NOTE Magnetic Resonance in Medicine 000:000–000 (2012) Turbo Fast Three-Dimensional Carotid Artery Black-Blood MRI by Combining Three-Dimensional MERGE Sequence with Compressed Sensing Bo Li,1 Li Dong,2 Bin Chen,3 Shuangxi Ji,1 Wenchao Cai,4 Ye Wang,3 Jue Zhang,1,3* Zhaoqi Zhang,2 Xiaoying Wang,3,4 and Jing Fang1,3 INTRODUCTION Purpose: In this study, we sought to investigate the feasibility of turbo fast three-dimensional (3D) black-blood imaging by A three-dimensional (3D) motion-sensitizing driven combining a 3D motion-sensitizing driven equilibrium rapid equilibrium (MSDE) rapid gradient echo (3D MERGE) gradient echo sequence with compressed sensing. technique has been demonstrated as a useful tool for in Methods: A pseudo-centric phase encoding order was devel- vivo assessment of atherosclerotic disease in 3D black- oped for compressed sensing-3D motion-sensitizing driven blood MRI (1). It can accurately depict plaque in all equilibrium rapid gradient echo to suppress flow signal in three spatial directions and thus provide more accurate undersampled 3D k-space. Nine healthy volunteers were measurement of plaque morphology, improve the repro- recruited for this study. Signal-to-tissue ratio, contrast-to-tissue ducibility of artery MRI, and allow registration of images ratio (CTR) and CTR efficiency (CTR ) between fully sampled eff in serial studies (2,3). However, a relatively long scan and undersampled images were calculated and compared in seven subjects. Moreover, isotropic high resolution images time for 3D phase encoding is needed to sufficiently using different compressed sensing acceleration factors were cover image volume and to achieve satisfactory spatial evaluated in two other subjects. resolution (4). In particular, the frequent repetition of black-blood preparation ahead of the imaging acquisition Results: Wall-lumen signal-to-tissue ratio or CTR were compa- further decreases scan efficiency. As a result of long rable between the undersampled and the fully sampled acquisition time, image quality is more likely to be nega- images, while significant improvement of CTReff was achieved in the undersampled images. At an isotropic high spatial reso- tively affected by motion such as swallowing, respiration lution of 0.7 3 0.7 3 0.7 mm3, all undersampled images exhib- and neck movements (5–7). Therefore, a method to accel- ited similar level of the flow suppression efficiency and the erate 3D black-blood MRI is highly desirable. capability of delineating outer vessel wall boundary and lumen- Many efforts have been made for the development of wall interface, when compared with the fully sampled images. undersampled MR acquisitions to reduce scan time Conclusion: The proposed turbo fast compressed sensing 3D (8–10). Among them, compressed sensing (CS) method black-blood imaging technique improves scan efficiency with- has attracted wide attention due to its ability to recover out sacrificing flow suppression efficiency and vessel wall an image from data sampled below the Nyquist frequency image quality. It could be a valuable tool for rapid 3D vessel without degrading image quality (11–15). In CS, if the wall imaging. Magn Reson Med 000:000–000, 2012. VC 2012 underlying imaging exhibits sparsity in the image (pixel) Wiley Periodicals, Inc. or a transform domain, then the image can be recovered Key words: compressed sensing; 3D-MERGE; vessel wall from a randomly undersampled dataset (14). Most MR imaging; random sampling; pseudo-centric phase encoding images are sparse within the finite differences transform, order; CS-3D MERGE wavelet transform and other transform domains (14). In this study, we sought to investigate the feasibility of turbo fast 3D black-blood imaging by combining a 3D MERGE sequence with CS (CS-3D MERGE) at a 3 T MR scanner. To effectively suppress flow signal in under- sampled k-space, a pseudo-centric phase encoding order 1College of Engineering, Peking University, Beijing, People’s Republic of China. was developed for CS-3D MERGE. We quantitatively 2Department of Radiology, Beijing Anzhen Hospital, Capital Medical measured undersampled and fully sampled images and University, Beijing, People’s Republic of China. performed statistical analyses on healthy volunteers for 3 Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, in vivo experiments. Moreover, isotropic high resolution People’s Republic of China. 