GRAPPA Algorithm Research Articles

A GRAPPA algorithm for arbitrary 2D/3D non-Cartesian sampling trajectories with rapid calibration.

GRAPPA is a popular reconstruction method for Cartesian parallel imaging, but is not easily extended to non-Cartesian sampling. We introduce a general and practical GRAPPA algorithm for arbitrary non-Cartesian imaging. We formulate a general GRAPPA reconstruction by associating a unique kernel with each unsampled k-space location with a distinct constellation, that is, local sampling pattern. We calibrate these generalized kernels using the Fourier transform phase shift property applied to fully gridded or separately acquired Cartesian Autocalibration signal (ACS) data. To handle the resulting large number of different kernels, we introduce a fast calibration algorithm based on nonuniform FFT (NUFFT) and adoption of circulant ACS boundary conditions. We applied our method to retrospectively under-sampled rotated stack-of-stars/spirals in vivo datasets, and to a prospectively under-sampled rotated stack-of-spirals functional MRI acquisition with a finger-tapping task. We reconstructed all datasets without performing any trajectory-specific manual adaptation of the method. For the retrospectively under-sampled experiments, our method achieved image quality (i.e., error and g-factor maps) comparable to conjugate gradient SENSE (cg-SENSE) and SPIRiT. Functional activation maps obtained from our method were in good agreement with those obtained using cg-SENSE, but required a shorter total reconstruction time (for the whole time-series): 3minutes (proposed) vs 15minutes (cg-SENSE). This paper introduces a general 3D non-Cartesian GRAPPA that is fast enough for practical use on today's computers. It is a direct generalization of original GRAPPA to non-Cartesian scenarios. The method should be particularly useful in dynamic imaging where a large number of frames are reconstructed from a single set of ACS data.

Autocalibrated multiband CAIPIRINHA with through-time encoding: Proof of principle and application to cardiac tissue phase mapping.

In conventional multiband (MB) CAIPIRINHA, additional reference scans are acquired to allow the separation of the excited slices. In this study, an acquisition-reconstruction technique that makes use of the MB data to calculate these reference data is presented. The method was integrated into a 2D time-resolved phase-contrast MR sequence used to assess velocities of the myocardium. The RF phases of the MB pulse are cycled through time so that consecutive cardiac phases can be grouped to form reference scans at a lower temporal resolution. These reference data are subsequently used to separate the original slices at the original, high temporal resolution using slice/split-slice GRAPPA algorithms. Slice separation performances are evaluated and compared with conventional methods at 3T, and 3 different strategies for the calibration of the kernels are proposed and compared. Finally, 6 subjects were scanned to assess velocities of the myocardium. Because the acquisition of external references is not needed, no additional breath-holds are required and the full MB acceleration could be exploited. Because the reference and MB data have the same resolution and phase structure, better slice separation was achieved when comparing the proposed technique to conventional workflows. Finally, time-resolved velocities of the myocardial tissue were successfully quantified from MB data, showing good agreement with single-band measurements. Our built-in reference method allows the full exploitation of the MB acceleration and it limits the number of breath-holds.

Kernel Principal Component Analysis of Coil Compression in Parallel Imaging.

A phased array with many coil elements has been widely used in parallel MRI for imaging acceleration. On the other hand, it results in increased memory usage and large computational costs for reconstructing the missing data from such a large number of channels. A number of techniques have been developed to linearly combine physical channels to produce fewer compressed virtual channels for reconstruction. A new channel compression technique via kernel principal component analysis (KPCA) is proposed. The proposed KPCA method uses a nonlinear combination of all physical channels to produce a set of compressed virtual channels. This method not only reduces the computational time but also improves the reconstruction quality of all channels when used. Taking the traditional GRAPPA algorithm as an example, it is shown that the proposed KPCA method can achieve better quality than both PCA and all channels, and at the same time the calculation time is almost the same as the existing PCA method.

