. The applicability of this approach is validated on phantom studies and demonstrated using in vivo images for 1D and 2D parallel imaging.

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

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

Free-breathing cine MRI

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

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.

Self-calibrating GRAPPA operator gridding for radial and spiral trajectories

Self-calibrating GRAPPA operator gridding (GROG) is a method by which non-Cartesian MRI data can be gridded using spatial information from a multichannel coil array without the need for an additional calibration dataset. Using self-calibrating GROG, the non-Cartesian datapoints are shifted to nearby k-space locations using parallel imaging weight sets determined from the datapoints themselves. GROG employs the GRAPPA Operator, a special formulation of the general reconstruction method GRAPPA, to perform these shifts. Although GROG can be used to grid undersampled datasets, it is important to note that this method uses parallel imaging only for gridding, and not to reconstruct artifact-free images from undersampled data. The innovation introduced here, namely, self-calibrating GROG, allows the shift operators to be calculated directly out of the non-Cartesian data themselves. This eliminates the need for an additional calibration dataset, which reduces the imaging time and also makes the GROG reconstruction more robust by removing possible inconsistencies between the calibration and non-Cartesian datasets. Simulated and in vivo examples of radial and spiral datasets gridded using self-calibrating GROG are compared to images gridded using the standard method of convolution gridding.