Accelerated volumetric MRI with a SENSE/GRAPPA combination

PURPOSE: To combine the specific advantages of the generalized autocalibrating partially parallel acquisitions (GRAPPA) technique and sensitivity encoding (SENSE) with two-dimensional (2D) undersampling. MATERIALS AND METHODS: By splitting the 2D reconstruction process into multiple one-dimensional (1D) reconstructions, the normal 1D GRAPPA method can be used for image reconstruction. Due to this data-handling process, a GRAPPA reconstruction is performed along the phase-encoding (PE) direction and effectively a SENSE reconstruction is performed along the partition-encoding (PAE) direction. RESULTS: In vivo experiments demonstrate the successful implementation of the SENSE/GRAPPA combination. Experimental results with up to 9.6-fold acceleration using a prototype 32-channel receiver head coil array are presented. CONCLUSION: The proposed SENSE/GRAPPA combination for 3D imaging allows the GRAPPA method to be applied in combination with 2D undersampling. Because the SENSE/GRAPPA combination is not based on knowledge of spatial coil sensitivities, it should be the method of choice whenever it is difficult to extract the sensitivity information.     

Image reconstruction by regularized nonlinear inversion—Joint estimation of coil sensitivities and image content

The use of parallel imaging for scan time reduction in MRI faces problems with image degradation when using GRAPPA or SENSE for high acceleration factors. Although an inherent loss of SNR in parallel MRI is inevitable due to the reduced measurement time, the sensitivity to image artifacts that result from severe undersampling can be ameliorated by alternative reconstruction methods. While the introduction of GRAPPA and SENSE extended MRI reconstructions from a simple unitary transformation (Fourier transform) to the inversion of an ill‐conditioned linear system, the next logical step is the use of a nonlinear inversion. Here, a respective algorithm based on a Newton‐type method with appropriate regularization terms is demonstrated to improve the performance of autocalibrating parallel MRI—mainly due to a better estimation of the coil sensitivity profiles. The approach yields images with considerably reduced artifacts for high acceleration factors and/or a low number of reference lines. Magn Reson Med, 2008. © 2008 Wiley‐Liss, Inc.     

Field-of-view limitations in parallel imaging.

Parallel imaging is one of the most promising developments in recent years for the acceleration of MR acquisitions. One area of practical importance where different parallel imaging methods perform differently is the manner in which they deal with aliasing in the full-FOV reconstructed image. It has been reported that sensitivity encoding (SENSE) reconstruction fails whenever the reconstructed FOV is smaller than the object being imaged. On the other hand, generalized autocalibrating partially parallel acquisition (GRAPPA) has been used successfully to reconstruct images with aliasing in the reconstructed FOV, as in conventional imaging. The disparate behavior of these methods can be easily demonstrated by a few simple illustrative examples. Additional in vivo examples using GRAPPA and modified SENSE (mSENSE) make this distinction clear. These experiments demonstrate that SENSE fails to reconstruct correct images when coil sensitivity maps are used that do not automatically account for the object size and therefore the aliasing in the reconstructed images. However, with the use of aliased high-resolution coil sensitivity maps, accurate SENSE reconstructions can be generated. On the other hand, GRAPPA produces images with an aliasing appearance that is exactly as would be expected from normal nonaccelerated acquisitions. An understanding of these effects could potentially lead to fewer operator-dependent errors, as well as a better understanding of the differences between the underlying reconstruction processes.     

Using GRAPPA to improve autocalibrated coil sensitivity estimation for the SENSE family of parallel imaging reconstruction algorithms

Two strategies are widely used in parallel MRI to reconstruct subsampled multicoil image data. SENSE and related methods employ explicit receiver coil spatial response estimates to reconstruct an image. In contrast, coil‐by‐coil methods such as GRAPPA leverage correlations among the acquired multicoil data to reconstruct missing k‐space lines. In self‐referenced scenarios, both methods employ Nyquist‐rate low‐frequency k‐space data to identify the reconstruction parameters. Because GRAPPA does not require explicit coil sensitivities estimates, it needs considerably fewer autocalibration signals than SENSE. However, SENSE methods allow greater opportunity to control reconstruction quality though regularization and thus may outperform GRAPPA in some imaging scenarios. Here, we employ GRAPPA to improve self‐referenced coil sensitivity estimation in SENSE and related methods using very few auto‐calibration signals. This enables one to leverage each methods' inherent strength and produce high quality self‐referenced SENSE reconstructions. Magn Reson Med 60:462–467, 2008. © 2008 Wiley‐Liss, Inc.     

