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.     

Self-calibrating parallel imaging with automatic coil sensitivity extraction.

Calibration of the spatial sensitivity functions of coil arrays is a crucial element in parallel magnetic resonance imaging (PMRI). The most common approach has been to measure coil sensitivities directly using one or more low-resolution images acquired before or after accelerated data acquisition. However, since it is difficult to ensure that the patient and coil array will be in exactly the same positions during both calibration scans and accelerated imaging, this approach can introduce sensitivity miscalibration errors into PMRI reconstructions. This work shows that it is possible to extract sensitivity calibration images directly from a fully sampled central region of a variable-density k-space acquisition. These images have all the features of traditional PMRI sensitivity calibrations and therefore may be used for any PMRI reconstruction technique without modification. Because these calibration data are acquired simultaneously with the data to be reconstructed, errors due to sensitivity miscalibration are eliminated. In vivo implementations of self-calibrating parallel imaging using a flexible coil array are demonstrated in abdominal imaging and in real-time cardiac imaging studies.     

Auto-calibrated parallel spiral imaging.

This work describes an auto-calibrated method for parallel imaging with spiral trajectory. The method is a k-space approach where an interpolation kernel, accounting for coil sensitivity factors, is derived from experimental data and used to interpolate the reduced data set in parallel imaging to estimate the missing k-space data. For the case of spiral imaging, this interpolation kernel is defined along radial directions so that missing spiral interleaves can be estimated directly from neighboring interleaves. This kernel is invariant along the radial direction but varies azimuthally. Therefore, the k-space is divided into angular sectors and sector-specific kernels are used. It is demonstrated experimentally that relatively few sectors are sufficient for accurate reconstruction, allowing for efficient implementation. The interpolation kernels can be derived either from a separate calibration scan or self-calibration data available with a dual-density spiral acquisition. The reconstruction method is implemented with two sampling strategies and experimentally demonstrated to be robust.     

Broadband multicoil imaging using multiple demodulation hardware: a feasibility study.

Multiple receiver-coil data collection is an effective approach to reduce scan time. There are many parallel imaging techniques that reduce scan time using multiple receiver coils. One of these methods, partially parallel imaging with localized sensitivities (PILS), utilizes the localized sensitivity of each coil. The advantages of PILS over other parallel imaging methods include the simplicity of the algorithm, good signal-to-noise ratio (SNR) properties, and the fact that there is no additional complexity involved in applying the algorithm to arbitrary k-space trajectories. This PILS method can be further improved to provide truly parallel broadband imaging with the use of multiple-demodulation hardware. By customizing the demodulation based on each coil's location, the k-space sampling rate can be chosen based on each coil's localized sensitivity region along the readout direction. A simulated demodulation of data from 2D Fourier transform (FT) and spiral trajectories is shown to demonstrate the method's feasibility.     

VD-AUTO-SMASH imaging.

Recently a self-calibrating SMASH technique, AUTO-SMASH, was described. This technique is based on PPA with RF coil arrays using auto-calibration signals. In AUTO-SMASH, important coil sensitivity information required for successful SMASH reconstruction is obtained during the actual scan using the correlation between undersampled SMASH signal data and additionally sampled calibration signals with appropriate offsets in k-space. However, AUTO-SMASH is susceptible to noise in the acquired data and to imperfect spatial harmonic generation in the underlying coil array. In this work, a new modified type of internal sensitivity calibration, VD-AUTO-SMASH, is proposed. This method uses a VD k-space sampling approach and shows the ability to improve the image quality without significantly increasing the total scan time. This new k-space adapted calibration approach is based on a k-space-dependent density function. In this scheme, fully sampled low-spatial frequency data are acquired up to a given cutoff-spatial frequency. Above this frequency, only sparse SMASH-type sampling is performed. On top of the VD approach, advanced fitting routines, which allow an improved extraction of coil-weighting factors in the presence of noise, are proposed. It is shown in simulations and in vivo cardiac images that the VD approach significantly increases the potential and flexibility of rapid imaging with AUTO-SMASH.     

Artifact reduction in moving-table acquisitions using parallel imaging and multiple averages.

