NOTE Magnetic Resonance in Medicine 75:280–286 (2016)
DWI Using Navigated Interleaved Multishot EPI with Realigned GRAPPA Reconstruction Wentao Liu,1,2 Xuna Zhao,1,2 Yajun Ma,1,2 Xin Tang,1,2 and Jia-Hong Gao1,2,3* Purpose: A novel k-space reconstruction method is proposed for generating diffusion-weighted imaging (DWI) using navigated interleaved multishot EPI (msEPI). Theory and Methods: In interleaved msEPI, each shot of data acquired from one coil channel is a subset of the full k-space of that channel. All the k-space subsets of one channel can be treated as an undersampled dataset of a virtual multichannel data, which can be reconstructed by the GRAPPA algorithm after k-space realignment. The intershot phase variations are directly compensated using navigator echoes as the autocalibrating data in GRAPPA reconstruction. In cases of multichannel msEPI data, all the virtual channels and actual channels can be integrated into a single GRAPPA reconstruction step. The proposed method is tested using both simulation and in-vivo data. The simulation results produced by the proposed method and a SENSE-based method are compared. Results: The simulated images generated by the proposed method exhibit less relative error compared with those generated by the SENSE method. Inconsistent shot-to-shot phase variation is naturally resolved by GRAPPA calibration without additional phase map processing. High-quality brain DWI with submillimeter resolution is obtained using our proposed reconstruction method. Conclusion: A novel k-space msEPI reconstruction method has been developed for generating high-quality diffusion imagC 2015 Wiley Periing. Magn Reson Med 75:280–286, 2016. V odicals, Inc. Key words: diffusion imaging; multishot EPI; navigator; realigned GRAPPA
INTRODUCTION Conventional diffusion-weighted imaging (DWI) is acquired using single-shot echo planar imaging (ssEPI) with a major advantage of time efficiency (1). However, the obtainable spatial resolution of DWI using ssEPI is limited by the acquisition window in a single shot (2). ssEPI is also very sensitive to the magnetic field inhomogeneities, including 1 Beijing City Key Lab for Medical Physics and Engineering, Institute of Heavy Ion Physics, School of Physics, Peking University, Beijing, China. 2 Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China. 3 McGovern Institute for Brain Research, Peking University, Beijing, China. Grant sponsor: China’s National Strategic Basic Research Program (973); Grant number: 2012CB720700; Grant sponsor: The Natural Science Foundation of China; Grant numbers: 81227003, 81430037, 31421003. *Correspondence to: Jia-Hong Gao, Ph.D., Center for MRI Research, Peking University, Beijing, China 100871. E-mail: [email protected]
Received 16 July 2014; revised 23 October 2014; accepted 26 November 2014 DOI 10.1002/mrm.25586 Published online 5 March 2015 in Wiley Online Library (wileyonlinelibrary. com). C 2015 Wiley Periodicals, Inc. V
those from gradient eddy currents, and often lead to severe image distortions and signal dropouts in ssEPI. Multishot EPI (msEPI) has been developed to alleviate the issues in ssEPI. Acquiring k-space in multiple excitations reduces the echo train length, so msEPI can provide images of high spatial resolution and less blurring. Moreover, for interleaved msEPI acquisitions, the increased bandwidth can reduce off-resonance effects such as susceptibility artifacts, eddy-current-induced distortion, and signal dropout (3). The major challenge of msEPI in DWI is that the image is typically corrupted by ghosting artifacts due to the phase variations from shot to shot. Even the effect of a tiny motion would be amplified by diffusion-sensitizing gradients and could produce intershot phase variations (4). The phase variations between different shots can be effectively probed by navigator techniques (5–9). Several methods have been proposed to correct for the shot-to-shot phase variations (4,10–12), which include both linear and nonlinear components (13). The linear phase variations are attributed to rigid motions (rotation and translation), while pulsing of cerebrospinal fluid produces irregular and nonlinear intershot phase shifts. Therefore, correction methods applicable to arbitrary phase