4Department of Radiology, Peking University First Hospital, Beijing, People’s images using different CS acceleration factors were Republic of China. acquired to further evaluate the performance of the pro- Grant sponsor: Fundamental Research Funds for the Central Universities. posed technique. *Correspondence to: Jue Zhang, Ph.D., College of Engineering, Peking University, Yiheyuan Road No. 5, Beijing, 100871, People’s Republic of China. E-mail: [email protected] METHODS Received 14 May 2012; revised 3 November 2012; accepted 11 November 2012. In this article, kx, ky, and kz represent frequency encod- DOI 10.1002/mrm.24579 ing, in-plane phase encoding and slice phase encoding Published online in Wiley Online Library (wileyonlinelibrary.com). in a Cartesian 3D k-space. VC 2012 Wiley Periodicals, Inc. 1 2 Li et al. encoding number of each group is equal to the slice number. In the last group, however, it has less encoding number than the slice number (red group). Of note, groups with approximate CPEOs may collect more than one phase encoding at the same kz coordinate (green and purple groups). In such groups, according to the CPEO, the encodings on the same row should be acquired completely before collecting the next sample (numbers 3 and 4 in the green group and numbers 1 and 2 in the purple group). This is defined as pseudo-centric phase encoding order for CS-3D MERGE. FIG. 1. Sequence diagram of a 3D MERGE sequence. An MSDE 3D CS Reconstruction black-blood preparation with a length of TM, consists of a 90- 180-180-90 hard RF pulses and motion sensitizing gradients. For 3D MRI, after one-dimensional inverse Fourier trans- formation along kx, the signal s at each x position is 3D MERGE Sequence obtained and can be expressed as: The 3D MERGE black-blood sequence consists of a 3D s ¼ Fm þ n; ½1 spoiled segmented fast low angle shot sequence and an MSDE preparation (1) (Fig. 1). The MSDE black-blood where s is the signal vector, F is the undersampled Fou- preparation consists of a 90 x hard RF pulse, two 180 y rier operator obtained by a measurement matrix. A refocusing hard RF pulses, a 90 Àxhard RF pulse and Monte-Carlo method is used to construct the measure- four motion sensitizing gradients. Within the sequence, ment matrix (14). m is the unknown image estimation spoiler gradients are applied to crush residual transverse and n is a vector representing independent and identi- magnetization and fat suppression is used to generate cally distributed (i.d.d.) additive white gaussian noise. optimal delineation of the outer vessel wall. The imaging Thus, it is probable that m can be exactly reconstructed sequence is a fast low angle shot sequence with centric if m is sparse in a transform domain by solving the phase-encoding order (CPEO). following ‘1-norm optimization problem: F 2 l F l ; A Pseudo-Centric Phase Encoding Order for Maintaining minimize jj m À sjj2 þ Wjj mjj1 þ TVTVðmÞ ½2 Black-Blood Contrast in CS-3D MERGE where c is the sparsifying transform, TV is the total varia- In a 3D-MERGE sequence, maximal blood suppression tion of m, lW is the regularization weight for the sparsify- occurs immediately following the black-blood prepara- ing transform and lTV is the TV regularization term. The tion. Thus, only a limited amount of phase encoding total variation is the ‘1-norm of the finite differences: samples can be collected after preparation. The acquisi- X qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tion order of these phase encoding samples should be 2 2 TVðxÞ¼ ðxiþ1;j À xi;jÞ þðxi;jþ1 À xi;jÞ ; ½3 arranged in CPEO with a symmetrical low-high order. i;j Therefore, the full 3D k-space is usually separated into several groups or segments to fill k-space in this order. where x is a image matrix. In the undersampled k-space of CS-3D MERGE, the acquisition order of those random samples also needs to be arranged so as to be consistent with the CPEO. As illustrated in Figure 2, the 3D phase encoding loop structure in a 3D-MERGE sequence is a centric kz (slice) loop nested within a sequential ky (phase) loop, and the number of acquisitions following one MSDE preparation is equal to the number of slice. In Figure 2, the bold numbers on the left side of the k-space represent the filling sequence in a con- ventional CPEO for full sampling, and the colored solid circles are the random samples in the undersampled k- space. The colored solid circles linked in a line represent a group of samples acquired after one black-blood preparation. FIG. 2. Schematic diagram of pseudo-centric phase encoding First, random samples with positions that perfectly order. The bold numbers on the left side of the 3D k-space repre- sent the filling sequence in a conventional CPEO, and the colored match the CPEO along kz are grouped into segments (blue and orange groups in Fig. 2). In this case, the solid circles are the random samples in the 3D k-space. The blue and orange groups perfectly match the CPEO. The green, purple, encoding number of each segment is equal to the slice and red groups approximately coincide with the centric order. The number. The numbers in the colored solid circles show numbers in the colored solid circles show the order in which that the order in which that group is filled.