Robust GRAPPA reconstruction and its evaluation with the perceptual difference model

PURPOSE: To develop and optimize a new modification of GRAPPA (generalized autocalibrating partially parallel acquisitions) MR reconstruction algorithm named "Robust GRAPPA." MATERIALS AND METHODS: In Robust GRAPPA, k-space data points were weighted before the reconstruction. Small or zero weights were assigned to "outliers" in k-space. We implemented a Slow Robust GRAPPA method, which iteratively reweighted the k-space data. It was compared to an ad hoc Fast Robust GRAPPA method, which eliminated (assigned zero weights to) a fixed percentage of k-space "outliers" following an initial estimation procedure. In comprehensive experiments the new algorithms were evaluated using the perceptual difference model (PDM), whereby image quality was quantitatively compared to the reference image. Independent variables included algorithm type, total reduction factor, outlier ratio, center filling options, and noise across multiple image datasets, providing 10,800 test images for evaluation. RESULTS: The Fast Robust GRAPPA method gave results very similar to Slow Robust GRAPPA, and showed significant improvements as compared to regular GRAPPA. Fast Robust GRAPPA added little computation time compared with regular GRAPPA. CONCLUSION: Robust GRAPPA was proposed and proved useful for improving the reconstructed image quality. PDM was helpful in designing and optimizing the MR reconstruction algorithms.     

Clinical multishot DW-EPI through parallel imaging with considerations of susceptibility, motion, and noise.

Geometric distortions and poor image resolution are well known shortcomings of single-shot echo-planar imaging (ss-EPI). Yet, due to the motion immunity of ss-EPI, it remains the most common sequence for diffusion-weighted imaging (DWI). Moreover, both navigated DW interleaved EPI (iEPI) and parallel imaging (PI) methods, such as sensitivity encoding (SENSE) and generalized autocalibrating parallel acquisitions (GRAPPA), can improve the image quality in EPI. In this work, DW-EPI accelerated by PI is proposed as a self-calibrated and unnavigated form of interleaved acquisition. The PI calibration is performed on the b = 0 s/mm2 data and applied to each shot in the rest of the DW data set, followed by magnitude averaging. Central in this study is the comparison of GRAPPA and SENSE in the presence of off-resonances and motion. The results show that GRAPPA is more robust than SENSE against both off-resonance and motion-related artifacts. The SNR efficiency was also investigated, and it is shown that the SNR/scan time ratio is equally high for one- to three-shot high-resolution diffusion scans due to the shortened EPI readout train length. The image quality improvements without SNR efficiency loss, together with motion tolerance, make the GRAPPA-driven DW-EPI sequence clinically attractive.     

Quantitative metrics for evaluating parallel acquisition techniques in diffusion tensor imaging at 3 Tesla

OBJECTIVES: Single-shot echo-planar based diffusion tensor imaging is prone to geometric and intensity distortions. Parallel imaging is a means of reducing these distortions while preserving spatial resolution. A quantitative comparison at 3 T of parallel imaging for diffusion tensor images (DTI) using k-space (generalized auto-calibrating partially parallel acquisitions; GRAPPA) and image domain (sensitivity encoding; SENSE) reconstructions at different acceleration factors, R, is reported here. MATERIALS AND METHODS: Images were evaluated using 8 human subjects with repeated scans for 2 subjects to estimate reproducibility. Mutual information (MI) was used to assess the global changes in geometric distortions. The effects of parallel imaging techniques on random noise and reconstruction artifacts were evaluated by placing 26 regions of interest and computing the standard deviation of apparent diffusion coefficient and fractional anisotropy along with the error of fitting the data to the diffusion model (residual error). RESULTS: The larger positive values in mutual information index with increasing R values confirmed the anticipated decrease in distortions. Further, the MI index of GRAPPA sequences for a given R factor was larger than the corresponding mSENSE images. The residual error was lowest in the images acquired without parallel imaging and among the parallel reconstruction methods, the R = 2 acquisitions had the least error. The standard deviation, accuracy, and reproducibility of the apparent diffusion coefficient and fractional anisotropy in homogenous tissue regions showed that GRAPPA acquired with R = 2 had the least amount of systematic and random noise and of these, significant differences with mSENSE, R = 2 were found only for the fractional anisotropy index. CONCLUSION: Evaluation of the current implementation of parallel reconstruction algorithms identified GRAPPA acquired with R = 2 as optimal for diffusion tensor imaging.     