variations are required for a robust msEPI reconstruction in DWI. Currently, the sensitivity encoding (SENSE) algorithm (14) has been considered as an effective method for phase correction in msEPI. In the case of an N-shot EPI, data acquired from each shot is a subset of full k-space that is modulated by a potential extra motion-induced phase variation. The SENSE-based method then uses the N fold undersampled data to reconstruct an unfolded diffusion image; and the intershot phase variations are compensated in the sensitivity maps by means of incorporating phase information extracted from navigators in the SENSE encoding matrix (8,12). A potential problem associated with the SENSE-based msEPI method is that the high accelerating acquisition is only performed on imaging-echoes, not on navigator-echoes. As a result, the acquisition bandwidths along the phase-encoding (PE) direction of navigator-echo and imaging-echo are different, which leads to different offresonance induced image distortion in the navigatorecho and imaging-echo, and hence impairs the direct use of phase information probed by navigator echoes in SENSE-based msEPI reconstruction. An accelerated navigator echo can be used to alleviate the inconsistency of image-echo and navigator-echo. To completely solve this problem, additional off-resonance measurements and phase map processing is needed (12). In this study, a novel k-space-based interleaved msEPI reconstruction method is developed to produce images of high quality in DWI. The intershot phase variations
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are conveniently and effectively compensated by directly using the navigator echoes as auto-calibrating signals (ACS) for coefficient-fitting in the generalized autocalibrating partially parallel acquisitions (GRAPPA) algorithm (15), so there are no additional measurements and phase map processing as in the SENSE-based method. Each coil channel data acquired after one excitation of an N-shot msEPI forms a subset of the entire k-space of that channel with a reduction factor N. All these N kspace subsets of one channel can be treated as N-channel undersampled data that are misaligned in the PE direction. After simple realignment in k-space, these data can be converted to virtual multichannel datasets. The virtual channels and actual channels can be integrated into a mixed channel dataset, which can be reconstructed by means of a single GRAPPA reconstruction. The final image can be combined from all the channels using the sum of squares (SOS) method (16). Simulation of phantom multishot data was performed to compare the reconstruction quality of the proposed method with the conventional SENSE-based method. Isotropic diffusionweighted msEPI of healthy volunteers at 1.5T was performed, and the DWI was reconstructed using the proposed method.
THEORY Realigned GRAPPA Reconstruction For brevity and clarity, the discussion in this part is based on the one channel situation. The case of multiple channels is to be discussed in a later section. In msEPI with an interleave factor of N, every imageecho acquired after an excitation is a subset of k-space with undersampling factor N, and the n-th image-echo signal has (n-1) k-space displacement along PE direction: Z ~ ~ Sn ð~ k img;n Þ ¼ rimg ð~ r Þeiwn ð~r Þ e-i½k img þðn-1ÞDk y ~r d~ r [1] where rimg ð~ r Þ denotes the msEPI image domain data at spatial position ~ r , and wn denotes the motion induced extra phase of excitation n. ~ k img is the k-space position of the image-echo data and D~ k y denotes the minimum step length in k-space along the PE direction. The navigatorecho is fully sampled in the k-space center: Z ~ Sn ð~ k nav Þ ¼ rnav ð~ r Þeiwn ð~r Þ e-ik nav ~r d~ r [2] where rnav ð~ r Þ denotes the navigator signal at spatial position ~ r , and ~ k nav is the k-space position of the navigatorecho data. Simple variable transformation is implemented for analogy with GRAPPA formalism: r Þ ¼ ei½wn ð~r Þ-ðn-1ÞDk y ~r Cn ð~ ~
[3]
where Cn ð~ r Þ are virtual coil sensitivity maps. According to the analysis in our previous work (17), both imageecho data and navigator-echo data can be synthesized by linear combination of neighboring k-space samples with the same set of fitting coefficients Wj; l; r .