A Matlab-Based Advance MR Image Reconstruction Package with Interactive Graphical User Interface

Parallel magnetic resonance imaging (PMRI) has the potential to reduce the MRI scan time by acquiring fewer k-space lines using multiple independent receiver coils instead of a single coil for data acquisition. Many advance reconstruction algorithms have been proposed in the recent past to reconstruct fully sampled images from these undersampled data. These algorithms are mainly categorized into k-space and image domain methods. The work presented in this paper develops an interactive graphical user interface (GUI) tool for a variety of advance reconstruction algorithms in MRI, namely, sensitivity encoding (SENSE) [1], conjugate gradient SENSE (CG-SENSE) [2], compressed sensing [3], and radial GRAPPA algorithms [4–7]. The proposed GUI tool environment is a multiple window interface developed using MATLAB (R2013a). The user has the option of loading the undersampled data in an interactive fashion, and image reconstruction can be performed using any of the available algorithms. The quality of the reconstructed images is evaluated using artifact power (AP) and SNR maps. This interactive platform is aimed at providing the researchers and medical practitioners an easy and interactive tool to test their data using various advance reconstruction algorithms in MRI.

Improved multi-shot diffusion imaging using GRAPPA with a compact kernel

In multi-shot diffusion imaging, motion induced phase variations are traditionally seen as a source of artifacts and corrected in the image domain using SENSE-based methods. This correction usually requires image echo and navigator echo to be geometrically matched. Recently, a k-space based method, realigned GRAPPA, has been proposed. It realigns data from different shots into the same k-space locations, and then synthesizes the missing data using GRAPPA algorithm. In this study, we refined the theory for GRAPPA-based method. In the revised theory, phase variations are treated as a kind of encoding, similar to coil sensitivity encoding. Based on this, the missing data can be synthesized using k-space correlations among different shots and channels. Then a compact kernel is used which only includes acquired data with significant contribution for the data synthesis, and can generate accurate weights without strict navigator size requirements. Simulation studies as well as brain and cervical spine experiments demonstrate that the proposed reconstruction method can effectively suppress artifacts caused by phase variations, and provide diffusion images with high resolution and low distortion. Compared with SENSE-based methods, the proposed method is less sensitive to mismatch between image echo and navigator echo.

DWI using navigated interleaved multishot EPI with realigned GRAPPA reconstruction.

A novel k-space reconstruction method is proposed for generating diffusion-weighted imaging (DWI) using navigated interleaved multishot EPI (msEPI). In interleaved msEPI, each shot of data acquired from one coil channel is a subset of the full k-space of that channel. All the k-space subsets of one channel can be treated as an undersampled dataset of a virtual multichannel data, which can be reconstructed by the GRAPPA algorithm after k-space realignment. The intershot phase variations are directly compensated using navigator echoes as the auto-calibrating data in GRAPPA reconstruction. In cases of multichannel msEPI data, all the virtual channels and actual channels can be integrated into a single GRAPPA reconstruction step. The proposed method is tested using both simulation and in-vivo data. The simulation results produced by the proposed method and a SENSE-based method are compared. The simulated images generated by the proposed method exhibit less relative error compared with those generated by the SENSE method. Inconsistent shot-to-shot phase variation is naturally resolved by GRAPPA calibration without additional phase map processing. High-quality brain DWI with submillimeter resolution is obtained using our proposed reconstruction method. A novel k-space msEPI reconstruction method has been developed for generating high-quality diffusion imaging.

Accelerated acquisition of tagged MRI for cardiac motion correction in simultaneous PET-MR: phantom and patient studies.

Degradation of image quality caused by cardiac and respiratory motions hampers the diagnostic quality of cardiac PET. It has been shown that improved diagnostic accuracy of myocardial defect can be achieved by tagged MR (tMR) based PET motion correction using simultaneous PET-MR. However, one major hurdle for the adoption of tMR-based PET motion correction in the PET-MR routine is the long acquisition time needed for the collection of fully sampled tMR data. In this work, the authors propose an accelerated tMR acquisition strategy using parallel imaging and/or compressed sensing and assess the impact on the tMR-based motion corrected PET using phantom and patient data. Fully sampled tMR data were acquired simultaneously with PET list-mode data on two simultaneous PET-MR scanners for a cardiac phantom and a patient. Parallel imaging and compressed sensing were retrospectively performed by GRAPPA and kt-FOCUSS algorithms with various acceleration factors. Motion fields were estimated using nonrigid B-spline image registration from both the accelerated and fully sampled tMR images. The motion fields were incorporated into a motion corrected ordered subset expectation maximization reconstruction algorithm with motion-dependent attenuation correction. Although tMR acceleration introduced image artifacts into the tMR images for both phantom and patient data, motion corrected PET images yielded similar image quality as those obtained using the fully sampled tMR images for low to moderate acceleration factors (<4). Quantitative analysis of myocardial defect contrast over ten independent noise realizations showed similar results. It was further observed that although the image quality of the motion corrected PET images deteriorates for high acceleration factors, the images were still superior to the images reconstructed without motion correction. Accelerated tMR images obtained with more than 4 times acceleration can still provide relatively accurate motion fields and yield tMR-based motion corrected PET images with similar image quality as those reconstructed using fully sampled tMR data. The reduction of tMR acquisition time makes it more compatible with routine clinical cardiac PET-MR studies.