UNFOLD-SENSE: a parallel MRI method with self-calibration and artifact suppression.

This work aims at improving the performance of parallel imaging by using it with our "unaliasing by Fourier-encoding the overlaps in the temporal dimension" (UNFOLD) temporal strategy. A self-calibration method called "self, hybrid referencing with UNFOLD and GRAPPA" (SHRUG) is presented. SHRUG combines the UNFOLD-based sensitivity mapping strategy introduced in the TSENSE method by Kellman et al. (5), with the strategy introduced in the GRAPPA method by Griswold et al. (10). SHRUG merges the two approaches to alleviate their respective limitations, and provides fast self-calibration at any given acceleration factor. UNFOLD-SENSE further includes an UNFOLD artifact suppression scheme to significantly suppress artifacts and amplified noise produced by parallel imaging. This suppression scheme, which was published previously (4), is related to another method that was presented independently as part of TSENSE. While the two are equivalent at accelerations < or = 2.0, the present approach is shown here to be significantly superior at accelerations > 2.0, with up to double the artifact suppression at high accelerations. Furthermore, a slight modification of Cartesian SENSE is introduced, which allows departures from purely Cartesian sampling grids. This technique, termed variable-density SENSE (vdSENSE), allows the variable-density data required by SHRUG to be reconstructed with the simplicity and fast processing of Cartesian SENSE. UNFOLD-SENSE is given by the combination of SHRUG for sensitivity mapping, vdSENSE for reconstruction, and UNFOLD for artifact/amplified noise suppression. The method was implemented, with online reconstruction, on both an SSFP and a myocardium-perfusion sequence. The results from six patients scanned with UNFOLD-SENSE are presented.     

Improved parallel MR imaging using a coefficient penalized regularization for GRAPPA reconstruction

A novel coefficient penalized regularization method for generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction is developed for improving MR image quality. In this method, the fitting coefficients of the source data are weighted with different penalty factors, which are highly dependent upon the relative displacements from the source data to the target data in k‐space. The imaging data from both phantom testing and in vivo MRI experiments demonstrate that the coefficient penalized regularization method in GRAPPA reconstruction is able to reduce noise amplification to a greater degree. Therefore, the method enhances the quality of images significantly when compared to the previous least squares and Tikhonov regularization methods. Magn Reson Med 69:1109–1114, 2013. © 2012 Wiley Periodicals, Inc.     

Generalized autocalibrating partially parallel acquisitions (GRAPPA).

In this study, a novel partially parallel acquisition (PPA) method is presented which can be used to accelerate image acquisition using an RF coil array for spatial encoding. This technique, GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) is an extension of both the PILS and VD-AUTO-SMASH reconstruction techniques. As in those previous methods, a detailed, highly accurate RF field map is not needed prior to reconstruction in GRAPPA. This information is obtained from several k-space lines which are acquired in addition to the normal image acquisition. As in PILS, the GRAPPA reconstruction algorithm provides unaliased images from each component coil prior to image combination. This results in even higher SNR and better image quality since the steps of image reconstruction and image combination are performed in separate steps. After introducing the GRAPPA technique, primary focus is given to issues related to the practical implementation of GRAPPA, including the reconstruction algorithm as well as analysis of SNR in the resulting images. Finally, in vivo GRAPPA images are shown which demonstrate the utility of the technique.     

Breathheld autocalibrated phase‐contrast imaging

Purpose:

To compare generalized autocalibrating partially parallel acquisitions (GRAPPA), modified sensitivity encoding (mSENSE), and SENSE in phase‐contrast magnetic resonance imaging (PC‐MRI) applications.

Materials and Methods:

Aliasing of the torso can occur in PC‐MRI applications. If the data are further undersampled for parallel imaging, SENSE can be problematic in correctly unaliasing signals due to coil sensitivity maps that do not match that of the aliased volume. Here, a method for estimating coil sensitivities in flow applications is described. Normal volunteers (n = 5) were scanned on a 1.5 T MRI scanner and underwent PC‐MRI scans using GRAPPA, mSENSE, SENSE, and conventional PC‐MRI acquisitions. Peak velocity and flow through the aorta and pulmonary artery were evaluated.

Results:

Bland–Altman statistics for flow in the aorta and pulmonary artery acquired with mSENSE and GRAPPA methods (R = 2 and R = 3 cases) have comparable mean differences to flow acquired with conventional PC‐MRI. GRAPPA and mSENSE PC‐MRI have more robust measurements than SENSE when there is aliasing artifact caused by insufficient coil sensitivity maps. For peak velocity, there are no considerable differences among the mSENSE, GRAPPA, and SENSE reconstructions and are comparable to conventional PC‐MRI.