8 L X > > ~ > S ð k Þ ¼ Sl ð~ k img;l Þ Wj; l; r > j img;j > < l¼1 > L X > > > ~ ~ ~ ~ > S þ ðj-1ÞD k S þ ðl-1ÞD k k ¼ k Wj; l; r j nav y nav y l : l¼1
[4] where l denotes the l-th channel, L is the total number of channels, R is the acceleration factor and r (r R) is the index of the skipped lines in a block. Therefore, the navigator-echoes can be used as ACS to calculate the fitting coefficients, and then these fitting coefficients are used to reconstruct the N undersampled image-echoes using the GRAPPA algorithm. According to Eq. [4], only realigning of the misaligned image-echoes and shifting of navigator-echoes with corresponding displacements are required before the GRAPPA reconstruction. The principal procedure of the realigned GRAPPA method is shown schematically in Figure 1. Adjustment of Navigator Acquisition Window The navigator-echo used as ACS data is fully sampled at k-space center, whereas the image-echo is acquired with an acceleration factor N. Due to the off-resonance effects r Þ, the phase processions are incoherent between of DB0 ð~ navigator-echo signals and image-echo signals. The incoherence will lead to errors in GRAPPA coefficient fitting, which may lead to residual artifacts in the final reconstructed images. To address this problem, the echo spacing of the navigator-echo should be reduced by N times to make the acquisition BWs along the PE direction of the navigator-echo and image-echo consistent. If the navigator echo and image-echo are acquired with the same sampling interval t and gradient ascending/descending ramp time tramp , number of samples along the readout (RO) direction for the navigator echo should be reduced 0 from nx to nx : 0
nx ¼
nx -2ðN-1Þtramp =t : N
[5]
The acquisition window of navigator-echoes is reduced to accelerate the sample rate along the PE direction (as shown in Figure 2b), so the effective phase procession of navigator-echo signals is sampled at the same rate as the image-echo signals. Integrated Reconstruction of Virtual-Actual-Mixed Channels For multiple channels case, each individual channel can be processed separately and combined together using the SOS method. Alternately, all the virtual channels and actual channels can be integrated into a single GRAPPA reconstruction framework. For example, the eight-shot DWI data of eight coil elements can be formed as a combination of 64 virtual-actual mixed channels. The data processing will be more convenient and clearer in this manner because only a single GRAPPA reconstruction of the mixed channels is needed. Additional advantage of
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FIG. 1. The proposed realigned GRAPPA reconstruction of a typical four-shot interleaved msEPI k-space data set is shown schematically. Red, green, blue, and purple circles denote k-space lines acquired by the 1st, 2nd, 3rd, and 4th shot, respectively. White circles denote unacquired lines and gray circles are the reconstructed lines by GRAPPA algorithm. Left–right direction is the phase encoding direction, only the first 8 and the last 8 lines of total 256 lines in PE direction are shown and other lines are omitted and represented by ellipses. In the first stage, multishot EPI data are converted to multichannel data, and then the lines of the n-th excitation are shifted (n-1) steps backward along the PE direction to form realigned data, which are reconstructed by the GRAPPA algorithm in the third stage. Dashed arrows indicate the data moving paths and solid arrows denote an example fitting process in GRAPPA reconstruction.
using virtual-actual-mixed channels reconstruction is that it enables the acceleration of the proposed multishot DWI approach. METHODS Simulation of multishot k-space data reconstruction was performed to compare the proposed method with the conventional SENSE-based method. The simulated eightshot data were generated using the Shepp-Logan phantom that is modulated by sensitivity maps of a simulated eight-channel head coil. Random Gaussian noise with mean ¼ 0 and standard deviation SD ¼ 0.1 was added to the simulated phantom data and different nonlinear extra phases were added to the each shot image to simulate the motion-induced phase variations. Only a 1/8 subset of k-space samples from each image was used to form an eight-shot raw data set. The simulated raw data were then used in msEPI reconstruction both using the SENSE-based method (9,12,18) and the proposed GRAPPA-based method. A quantitative measure of the reconstruction performance was evaluated by calculating the relative errors between the reference and
reconstructed images: Er ¼
P
jIref ðrÞ-Irecon ðrÞj
P
jIref ðrÞj
100%, where
Iref (r) and Irecon (r) denote the intensity of the reference and P the reconstructed images at position r, respectively, denotes the sum over all the pixels across the entire field of view (FOV) in the images. The simulation data were constructed at an acceleration factor of 2 by only using the 2nd, 4th, 6th, and 8th shot data, and the data were processed by the integrated approach to form a 32 virtual-actual mixed channel undersampled dataset. Then the proposed realigned GRAPPA algorithm was performed to reconstruct the 32 channel data. To test the proposed method with different levels of motion-induced phase, extra nonlinear phases variations with different amplitude levels were added to the simulated eight-shot dataset. The amplitude level was defined by the standard deviation of the phase variations, denotes as SD(f). To test the utility of the proposed GRAPPA-based method for msEPI reconstruction in in vivo DWI, isotropic diffusion-weighted (19) brain imaging data were acquired from healthy volunteers on an Anke 1.5 Tesla
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FIG. 2. A typical dual refocusing SE diffusion-weighted msEPI sequence diagram (a) and the corresponding k-space trajectory of image-echo and navigator-echo of an eight-shot msEPI (b). The diffusion-sensitizing gradients are represented by dotted lines. The acquisition window of navigator-echo is adjusted to maintain the phase procession coherent with image-echo.