Cortical Thickness Estimation Using DIR Imaging with GRAPPA Factor 2

Purpose : DIR image is relatively free from susceptibility artifacts therefore, DIR image can make it possible to reliably measure cortical thickness/volume. One drawback of the DIR acquisition is the long scan time to acquire the fully sampled 3D data set. To solve this problem, we applied a parallel imaging method (GRAPPA) and verify the reliability of using the volumetric study. Materials and methods : Six healthy volunteers (3 males and 3 females; age years) underwent MRI using the 3D DIR sequence at a 3.0T Siemens Tim Trio MRI scanner. GRAPPA simulation was performed from the fully sampled data set for reduction factor 2. Data reconstruction was performed using MATLAB R2009b. Freesurfer v.4.3.0 was used to evaluate the cortical thickness of the entire brain, and to extract white matter information from the DIR image, Analyze 9.0 was used. The global cortical thickness estimated from the reconstructed image was compared with reference image by using a T-test in SPSS. Results : Although reduced SNR and blurring are observed from the reconstructed image, in terms of segmentation the effect was not so significant. The volumetric result was validated that there were no significant differences in many cortical regions. Conclusion : This study was performed with DIR image for a volumetric MRI study. To solve the long scan time of 3D DIR imaging, we applied GRAPPA algorithm. According to the results, fast imaging can be done with reduction factor 2 with little loss of image quality at 3.0T.

Increasing efficiency of parallel imaging for 2D multislice acquisitions

Parallel imaging algorithms require precise knowledge about the spatial sensitivity variation of the receiver coils to reconstruct images with full field of view (FOV) from undersampled Fourier encoded data. Sensitivity information must either be given a priori, or estimated from calibration data acquired along with the actual image data. In this study, two approaches are presented, which require very little or no additional data at all for calibration in two-dimensional multislice acquisitions. Instead of additional data, information from spatially adjacent slices is used to estimate coil sensitivity information, thereby increasing the efficiency of parallel imaging. The proposed approaches rely on the assumption that over a small range of slices, coil sensitivities vary smoothly in slice direction. Both methods are implemented as variants of the GRAPPA algorithm. For a given effective acceleration, superior image quality is achieved compared to the conventional GRAPPA method. For the latter calibration lines for coil weight computation must be acquired in addition to the undersampled k-spaces for coil weight computation, thus requiring higher k-space undersampling, that is, a higher reduction factor to achieve the same effective acceleration. The proposed methods are particularly suitable to speed up parallel imaging for clinical applications where the reduction factor is limited to two or three.

Parallel spectroscopic imaging reconstruction with arbitrary trajectories using k‐space sparse matrices

Parallel imaging reconstruction has been successfully applied to magnetic resonance spectroscopic imaging (MRSI) to reduce scan times. For undersampled k-space data on a Cartesian grid, the reconstruction can be achieved in image domain using a sensitivity encoding (SENSE) algorithm for each spectral data point. Alternative methods for reconstruction with undersampled Cartesian k-space data are the SMASH and GRAPPA algorithms that do the reconstruction in the k-space domain. To reconstruct undersampled MRSI data with arbitrary k-space trajectories, image-domain-based iterative SENSE algorithm has been applied at the cost of long computing times. In this paper, a new k-space domain-based parallel spectroscopic imaging reconstruction with arbitrary k-space trajectories using k-space sparse matrices is applied to MRSI with spiral k-space trajectories. The algorithm achieves MRSI reconstruction with reduced memory requirements and computing times. The results are demonstrated in both phantom and in vivo studies. Spectroscopic images very similar to that reconstructed with fully sampled spiral k-space data are obtained at different reduction factors.