Conclusion:

Flow measurements of images reconstructed with autocalibration techniques have comparable agreement with conventional PC‐MRI and provide robust measurements in the presence of wraparound. J. Magn. Reson. Imaging 2010;31:1004–1014. ©2010 Wiley‐Liss, Inc.     

Nonlinear GRAPPA: a kernel approach to parallel MRI reconstruction

GRAPPA linearly combines the undersampled k-space signals to estimate the missing k-space signals where the coefficients are obtained by fitting to some auto-calibration signals (ACS) sampled with Nyquist rate based on the shift-invariant property. At high acceleration factors, GRAPPA reconstruction can suffer from a high level of noise even with a large number of auto-calibration signals. In this work, we propose a nonlinear method to improve GRAPPA. The method is based on the so-called kernel method which is widely used in machine learning. Specifically, the undersampled k-space signals are mapped through a nonlinear transform to a high-dimensional feature space, and then linearly combined to reconstruct the missing k-space data. The linear combination coefficients are also obtained through fitting to the ACS data but in the new feature space. The procedure is equivalent to adding many virtual channels in reconstruction. A polynomial kernel with explicit mapping functions is investigated in this work. Experimental results using phantom and in vivo data demonstrate that the proposed nonlinear GRAPPA method can significantly improve the reconstruction quality over GRAPPA and its state-of-the-art derivatives.     

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. Magn Reson Med 61:267–272, 2009. © 2009 Wiley‐Liss, Inc.     

High-pass GRAPPA: an image support reduction technique for improved partially parallel imaging.

Partially parallel imaging (PPI) is a widely used technique in clinical applications. A limitation of this technique is the strong noise and artifact in the reconstructed images when high reduction factors are used. This work aims to increase the clinical applicability of PPI by improving its performance at high reduction factors. A new concept, image support reduction, is introduced. A systematic filter-design approach for image support reduction is proposed. This approach shows more advantages when used with an important existing PPI technique, GRAPPA. An improved GRAPPA method, high-pass GRAPPA (hp-GRAPPA), was developed based on this approach. The new technique does not involve changing the original GRAPPA kernel and performs reconstruction in almost the same amount of time. Experimentally, it is demonstrated that the reconstructed images using hp-GRAPPA have much lower noise/artifact level than those reconstructed using GRAPPA.     

Accelerated proton echo planar spectroscopic imaging (PEPSI) using GRAPPA with a 32-channel phased-array coil.

Parallel imaging has been demonstrated to reduce the encoding time of MR spectroscopic imaging (MRSI). Here we investigate up to 5-fold acceleration of 2D proton echo planar spectroscopic imaging (PEPSI) at 3T using generalized autocalibrating partial parallel acquisition (GRAPPA) with a 32-channel coil array, 1.5 cm(3) voxel size, TR/TE of 15/2000 ms, and 2.1 Hz spectral resolution. Compared to an 8-channel array, the smaller RF coil elements in this 32-channel array provided a 3.1-fold and 2.8-fold increase in signal-to-noise ratio (SNR) in the peripheral region and the central region, respectively, and more spatial modulated information. Comparison of sensitivity-encoding (SENSE) and GRAPPA reconstruction using an 8-channel array showed that both methods yielded similar quantitative metabolite measures (P > 0.1). Concentration values of N-acetyl-aspartate (NAA), total creatine (tCr), choline (Cho), myo-inositol (mI), and the sum of glutamate and glutamine (Glx) for both methods were consistent with previous studies. Using the 32-channel array coil the mean Cramer-Rao lower bounds (CRLB) were less than 8% for NAA, tCr, and Cho and less than 15% for mI and Glx at 2-fold acceleration. At 4-fold acceleration the mean CRLB for NAA, tCr, and Cho was less than 11%. In conclusion, the use of a 32-channel coil array and GRAPPA reconstruction can significantly reduce the measurement time for mapping brain metabolites.     