(T) MRI Scanner (SuZhouAnke Medical System, China) using a dual refocusing spin-echo (SE) diffusionweighted msEPI sequence (as shown in Figure 2a) with acquisition parameters as follows: repetition time/echo time (TR/TE) ¼ 3200 ms/92 ms, matrix size ¼ 256 256, field of view (FOV) ¼ 240 240 mm2, number of slices ¼ 15, slice thickness ¼ 6 mm. The imaging data were acquired with an 8-channel head coil. The acquisition of the navigator-echo was after the second refocusing radiofrequency pulse, and the acquisition central time of the navigator-echo was 144 ms. The crusher gradients implemented along slice selective (SS) direction were different in magnitude to eliminate the effect of stimulated echoes. An interleave factor of 8 was used in msEPI, the echo train length of both image-echo and navigator-echo was 32. Three orthogonal diffusion gradient direction imaging with b-value ¼ 1000 s/mm2 was performed with three averages for each direction, and the final image was combined using the geometric mean of three diffusion direction images. This study was approved by institutional internal reviewed board at Peking University. Informed written consent was obtained from volunteers. For image reconstruction, the integrated realigned GRAPPA method was applied to the multichannel MR data. k-space position shifting of both image-echo and navigator-echo was implemented first, data of the n-th excitation was shifted (n-1) steps backward along PE direction. The GRAPPA fitting kernel size was of four blocks and three columns, and 32 lines of navigator echoes were used as ACS for calibrating the GRAPPA algorithms. After the integrated GRAPPA reconstruction of
virtual-actual-mixed channels, the final image was the combination of all the channels using the SOS method. RESULTS The simulation results are shown in Figure 3. No obvious residual artifacts were present in either images reconstructed using the SENSE-based method or the proposed method, and the noise level increased in both images as compared to the reference image. However, the relative reconstruction error of the proposed method was 10.1% and was less than 11.6% of the SENSE-based method. Also the signal-to-noise ratio of the proposed method is no less than the conventional SENSE-based method. The result of the simulation data with acceleration factor R ¼ 2 was shown at the rightmost of the first row in Figure 3 with a relative reconstruction error of 14.8%. The results of the simulation data with different phase variation levels SD(f) ¼ 0, 1.4, 2.8, and 4.2 rad are shown in the second row in Figure 3 with relative errors of 9.9%, 10.1%, 10.7%, and 12.2%, respectively. An example of eight-shot DWI is shown in Figure 4. The first row shows the images directly reconstructed by means of Fast Fourier Transform (FFT) without motion correction, severe ghosting artifacts are present due to the random motion-induced phase errors. The second row shows the results using the proposed method; the phase errors are naturally compensated by using navigator-echo signals as ACS in GRAPPA reconstruction. No residual ghosting artifacts were visible in these images. From left to right columns, images are diffusion encoded along the RO, PE, and SS
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FIG. 3. In the first row, simulation eight-shot images were reconstructed using both conventional SENSE-based method (12) and the proposed GRAPPA-based method with acceleration factor R ¼ 1 and R ¼ 2, respectively. In the second row, simulation images were reconstructed using the proposed method with different phase variation levels SD(f) ¼ 0, 1.4, 2.8, and 4.2 rad. The relative reconstruction errors comparing to the reference image are shown in the top-right corner of each image.
directions respectively, and the rightmost column shows isotropic diffusion weighted images combined from the geometric mean of the left three images. The average phase variation (SD(f)) in vivo was found to be around 1.35 rad.
