2D-GRAPPA-operator for faster 3D parallel MRI.

When using parallel MRI (pMRI) methods in combination with three-dimensional (3D) imaging, it is beneficial to subsample the k-space along both phase-encoding directions because one can then take advantage of coil sensitivity variations along two spatial dimensions. This results in an improved reconstruction quality and therefore allows greater scan time reductions as compared to subsampling along one dimension. In this work we present a new approach based on the generalized autocalibrating partially parallel acquisitions (GRAPPA) technique that allows Fourier-domain reconstructions of data sets that are subsampled along two dimensions. The method works by splitting the 2D reconstruction process into two separate 1D reconstructions. This approach is compared with an extension of the conventional GRAPPA method that directly regenerates missing data points of a 2D subsampled k-space by performing a linear combination of acquired data points. In this paper we describe the theoretical background and present computer simulations and in vivo experiments.     

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.     

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.     

IIR GRAPPA for parallel MR image reconstruction

Accelerated parallel MRI has advantage in imaging speed, and its image quality has been improved continuously in recent years. This paper introduces a two‐dimensional infinite impulse response model of inverse filter to replace the finite impulse response model currently used in generalized autocalibrating partially parallel acquisitions class image reconstruction methods. The infinite impulse response model better characterizes the correlation of k‐space data points and better approximates the perfect inversion of parallel imaging process, resulting in a novel generalized image reconstruction method for accelerated parallel MRI. This k‐space‐based reconstruction method includes the conventional generalized autocalibrating partially parallel acquisitions class methods as special cases and has a new infinite impulse response data estimation mechanism for effective improvement of image quality. The experiments on in vivo MRI data show that the proposed method significantly reduces reconstruction errors compared with the conventional two‐dimensional generalized autocalibrating partially parallel acquisitions method, particularly at the high acceleration rates. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

Parallel MRI with extended and averaged GRAPPA kernels (PEAK-GRAPPA): optimized spatiotemporal dynamic imaging

Purpose

To evaluate an optimized k‐t‐space related reconstruction method for dynamic magnetic resonance imaging (MRI), a method called PEAK‐GRAPPA (Parallel MRI with Extended and Averaged GRAPPA Kernels) is presented which is based on an extended spatiotemporal GRAPPA kernel in combination with temporal averaging of coil weights.

Materials and Methods

The PEAK‐GRAPPA kernel consists of a uniform geometry with several spatial and temporal source points from acquired k‐space lines and several target points from missing k‐space lines. In order to improve the quality of coil weight estimation sets of coil weights are averaged over the temporal dimension.

Results

The kernel geometry leads to strongly decreased reconstruction times compared to the recently introduced k‐t‐GRAPPA using different kernel geometries with only one target point per kernel to fit. Improved results were obtained in terms of the root mean square error and the signal‐to‐noise ratio as demonstrated by in vivo cardiac imaging.

Conclusion

Using a uniform kernel geometry for weight estimation with the properties of uncorrelated noise of different acquired timeframes, optimized results were achieved in terms of error level, signal‐to‐noise ratio, and reconstruction time. J. Magn. Reson. Imaging 2008;28:1226–1232. © 2008 Wiley‐Liss, Inc.     

Accelerated cardiac perfusion imaging using k‐t SENSE with SENSE training

In k‐t sensitivity encoding (SENSE), MR data acquisition performed in parallel by multiple coils is accelerated by sparsely sampling the k‐space over time. The resulting aliasing is resolved by exploiting spatiotemporal correlations inherent in dynamic images of natural objects. In this article, a modified k‐t SENSE reconstruction approach is presented, which aims at improving the temporal fidelity of first‐pass, contrast‐enhanced myocardial perfusion images at high accelerations. The proposed technique is based on applying parallel imaging on the training data in order to increase their spatial resolution. At a net acceleration of 5.8 (k‐t factor = 8, training profiles = 11) accurate representations of dynamic signal‐intensities were achieved. The efficacy of this approach as well as limitations due to noise amplification were investigated in computer simulations and in vivo experiments. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Continuously moving table SENSE imaging.

