Fast Method for 1D Non-Cartesian Parallel Imaging Using GRAPPA Robin M. Heidemann, 1,2 * Mark A. Griswold, 1,3 Nicole Seiberlich, 1 Mathias Nittka, 2 Stephan A.R. Kannengiesser, 2 Berthold Kiefer, 2 and Peter M. Jakob 1 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 over- sampled 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 arti- fact 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 autocali- brating 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 rea- sons 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 complex- ity of the calculations by exploiting a few specific properties of k-space-based pMRI. Magn Reson Med 57:1037–1046, 2007. © 2007 Wiley-Liss, Inc. Key words: parallel imaging; GRAPPA; SENSE; variable density sampling; non-Cartesian trajectories It has been shown (e.g., in Refs. 1–3) that non-Cartesian sampling trajectories can offer inherent advantages for magnetic resonance imaging (MRI) compared to Cartesian acquisition schemes. Spiral trajectories, for example, make efficient use of the gradient performance of an MR system, while radial sampling schemes are known to be very ro- bust even in the case of vast undersampling. Radial and spiral trajectories are two-dimensional (2D) non-Cartesian sampling strategies. However, the use of trajectories that are non-Cartesian along one dimension in k-space and Cartesian along the other can also be advantageous. These so-called one-dimensional (1D) non-Cartesian trajectories can be designed and optimized for a robust foldover arti- fact behavior. Even though the advantages of non-Carte- sian trajectories are well known, these trajectories are not in common use in clinical MRI. In comparison, it is stan- dard in clinical routine to use parallel imaging (4,5) to speed up the acquisition of MR examinations. However, parallel MRI (pMRI) is not without its limitations. All pMRI acquisitions are affected by an inherent signal-to- noise ratio (SNR) loss, which is, as a rule of thumb, at least proportional to the square root of the acceleration factor (AF). Additionally, noise introduced by imperfections in the coil geometry and reconstruction algorithms further degrades the SNR. In the sensitivity encoding (SENSE) method (4), reconstruction is performed in the image do- main on a pixel-by-pixel basis. Therefore, errors in this procedure are local and appear as a kind of noise enhance- ment in the image. In contrast, the generalized autocali- brating partially parallel acquisitions (GRAPPA) recon- struction (5) is performed in k-space using a fit procedure between adjacent k-space lines or data points. Since a single data line or data point in k-space affects the whole image in the image domain, errors in this procedure are global and appear as remaining foldover artifacts in the final image. The more relaxed foldover artifact behavior of non-Cartesian trajectories is beneficial for reducing poten- tial remaining foldover artifacts. Non-Cartesian trajectories have another advantage for pMRI. Whenever they are de- signed to oversample a certain part or several parts of k-space, they are inherently autocalibrated. The autocali- bration approach (6) is a method in which a few k-space data lines or points are sampled densely enough to fulfill the Nyquist criterion (and may be sampled so densely that they surpass the Nyquist criterion). The densely sampled k-space data (otherwise known as the autocalibration sig- nal (ACS)) are then used to derive the reconstruction pa- rameters (i.e., the coil weights). The ACS data can be acquired before, after, or during the actual accelerated scan. The acquisition of the ACS data during the acceler- ated scan as suggested in Ref. 7, the so-called variable density (VD) approach, has the advantage that the ACS data can be incorporated into the reconstructed data set. This can significantly increase the overall image quality of the reconstruction. From the VD approach proposed in Ref. 7, which mainly used two different sampling densi- ties, it is a logical step to move to a continuously VD sampling scheme using a 1D non-Cartesian trajectory, as suggested in Ref. 8. The more relaxed foldover artifact behavior of non-Cartesian imaging makes such a trajectory an ideal complement to pMRI. Although parallel imaging can benefit from the advantages of non-Cartesian trajecto- ries described above, and vice versa, the combination of these acquisition schemes with parallel imaging has yet not entered routine use. One of the main reasons for this is the long reconstruction times required due to the complex calculations necessary for non-Cartesian parallel imaging. In this work, which is based on ideas presented at the 11th Annual Meeting of ISMRM in Toronto (9) and the 1 Universita ¨ t Wu ¨ rzburg, Physikalisches Institut, Wu ¨ rzburg, Germany. 2 Siemens Medical Solutions, Erlangen, Germany. 3 Department of Radiology, University Hospitals of Cleveland, Cleveland, USA. *Correspondence to: Robin M. Heidemann, Siemens AG, Med MREA-Adv- Neuro, P.O. Box 3260, D-91050 Erlangen, Germany. E-mail: robin.heidemann@siemens.com Received 10 October 2006; revised 29 January 2007; accepted 8 February 2007. DOI 10.1002/mrm.21227 Published online in Wiley InterScience (www.interscience.wiley.com). Magnetic Resonance in Medicine 57:1037–1046 (2007) © 2007 Wiley-Liss, Inc. 1037