To demonstrate the robustness of the proposed method, additional results of the isotropic DWI images are shown in Figure 5. Different slices from top to bottom of the brain (as shown in Figures 5a–h) are reconstructed using
FIG. 4. Images reconstructed using direct FFT (a–d) and our proposed method (e–h). (a) and (e) are the msEPI data with diffusion encoded along RO direction, (b) and (f) are diffusion encoded along PE direction, (c) and (g) are diffusion encoded along SS direction, and (d) and (h) are the geometric average combined images with isotropic diffusion weighted.
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FIG. 5. Isotropic diffusion weighted images for b-value ¼ 1000 s/mm2 using the proposed msEPI method on different slice positions in human brain from top to bottom (a–h), respectively.
isotropic diffusion-weighted msEPI data with b-value ¼ 1000 s/mm2 by the proposed method. High quality DWI images of submillimeter in-plane resolution were obtained, and no obvious geometric distortion or artifacts were seen in the images. DISCUSSION A k-space GRAPPA algorithm based reconstruction method for multishot diffusion-weighted EPI reconstruction was proposed. The subsets of k-space data of each coil channel acquired by means of multi-excitations are treated as multichannel undersampled data in parallel imaging, and only simple k-space position realignment is needed before the reconstruction of these k-space data using the standard GRAPPA method. The key processing of the proposed method is to convert multishot data to virtual multichannel data (as shown in Figure 1: stages 1 and 2). N-shot DWI data form N undersampled k-space subsets. There are two distinctions between these and Nchannel undersampled data: (i) the n-th shot data has kspace displacement of (n-1)*dky along the PE direction compared with the first shot data and (ii) different motion-induced phases exist in each shot’s data. To convert the N-shot data to a N-channel data, the n-th shot data were shifted -(n-1) steps in k-space along the PE direction to align to the first shot, this consequently introduces an extra image-domain linear phase to each shot (n > 1) of data. This extra linear phase together with the motion-induce phase can be represented by a virtual coil sensitivity map (as expressed in Eq. [3]). Therefore, when the virtual coil sensitivity was regarded as coil sensitivity in multichannel data, the realigned multishot data can be identically treated as multichannel data. In this method, the intershot phase variations are directly compensated by using the navigator-echo as ACS
data for calculating the fitting coefficients in a GRAPPA reconstruction, and the incoherence between the imageecho and navigator-echo can be alleviated by adjustment of the navigator-echo acquisition window. Therefore, no additional measurement or process is necessary to extract and correct the intershot phase information as in the SENSE-based multishot reconstruction method. The adjustment of the navigator-echo acquisition window can be integrated with an accelerated navigator to increase the spatial resolution of navigator echo while keeping the appropriate phase-encoding bandwidth. However, this approach needs additional calibration data acquisition and parallel imaging reconstruction of the navigator echo. To test the benefits of a high resolution navigator echo, the simulated multishot data described in the Methods section have been reconstructed by realigned GRAPPA reconstruction with navigator echoes of high resolution (128 64) and low resolution (32 32). The resulting relative reconstruction errors were 9.9% and 10.1%, respectively. Hence the improvement of realigned GRAPPA reconstruction with high-resolution navigator echo is not significant. The usage of msEPI in DWI offers significant advantages compared with the conventional ssEPI approach: high spatial resolution, reduced image blur, and image distortions due to static off-resonance and eddy-current effects. The proposed method provides a unique and relatively simple approach to reconstruct multishot diffusion-weighted EPI data using the GRAPPA algorithm, and the nature of the intrinsic compensation of the motion-induced phase errors makes the proposed method robust and convenient. The reconstruction algorithm proposed in this work was applied to PE interleaved multishot EPI data, but highresolution DWI can also be achieved with other pulse sequences such as multishot spiral imaging, readout
