Turbo Fast Three-Dimensional Carotid Artery Black-Blood MRI by Combining Three-Dimensional MERGE Sequence with Compressed Sensing

NOTE Magnetic Resonance in Medicine 000:000–000 (2012)

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 undersampled 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 transformation 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 xhard 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 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 xi;jÞ þðxi;jþ1 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 conventional 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 represent 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. Next, all remain- group is filled. The encoding number of every group equals the ing samples are grouped into segments (green and purple slice number, but the last one (red group) may have less encod- groups). Although their positions do not perfectly match, ings. In the green and purple groups, the encodings on the same they approximately coincide with the CPEO. Here, the row should be acquired completely before collecting next sample. Turbo Fast Vessel Wall Imaging Using CS 3

Table 1 STR Comparisons Between Full Sampled Dataset and Each Undersampled Dataset for In Vivo Experiments Undersampled datasets Full sampled Subjects dataset (1x) 2x 2.5x 3x 4x 5x A 9.8 10.9 12.7 14.9 14.8 15.0 B 11.7 13.2 12.5 16.7 14.4 20.3 C 20.0 14.5 16.3 17.8 13.2 16.3 D 20.0 18.3 24.2 26.5 17.9 19.7 E 18.5 19.8 22.1 21.6 23.6 25.0 F 15.4 11.9 12.3 13.8 16.9 18.4 G 21.3 19.6 20.7 22.6 19.2 22.1 Mean 6 SD 16.67 6 4.48 15.46 6 3.73 17.26 6 5.04 19.13 6 4.59 17.14 6 3.54 19.54 6 3.40 P value N.A. 0.276 0.644 0.105 0.640 0.125 N.A. ¼ not applicable.

In this study, C is the identity transform. After one- matrix size 256 256, slice thickness 2 mm, number of dimensional inverse Fourier transformation along the fre- slices 32, signal acquisition 1. The spatial resolution was quency encoding, two-dimensional CS reconstruction was 0.78 0.78 2mm3. After zero fill interpolation, it was performed by solving m with the undersampled k-space 0.39 0.39 2mm3. The scan time for the six sequen- data for each coronal slice. The steps of reconstruction tial 3D MERGEs was 65, 33, 26, 22, 16, and 13 s, respec- are as follows. We first chose an undersampled dataset tively, at 1, 2, 2.5, 3, 4, and 5-fold accelerations. from one channel of the eight-channel coil for coronal For part II, the parameters were: pulse repetition time/ reconstruction. Initial values of lW and lTV were set to be echo time 6.7/3.0 ms, flip angle 8 , field of view 180 0.02. The undersampled datasets were reconstructed by 180 mm2, receiver bandwidth 244 Hz/pixel, matrix size changing lW and lTV until an acceptable quality for each 256 256, interpolated to 512 512, slice thickness 0.7 coronal image was obtained. We then recorded the values mm, number of slices 64, signal acquisition 1. The of the two parameters and used them for the reconstruc- spatial resolution was 0.7 0.7 0.7 mm3, and it was tion of the other seven channel datasets. zero interpolated to 0.35 0.35 0.35 mm3. The scan time was 120, 60, 48, 40, 30, and 24 s at 1, 2, 2.5, 3, 4, and 5-fold accelerations, respectively. In Vivo Experiments