A combination of continuously moving table imaging and parallel imaging based on sensitivity encoding (SENSE) is presented. One specific geometry is considered, where the receiver array is fixed to the MR magnet and does not move with the table, which allows for head-to-toe imaging with a small total number of coils. Sensitivity maps are defined for the enlarged virtual field of view and are composed according to the k-space sampling scheme such that established parallel reconstruction techniques are applicable to good approximation. In vivo experiments show the feasibility of this approach, and simulations determine the application range. Three-dimensional head-to-toe imaging of volunteers is performed in 77 s with a SENSE reduction factor of 2 in a virtual field of view of 1800 x 460 x 100 mm(3).     

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.     

Parallel magnetic resonance imaging using the GRAPPA operator formalism.

In this article it is shown that GRAPPA reconstruction can be reformulated as a matrix operator, similar to ladder or propagator operators used in quantum mechanics, that shifts data in k-space. Using this formalism, it is shown that there exists an infinitesimal GRAPPA operator that shifts data in k-space by arbitrarily small amounts. Other desired k-space shifts can then be accomplished through repeated applications of this infinitesimal GRAPPA operator. Implications of these ideas are described.     

On the undersampling strategies to accelerate time‐resolved 3D imaging using k‐t‐GRAPPA

The purpose of this study was to explore how to optimally undersample and reconstruct time‐resolved 3D data using a k‐t‐space‐based GRAPPA technique. The performance of different reconstruction strategies was evaluated using data sets with different ratios of phase (N_y) and partition (N_z) encoding lines (N_y × N_z = 64–128 × 40–64) acquired in a moving phantom. Image reconstruction was performed for different kernel configurations and different reduction factors (R = 5, 6, 8, and 10) and was evaluated using regional error quantification and SNR analysis. To analyze the temporal fidelity of the different kernel configurations in vivo, time‐resolved 3D phase contrast data were acquired in the thoracic aorta of two healthy volunteers. Results demonstrated that kernel configurations with a small kernel extension yielded superior results especially for more asymmetric data matrices as typically used in clinical applications. The application of k‐t‐GRAPPA to in vivo data demonstrated the feasibility of undersampling of time‐resolved 3D phase contrast data set with a nominal reduction factors of up to R_net = 8, while maintaining the temporal fidelity of the measured velocity field. Extended GRAPPA‐based parallel imaging with optimized multidimensional reconstruction kernels has the potential to substantially accelerate data acquisitions in time‐resolved 3D MRI. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Direct parallel image reconstructions for spiral trajectories using GRAPPA.

The use of spiral trajectories is an efficient way to cover a desired k-space partition in magnetic resonance imaging (MRI). Compared to conventional Cartesian k-space sampling, it allows faster acquisitions and results in a slight reduction of the high gradient demand in fast dynamic scans, such as in functional MRI (fMRI). However, spiral images are more susceptible to off-resonance effects that cause blurring artifacts and distortions of the point-spread function (PSF), and thereby degrade the image quality. Since off-resonance effects scale with the readout duration, the respective artifacts can be reduced by shortening the readout trajectory. Multishot experiments represent one approach to reduce these artifacts in spiral imaging, but result in longer scan times and potentially increased flow and motion artifacts. Parallel imaging methods are another promising approach to improve image quality through an increase in the acquisition speed. However, non-Cartesian parallel image reconstructions are known to be computationally time-consuming, which is prohibitive for clinical applications. In this study a new and fast approach for parallel image reconstructions for spiral imaging based on the generalized autocalibrating partially parallel acquisitions (GRAPPA) methodology is presented. With this approach the computational burden is reduced such that it becomes comparable to that needed in accelerated Cartesian procedures. The respective spiral images with two- to eightfold acceleration clearly benefit from the advantages of parallel imaging, such as enabling parallel MRI single-shot spiral imaging with the off-resonance behavior of multishot acquisitions.     

Multiple-mouse MRI.

Several theoretical parallel-imaging approaches are evaluated that seek to improve the efficiency of an MRI experiment involving multiple small samples, such as mice. The best method for our mouse phenotyping application is chosen in terms of efficiency and ease of implementation, and the approach is demonstrated at 1.5 T on a clinical scanner with an array of four shielded birdcage coils with four parallel receivers. Electronic interactions between the receiver channels in the system are quantified and a novel sensitivity-encoding (SENSE)-like postprocessing method is described to remove the resulting image ghosts. In parallel imaging with a four-coil array, the time required for three-dimensional (3D) high-resolution imaging of four mice is reduced to one-fourth the time that it would take to image the mice sequentially.     