Improved temporal resolution in cardiac imaging using through‐time spiral GRAPPA

Previous work has shown that the use of radial GRAPPA for the reconstruction of undersampled real‐time free‐breathing cardiac data allows for frame rates of up to 30 images/s. It is well known that the spiral trajectory offers a higher scan efficiency compared to radial trajectories. For this reason, we have developed a novel through‐time spiral GRAPPA method and demonstrate its application to real‐time cardiac imaging. By moving from the radial trajectory to the spiral trajectory, the temporal resolution can be further improved at lower acceleration factors compared to radial GRAPPA. In addition, the image quality is improved compared to those generated using the radial trajectory due to the lower acceleration factor. Here, we show that 2D frame rates of up to 56 images/s can be achieved using this parallel imaging method with the spiral trajectory. Magn Reson Med, 2011. © 2011 Wiley Periodicals, Inc.     

Parallel MR imaging

Parallel imaging is a robust method for accelerating the acquisition of magnetic resonance imaging (MRI) data, and has made possible many new applications of MR imaging. Parallel imaging works by acquiring a reduced amount of k-space data with an array of receiver coils. These undersampled data can be acquired more quickly, but the undersampling leads to aliased images. One of several parallel imaging algorithms can then be used to reconstruct artifact-free images from either the aliased images (SENSE-type reconstruction) or from the undersampled data (GRAPPA-type reconstruction). The advantages of parallel imaging in a clinical setting include faster image acquisition, which can be used, for instance, to shorten breath-hold times resulting in fewer motion-corrupted examinations. In this article the basic concepts behind parallel imaging are introduced. The relationship between undersampling and aliasing is discussed and two commonly used parallel imaging methods, SENSE and GRAPPA, are explained in detail. Examples of artifacts arising from parallel imaging are shown and ways to detect and mitigate these artifacts are described. Finally, several current applications of parallel imaging are presented and recent advancements and promising research in parallel imaging are briefly reviewed.     

k-t GRAPPA: a k-space implementation for dynamic MRI with high reduction factor.

A novel technique called "k-t GRAPPA" is introduced for the acceleration of dynamic magnetic resonance imaging. Dynamic magnetic resonance images have significant signal correlations in k-space and time dimension. Hence, it is feasible to acquire only a reduced amount of data and recover the missing portion afterward. Generalized autocalibrating partially parallel acquisitions (GRAPPA), as an important parallel imaging technique, linearly interpolates the missing data in k-space. In this work, it is shown that the idea of GRAPPA can also be applied in k-t space to take advantage of the correlations and interpolate the missing data in k-t space. For this method, no training data, filters, additional parameters, or sensitivity maps are necessary, and it is applicable for either single or multiple receiver coils. The signal correlation is locally derived from the acquired data. In this work, the k-t GRAPPA technique is compared with our implementation of GRAPPA, TGRAPPA, and sliding window reconstructions, as described in Methods. The experimental results manifest that k-t GRAPPA generates high spatial resolution reconstruction without significant loss of temporal resolution when the reduction factor is as high as 4. When the reduction factor becomes higher, there might be a noticeable loss of temporal resolution since k-t GRAPPA uses temporal interpolation. Images reconstructed using k-t GRAPPA have less residue/folding artifacts than those reconstructed by sliding window, much less noise than those reconstructed by GRAPPA, and wider temporal bandwidth than those reconstructed by GRAPPA with residual k-space. k-t GRAPPA is applicable to a wide range of dynamic imaging applications and is not limited to imaging parts with quasi-periodic motion. Since only local information is used for reconstruction, k-t GRAPPA is also preferred for applications requiring real time reconstruction, such as monitoring interventional MRI.     

SENSE phase-constrained magnitude reconstruction with iterative phase refinement.

Conventional sensitivity encoding (SENSE) reconstruction is based on equations in the complex domain. However, for many MRI applications only the magnitude is relevant. If there exists an estimate of the underlying phase information, a magnitude-only phase-constrained reconstruction can help to improve the conditioning of the SENSE reconstruction problem. Consequently, this reduces g-factor-related noise enhancement. In previous attempts at phase-constrained SENSE reconstruction, image quality was hampered by strong aliasing artifacts resulting from inadequate phase estimates and high sensitivity to phase errors. If a full-resolution phase image is used, a significant reduction in aliasing errors and better noise properties compared to SENSE can be obtained. An iterative scheme that improves the phase estimate to better approximate the phase is presented. The mathematical framework of the new approach is provided together with comparisons of conventional SENSE, phase-constrained SENSE, and the new phase-refinement method. Both theory and experimental verification demonstrate significantly better noise performance at high reduction factors, i.e., close to the theoretical limit. For applications that need only magnitude data, an iterative phase-constrained SENSE reconstruction can provide substantial SNR improvement over SENSE reconstruction and less artifacts than phase-constrained SENSE.