To assess the performance of the proposed technique of Image Analysis CS-3D MERGE, nine healthy volunteers (age 31 6 6years, five males, four females) were recruited. Written informed As noise depends on the parameters lW and lTV in the CS consent was received from each subject as approved by the reconstruction algorithm, the lumen signal-to-tissue ratio local institutional review board. MR images of the carotid (STR) was used as a measure of flow suppression efficiency arteries were acquired using a clinical 3 T scanner (Signa instead of the lumen signal-to-noise ratio. The contrast-to- TM; GE Medical Systems, Milwaukee, WI) with an eight- tissue ratio (CTR) between the carotid arterial lumen and channel phased-array bilateral carotid coil (GE Medical wall was used to evaluate the quality of black-blood imaging. Systems). The study design consisted of two parts: (1) Part The STR for lumen was defined by I, statistical comparison between the fully sampled and S undersampled images in seven subjects with a spatial reso- STR ¼ 100 ; ½4 lution of 0.78 0.78 2mm3; (2) Part II, qualitative evalu- T ation of isotropic high spatial resolution images for all where S is the signal intensity of lumen and T is the sig- acceleration factors in two other subjects with a spatial re- 3 nal intensity of the sternocleidomastoid, which is close solution of 0.7 0.7 0.7 mm . Part II studies were con- to the vessel and has a relatively uniform signal inten- ducted to further evaluate the performance of the proposed sity. The lumen signal (SL) was measured as the mean CS-3D MERGE in the presence of high noise level typically signal obtained from a regions-of-interest drawn in the observed in high-resolution images. vessel lumen, while the signal for carotid arterial wall Using an axial acquisition plane, one fully sampled 3D (SW) was measured as the average value of the manually MERGE (1-fold acceleration) and five CS-3D MERGEs at delineated 1 pixel width path to outline the carotid arte- 2, 2.5, 3, 4, and 5-fold accelerations were acquired in all rial wall. Twas measured as the mean signal intensity subjects. For MSDE black-blood preparation, the ampli- within a manually drawn regions-of-interest no smaller tude, slew rate and duration of the motion-sensitizing than 50 mm2 from the sternocleidomastoid. The CTR of gradients pulses were set to 30 mT/m, 120 mT/m/ms, wall-lumen was calculated by and 2 ms. Total time of the prepulse was 23.1 ms and maximum available gradient strength and slew rate were ðS S Þ CTR ¼ 100 W L : ½5 40 mT/m and 200 mT/m/ms, respectively. T For part I, the imaging parameters were: pulse repetition time/echo time 6.2/2.9 ms, flip angle 8, field of STR and CTR values were averaged to yield one STR view 200 200 mm2, receiver bandwidth 244 Hz/pixel, and one CTR for each acceleration. Thus, six sets of STR 4 Li et al.

Table 2 CTR Comparison Between Full Sampled Dataset and Each Undersampled Dataset for In Vivo Experiments Undersampled datasets Full sampled Subjects dataset (1x) 2x 2.5x 3x 4x 5x A 33.2 36.8 32.8 33.9 32.7 29.3 B 23.8 19.4 16.8 19.0 16.4 17.0 C 27.8 37.8 35.9 37.3 34.5 30.0 D 38.9 46.1 45.7 31.2 39.0 38.8 E 25.3 24.9 22.6 23.4 22.0 20.3 F 31.5 35.6 33.7 32.2 33.0 30.9 G 26.7 30.1 29.4 30.6 24.9 25.2 Mean 6 SD 29.60 6 5.28 32.96 6 8.90 30.99 6 9.36 29.66 6 6.31 28.93 6 8.00 27.36 6 7.26 P value N.A. 0.109 0.512 0.979 0.697 0.107 N.A. ¼ not applicable. and CTR values were obtained for each volunteer. T was and standard deviation were 16.67 6 4.48, 15.46 6 3.73, measured from a similar region for all accelerations for 17.26 6 5.04, 19.13 6 4.59, 17.14 6 3.54, and 19.54 6 3.40 each subject to ensure unbiased calculation of STR and for accelerations of 1x, 2x, 2.5x, 3x, 4x, and 5x in lumen CTR values. To fairly compare CTR values with respect STR, respectively (Table 1). There were no significant dif- to scan time differences, CTR efficiency (CTReff) was ferences between the fully sampled and undersampled calculated by the relation: datasets of 2 5x. The mean and standard deviation were 29.60 6 5.28, 32.96 6 8.90, 30.99 6 9.36, 29.66 6 6.31, CTRffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 28.93 6 8.00 and 27.36 6 7.26 for 1 5x acceleration CTReff ¼ p ; ½6 SLTH TASLICE acquisitions in wall-lumen CTR, respectively (Table 2). There were no statistically significant differences in wall- where SLTH is the imaging slice thickness (in milli- lumen CTR between the fully sampled dataset and each meters) and TASLICE is the imaging time per slice (in undersampled dataset either. For wall-lumen CTReff, the minutes). mean and standard deviation were 80.56 6 14.36, 125.69 For statistical comparison, the STR, CTR, and CTReff 6 33.93, 133.65 6 40.36, 137.90 6 29.34, 157.47 6 43.57, were calculated. Two board-certified radiologists with at and 164.97 6 43.76 for 1 5x accelerated imaging, respec- least 5 years of experience in vascular MR imaging, who tively (Table 3). CTReff for accelerations of 2 5x were sig- were blinded to the technique used, reviewed all images nificantly improved when compared to fully sampled for quality. imaging (P < 0.05 for all paired t-test comparisons). Figure 4a showed representative images with a resolu- Statistical Analysis tion of 0.78 0.78 2mm3 (Part I study). Both radiologists found that all of the undersampled images exhibited Ten axial images centered at the bifurcation of each comparable flow suppression efficiency, when compared carotid artery were used for analysis. Paired t-tests were with the fully sampled images. The delineations of outer performed for both STR and CTR comparison for the in vessel wall boundary and lumen-wall interface were also vivo experiments. P value less than 0.05 was considered comparable with the fully sampled images, except for significant. Statistical analysis was performed using the slightly blurred vessel wall boundary at 5-fold accel- SPSS (v11.0, SPSS Inc., Chicago, IL). eration. By using 3D multi planar reformatting, the oblique reformatted images at accelerations of 2 5x RESULTS exhibited comparable image quality to full acquisition, The measured values of lumen STR, wall-lumen CTR, and as demonstrated in Figure 4b. For all undersampled wall-lumen CTReff were presented in Figure 3. The mean images, comparable image quality at the carotid