Virtual coil concept for improved parallel MRI employing conjugate symmetric signals

A new approach for utilizing conjugate k‐space symmetry for improved parallel MRI performance is presented. By generating virtual coils containing conjugate symmetric k‐space signals from actual coils, additional image‐ and coil‐phase information can be incorporated into the reconstruction process for parallel acquisition techniques. In that way the reconstruction conditions are improved, resulting in less noise enhancement. In particular in combination with generalized autocalibrating partially parallel acquisitions (GRAPPA), the virtual coil concept represents a practical approach since no explicit spatial phase information is required. In addition, the influence of phase variations originating from the complex receiver coils as well as from the background is investigated. It is shown that there exist background phase distributions yielding an optimized pMRI reconstruction. Magn Reson Med 61:93–102, 2009. © 2008 Wiley‐Liss, Inc.     

Self-calibration method for radial GRAPPA/k-t GRAPPA.

Generalized autocalibrating partially parallel acquisitions (GRAPPA), an important parallel imaging technique, can be easily applied to radial k-space data by segmenting the k-space. The previously reported radial GRAPPA method requires extra calibration data to determine the relative shift operators. In this work it is shown that pseudo-full k-space data can be generated from the partially acquired radial data by filtering in image space followed by inverse gridding. The relative shift operators can then be approximated from the pseudo-full k-space data. The self-calibration method using pseudo-full k-space data can be applied in both k and k-t space. This technique avoids the prescans and hence improves the applicability of radial GRAPPA to image static tissue, and makes k-t GRAPPA applicable to radial trajectory. Experiments show that radial GRAPPA calibrated with pseudo-full calibration data generates results similar to radial GRAPPA calibrated with the true full k-space data for that image. If motion occurs during acquisition, self-calibrated radial GRAPPA protects structural information better than externally calibrated GRAPPA. However, radial GRAPPA calibrated with pseudo-full calibration data suffers from residual streaking artifacts when the reduction factor is high. Radial k-t GRAPPA calibrated with pseudo-full calibration data generates reduced errors compared to the sliding-window method and temporal GRAPPA (TGRAPPA).     

SENSE心脏阵列线圈在前列腺MRI检查中的初步应用研究

目的 对灵敏度编码(SENSE)心脏阵列线圈和直肠腔内线圈在前列腺MRI检查中的图像质量进行对比研究,初步评价SENSE心脏阵列线圈在前列腺MRI检查中的价值.资料与方法 选取前列腺病变患者50例.在相同扫描参数下,均使用SENSE心脏阵列线圈和直肠腔内线圈进行前列腺MRI常规检查,对使用两种线圈所分别获得的前列腺轴位(TRA)小视野、薄层T2WI图像的均匀度、对比信噪比(CNR)进行对比分析.结果 采用SENSE心脏阵列线圈所获得的图像均匀度优于采用直肠腔内线圈者(配对t检验,P＜0.05);采用SENSE心脏阵列线圈所获得的图像CNR亦优于采用直肠腔内线圈者(配对t检验,P＜0.05).结论 SENSE心脏阵列线圈在图像均匀度和CNR这两个图像评价指标方面都取得了较好的成像效果,在一定程度上可以替代直肠腔内线圈进行前列腺小视野、薄层、高分辨率T2W成像.     

Fast method for 1D non-cartesian parallel imaging using GRAPPA.

MRI with non-Cartesian sampling schemes can offer inherent advantages. Radial acquisitions are known to be very robust, even in the case of vast undersampling. This is also true for 1D non-Cartesian MRI, in which the center of k-space is oversampled or at least sampled at the Nyquist rate. There are two main reasons for the more relaxed foldover artifact behavior: First, due to the oversampling of the center, high-energy foldover artifacts originating from the center of k-space are avoided. Second, due to the non-equidistant sampling of k-space, the corresponding field of view (FOV) is no longer well defined. As a result, foldover artifacts are blurred over a broad range and appear less severe. The more relaxed foldover artifact behavior and the densely sampled central k-space make trajectories of this type an ideal complement to autocalibrated parallel MRI (pMRI) techniques, such as generalized autocalibrating partially parallel acquisitions (GRAPPA). Although pMRI can benefit from non-Cartesian trajectories, this combination has not yet entered routine clinical use. One of the main reasons for this is the need for long reconstruction times due to the complex calculations necessary for non-Cartesian pMRI. In this work it is shown that one can significantly reduce the complexity of the calculations by exploiting a few specific properties of k-space-based pMRI.