Hochaufgelöste quantitative MR-tomografische Bestimmung der subendo- und subepimyokardialen Perfusion unter Stress und in Ruhe

MR stress perfusion imaging of the heart allows the quantification of myocardial perfusion and the evaluation of myocardial perfusion reserve (MPR) and the ratio of subendocardial to subepicardial perfusion at rest and under adenosine stress. The aim of this study was to evaluate a high-resolution GRAPPA sequence for quantitative MR first pass perfusion imaging in healthy volunteers. First pass stress and rest perfusion studies were performed on 10 healthy volunteers using a 1.5 T MR scanner with a multislice SR-TrueFISP first pass perfusion sequence with a GRAPPA algorithm (acceleration factor 3) in prebolus technique and an image resolution of 1.8 x 1.8 mm. For the comparison group, we examined 12 different healthy volunteers with a standard first pass perfusion SR-TrueFISP sequence using a resolution of 2.7 x 3.3 mm. Myocardial contours were manually delineated followed by an automatic division of the myocardium into two rings with an equal thickness for the subendo- and subepicardial layer. Eight sectors per slice were evaluated using contamination and baseline correction. Using the GRAPPA sequence, the ratio of subendo- to subepimyocardial perfusion was 1.18 +/- 0.32 for the examination at rest. Under pharmacologically induced stress, the ratio was 1.08 +/- 0.27. For the standard sequence the ratio was 1.15 +/- 0.28 at rest and 1.11 +/- 0.33 under stress. For the high resolution sequence higher mean values for the subendo- to subepimyocardial ratio were obtained with comparable standard deviations. The difference between the sequences was not significant. The evaluation of subendomyocardial and subepimyocardial perfusion is feasible with a high-resolution first pass perfusion sequence. The use of a higher resolution to avoid systematic error leads to increased image noise. However, no relevant reduction in the quantitative perfusion values under stress and at rest was able to be depicted.

Genome Rearrangement Based on Reversals that Preserve Conserved Intervals

The order of genes in the genomes of species can change during evolution and can provide information about their phylogenetic relationship. An interesting method to infer the phylogenetic relationship from the gene orders is to use different types of rearrangement operations and to find possible rearrangement scenarios using these operations. One of the most common rearrangement operations is reversals, which reverse the order of a subset of neighbored genes. In this paper, we study the problem to find the ancestral gene order for three species represented by their gene orders. The rearrangement scenario should use a minimal number of reversals and no other rearrangement operations. This problem is called the Median problem and is known to be NP-complete. In this paper, we describe a heuristic algorithm for finding solutions to the Median problem that searches for rearrangement scenarios with the additional property that gene groups should not be destroyed by reversal operations. The concept of conserved intervals for signed permutations is used to describe such gene groups. We show experimentally, for different types of test problems, that the proposed algorithm produces very good results compared to other algorithms for the Median problem. We also integrate our reversal selection procedure into the well-known MGR and GRAPPA algorithms and show that they achieve a significant speedup while obtaining solutions of the same quality as the original algorithms on the test problems.

Dynamic autocalibrated parallel imaging using temporal GRAPPA (TGRAPPA)

Current parallel imaging techniques for accelerated imaging require a fully encoded reference data set to estimate the spatial coil sensitivity information needed for reconstruction. In dynamic parallel imaging a time-interleaved acquisition scheme can be used, which eliminates the need for separately acquiring additional reference data, since the signal from directly adjacent time frames can be merged to build a set of fully encoded full-resolution reference data for coil calibration. In this work, we demonstrate that a time-interleaved sampling scheme, in combination with autocalibrated GRAPPA (referred to as TGRAPPA), allows one to easily update the coil weights for the GRAPPA algorithm dynamically, thereby improving the acquisition efficiency. This method may update coil sensitivity estimates frame by frame, thereby tracking changes in relative coil sensitivities that may occur during the data acquisition.