FIG. 3. Lumen STR (a), wall-lumen CTR (b), and wall-lumen CTReff (c) comparisons between full sampled dataset and undersampled datasets of accelerations of 2 5x for in vivo experiments. The * represents a significant difference (P < 0.05) according to a paired t-test. Turbo Fast Vessel Wall Imaging Using CS 5

Table 3

CTReff Comparison Between Full Sampled Dataset and Each Undersampled Dataset for In Vivo Experiments Undersampled datasets Full sampled Subjects dataset (1x) 2x 2.5x 3x 4x 5x A 90.4 140.3 141.5 157.6 178.0 176.7 B 64.7 74.0 72.5 88.3 89.3 102.5 C 75.7 144.2 154.8 173.4 187.8 180.9 D 105.9 175.8 197.1 145.1 212.3 234.0 E 68.9 95.0 97.5 108.8 119.8 122.4 F 85.7 135.8 145.4 149.7 179.6 186.3 G 72.7 114.8 126.8 142.3 135.5 152.0 Mean 6 SD 80.56 6 14.36 125.69 6 33.93 133.65 6 40.36 137.90 6 29.34 157.47 6 43.57 164.97 6 43.76 P value N.A. < 0.05 < 0.05 < 0.05 < 0.05 < 0.05 N.A. ¼ not applicable. bifurcation, where atherosclerosis is usually caused by DISSCUSSION plaque deposition, were obtained. In this study, we have demonstrated the feasibility of Figure 5 depicted images from isotropic high spatial CS-3D MERGE for black-blood MRI. The total variation resolution imaging. In Figure 5a, there were three repre- (TV) penalty and identity transform based CS algorithm sentative axial slices. Each radiologist concluded that all was used. As mentioned in previous studies (9,16), TV is undersampled images exhibited comparable flow suppres- able to effectively remove noise and yield sharp edges in sion efficiency and delineation of outer vessel wall the reconstructed image and thus benefits the recovery boundary and lumen-wall interface with the fully of vessel wall for undersampled datasets. In addition, as sampled images. In the oblique reformatted images, image the vessel wall has relatively high contrast to other parts quality at the carotid bifurcation was comparable between in black-blood imaging and the proportion of the object undersampled and fully sampled images (Fig. 5b). to the whole image is very small, vessel wall imaging can be considered sparse in the pixel domain. Therefore, the identity transform was selected as the sparsity transform. According to the CS theory, the relatively high contrast can be recovered with very high probability by ‘1-norm minimization (11). This suggests that the vessel wall signal can be recovered effectively in undersampled k-space. Moreover, the results of in vivo experiments have verified this point, even at high accelerations.

FIG. 4. Representative images from one subject. a: Three axial slices showing the vessel wall with six levels of acceleration. Almost no difference could be found in blood suppression between the images at acceleration factors of 2, 2.5, 3, 4, and 5 and the corresponding fully sampled image (acceleration 1x). The FIG. 5. Representative images from one subject scanned with an delineation of vessel wall in the undersampled images is compara- isotropic high spatial resolution of 0.7 0.7 0.7 mm3, and the ble with the corresponding fully sampled image, except for the resolution were zero interpolated to 0.35 0.35 0.35 mm3. a: slightly blurred vessel wall boundary at 5x acceleration. b: The Three axial slices showing the vessel wall. Comparable flow sup- reformats of images in oblique planes demonstrated good vessel pression efficiency and delineation of outer vessel wall boundary wall delineation of right (top row) and left (bottom row) carotid and lumen-wall interface are found for each acceleration. b: arteries. The comparable quality of all the undersampled images Oblique reformats of images showing comparable vessel wall can be seen at the carotid bifurcation, where carotid atherosclero- delineation of the right carotid artery. The carotid bifurcations can sis usually occurs due to plaque deposition. be depicted clearly for all accelerations. 6 Li et al.

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