Two-dimensional (2D) axial continuously-moving-table imaging has to deal with artifacts due to gradient nonlinearity and breathing motion, and has to provide the highest scan efficiency. Parallel imaging techniques (e.g., generalized autocalibrating partially parallel acquisition GRAPPA)) are used to reduce such artifacts and avoid ghosting artifacts. The latter occur in T(2)-weighted multi-spin-echo (SE) acquisitions that omit an additional excitation prior to imaging scans for presaturation purposes. Multiple images are reconstructed from subdivisions of a fully sampled k-space data set, each of which is acquired in a single SE train. These images are then averaged. GRAPPA coil weights are estimated without additional measurements. Compared to conventional image reconstruction, inconsistencies between different subsets of k-space induce less artifacts when each k-space part is reconstructed separately and the multiple images are averaged afterwards. These inconsistencies may lead to inaccurate GRAPPA coil weights using the proposed intrinsic GRAPPA calibration. It is shown that aliasing artifacts in single images are canceled out after averaging. Phantom and in vivo studies demonstrate the benefit of the proposed reconstruction scheme for free-breathing axial continuously-moving-table imaging using fast multi-SE sequences.     

Self-calibrated spiral SENSE.

Current standard sensitivity-encoded parallel imaging (SENSE) utilizes a fully sampled low-resolution reference scan to estimate the coil sensitivities. This reference scan adds scan time and may introduce misregistration artifacts. The purpose of this study was to investigate the feasibility of estimating the coil sensitivities for spiral SENSE directly from an undersampled k-space center. The limited spatial frequencies of the coil sensitivities, and the undersampling beyond the Nyquist radius cause image artifacts. A point spread function (PSF) analysis and experiments on both phantoms and humans identified an optimal radius for the k-space center by minimizing these image artifacts. The preliminary data indicate that self-calibrated SENSE is as accurate as standard SENSE, which uses a fully sampled reference scan.     

Non-Cartesian data reconstruction using GRAPPA operator gridding (GROG).

A novel approach that uses the concepts of parallel imaging to grid data sampled along a non-Cartesian trajectory using GRAPPA operator gridding (GROG) is described. GROG shifts any acquired data point to its nearest Cartesian location, thereby converting non-Cartesian to Cartesian data. Unlike other parallel imaging methods, GROG synthesizes the net weight for a shift in any direction from a single basis set of weights along the logical k-space directions. Given the vastly reduced size of the basis set, GROG calibration and reconstruction requires fewer operations and less calibration data than other parallel imaging methods for gridding. Instead of calculating and applying a density compensation function (DCF), GROG requires only local averaging, as the reconstructed points fall upon the Cartesian grid. Simulations are performed to demonstrate that the root mean square error (RMSE) values of images gridded with GROG are similar to those for images gridded using the gold-standard convolution gridding. Finally, GROG is compared to the convolution gridding technique using data sampled along radial, spiral, rosette, and BLADE (a.k.a. periodically rotated overlapping parallel lines with enhanced reconstruction [PROPELLER]) trajectories.     

GRAPPA operator for wider radial bands (GROWL) with optimally regularized self‐calibration

A self‐calibrated parallel imaging reconstruction method is proposed for azimuthally undersampled radial dataset. A generalized auto‐calibrating partially parallel acquisition (GRAPPA) operator is used to widen each radial view into a band consisting of several parallel lines, followed by a standard regridding procedure. Self‐calibration is achieved by regridding the central k‐space region, where Nyquist criterion is satisfied, to a rotated Cartesian grid. During the calibration process, an optimal Tikhonov regularization factor is introduced to reduce the error caused by the small k‐space area of the self‐calibration region. The method was applied to phantom and in vivo datasets acquired with an eight‐element coil array, using 32‐64 radial views with 256 readout samples. When compared with previous radial parallel imaging techniques, GRAPPA operator for wider radial bands (GROWL) provides a significant speed advantage since calibration is carried out using the fully sampled k‐space center. A further advantage of GROWL is its applicability to arbitrary‐view angle ordering schemes. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

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.     

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-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).     

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.     

High-resolution diffusion-weighted imaging with interleaved variable-density spiral acquisitions

PURPOSE: To develop a multishot magnetic resonance imaging (MRI) pulse sequence and reconstruction algorithm for diffusion-weighted imaging (DWI) in the brain with submillimeter in-plane resolution. MATERIALS AND METHODS: A self-navigated multishot acquisition technique based on variable-density spiral k-space trajectory design was implemented on clinical MRI scanners. The image reconstruction algorithm takes advantage of the oversampling of the center k-space and uses the densely sampled central portion of the k-space data for both imaging reconstruction and motion correction. The developed DWI technique was tested in an agar gel phantom and three healthy volunteers. RESULTS: Motions result in phase and k-space shifts in the DWI data acquired using multishot spiral acquisitions. With the two-dimensional self-navigator correction, diffusion-weighted images with a resolution of 0.9 x 0.9 x 3 mm3 were successfully obtained using different interleaves ranging from 8-32. The measured apparent diffusion coefficient (ADC) in the homogenous gel phantom was (1.66 +/- 0.09) x 10(-3) mm2/second, which was the same as measured with single-shot methods. The intersubject average ADC from the brain parenchyma of normal adults was (0.91 +/- 0.01) x 10(-3) mm2/second, which was in a good agreement with the reported literature values. CONCLUSION: The self-navigated multishot variable-density spiral acquisition provides a time-efficient approach to acquire high-resolution diffusion-weighted images on a clinical scanner. The reconstruction algorithm based on motion correction in the k-space data is robust, and measured ADC values are accurate and reproducible.     

Artifact and noise suppression in GRAPPA imaging using improved k-space coil calibration and variable density sampling.

A parallel imaging technique, GRAPPA (GeneRalized Auto-calibrating Partially Parallel Acquisitions), has been used to improve temporal or spatial resolution. Coil calibration in GRAPPA is performed in central k-space by fitting a target signal using its adjacent signals. Missing signals in outer k-space are reconstructed. However, coil calibration operates with signals that exhibit large amplitude variation while reconstruction is performed using signals with small amplitude variation. Different signal variations in coil calibration and reconstruction may result in residual image artifact and noise. The purpose of this work was to improve GRAPPA coil calibration and variable density (VD) sampling for suppressing residual artifact and noise. The proposed coil calibration was performed in local k-space along both the phase and frequency encoding directions. Outer k-space was acquired with two different reduction factors. Phantom data were reconstructed by both the conventional GRAPPA and the improved technique for comparison at an acceleration of two. Under the same acceleration, optimal sampling and calibration parameters were determined. An in vivo image was reconstructed in the same way using the predetermined optimal parameters. The performance of GRAPPA was improved by the localized coil calibration and VD sampling scheme.     

Augmented generalized SENSE reconstruction to correct for rigid body motion.

The correction of motion artifacts continues to be a significant problem in MRI. In the case of uncooperative patients, such as children, or patients who are unable to remain stationary, the accurate determination and correction of motion artifacts becomes a very important prerequisite for achieving good image quality. The application of conventional motion-correction strategies often produces inconsistencies in k-space data. As a result, significant residual artifacts can persist. In this work a formalism is introduced for parallel imaging in the presence of motion. The proposed method can improve overall image quality because it diminishes k-space inconsistencies by exploiting the complementary image encoding capacity of individual receiver coils. Specifically, an augmented version of an iterative SENSE reconstruction is used as a means of synthesizing the missing data in k-space. Motion is determined from low-resolution navigator images that are coregistered by an automatic registration routine. Navigator data can be derived from self-navigating k-space trajectories or in combination with other navigation schemes that estimate patient motion. This correction method is demonstrated by interleaved spiral images collected from volunteers. Conventional spiral scans and scans corrected with proposed techniques are shown, and the results illustrate the capacity of this new correction approach.     

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.     

Description of parallel imaging in MRI using multiple coils.

A general formulation for parallel imaging using multiple coils is derived from the Fourier transform of coil sensitivity functions. This formulation provides a unified account for developed parallel imaging techniques such as subencoding, simultaneous acquisition of spatial harmonics (SMASH), and sensitivity encoding (SENSE), and indicates a guideline for coil configuration and k-space sampling in parallel imaging. The views that can be acquired simultaneously in parallel imaging have to be contained in the spatial frequency band of coil sensitivity functions.     

Spiral imaging: a critical appraisal

In view of recent applications in cardiovascular and functional brain imaging, this work revisits the basic performance characteristics of spiral imaging in direct comparison to echo-planar imaging (EPI) and conventional rapid gradient-echo imaging. Using both computer simulations and experiments on phantoms and human subjects at 2.9 T, the study emphasizes single-shot applications and addresses the design of a suitable trajectory, the choice of a gridding algorithm, and the sensitivity to experimental inadequacies. As a general result, the combination of a spiral trajectory with regridding of the k-space data poses no principle obstacle for high-quality imaging. On the other hand, experimental difficulties such as gradient deviations, resonance offset contributions, and concomitant field effects cause more pronounced and even less acceptable image artifacts than usually obtained for EPI. Moreover, when ignoring parallel imaging strategies that are also applicable to EPI, improvements of image quality via reduced acquisition periods are only achievable by interleaved multishot spirals because partial Fourier sampling and rectangular fields of view (FOVs) cannot be exploited for non-Cartesian trajectories. Taken together, while spiral imaging may find its niche applications, most high-speed imaging needs are more easily served by EPI.