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segmented EPI, and PROPELLER imaging. The core idea of the algorithm is to treat multishot data as multichannel data, so if an appropriate conversion of multishot sequence data to multichannel data exists, the proposed algorithm may be applied to other multishot DWI sequences. CONCLUSIONS In this note, a novel msEPI reconstruction method based on k-space GRAPPA for DWI is presented. Isotropic diffusion-weighted human brain imaging of healthy volunteers demonstrates that the proposed method provides robust reconstruction with excellent quality of high spatial resolution, no obvious residual artifacts, and no apparent distortion. REFERENCES 1. Turner R, Le Bihan D, Maier J, Vavrek R, Hedges LK, Pekar J. Echoplanar imaging of intravoxel incoherent motion. Radiology 1990;177: 407–414. 2. Farzaneh F, Riederer SJ, Pelc NJ. Analysis of T2 limitations and offresonance effects on spatial resolution and artifacts in echo-planar imaging. Magn Reson Med 1990;14:123–139. 3. Bernstein MA, King FK, Zhou XJ. Handbook of MRI pulse sequences. Burlington, MA: Elsevier Academic Press; 2004. 4. Butts K, de Crespigny A, Pauly JM, Moseley M. Diffusion-weighted interleaved echo-planar imaging with a pair of orthogonal navigator echoes. Magn Reson Med 1996;35:763–770. 5. Ordidge RJ, Helpern JA, Qing ZX, Knight RA, Nagesh V. Correction of motional artifacts in diffusion-weighted MR images using navigator echoes. Magn Reson Imaging 1994;12:455–460. 6. de Crespigny AJ, Marks MP, Enzmann DR, Moseley ME. Navigated diffusion imaging of normal and ischemic human brain. Magn Reson Med 1995;33:720–728.
Liu et al. 7. Butts K, Pauly J, de Crespigny A, Moseley M. Isotropic diffusionweighted and spiral-navigated interleaved EPI for routine imaging of acute stroke. Magn Reson Med 1997;38:741–749. 8. Liu C, Bammer R, Kim DH, Moseley ME. Self-navigated interleaved spiral (SNAILS): application to high-resolution diffusion tensor imaging. Magn Reson Med 2004;52:1388–1396. 9. Liu C, Moseley ME, Bammer R. Simultaneous phase correction and SENSE reconstruction for navigated multi-shot DWI with noncartesian k-space sampling. Magn Reson Med 2005;54:1412–1422. 10. Van AT, Karampinos DC, Georgiadis JG, Sutton BP. K-space and image-space combination for motion-induced phase-error correction in self-navigated multicoil multishot DWI. IEEE Trans Med Imaging 2009;28:1770–1780. 11. Chen NK, Avram AV, Song AW. Two-dimensional phase cycled reconstruction for inherent correction of echo-planar imaging nyquist artifacts. Magn Reson Med 2011;66:1057–1066. 12. Jeong HK, Gore JC, Anderson AW. High-resolution human diffusion tensor imaging using 2-D navigated multishot SENSE EPI at 7 T. Magn Reson Med 2013;69:793–802. 13. Anderson AW, Gore JC. Analysis and correction of motion artifacts in diffusion weighted imaging. Magn Reson Med 1994;32:379–387. 14. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn Reson Med 1999;42:952–962. 15. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med 2002;47:1202–1210. 16. Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR phased array. Magn Reson Med 1990;16:192–225. 17. Liu W, Tang X, Ma Y, Gao J. Improved parallel MR imaging using a coefficient penalized regularization for GRAPPA reconstruction. Magn Reson Med 2013;69:1109–1114. 18. Chen NK, Guidon A, Chang HC, Song AW. A robust multi-shot scan strategy for high-resolution diffusion weighted MRI enabled by multiplexed sensitivity-encoding (MUSE). Neuroimage 2013;72:41–47. 19. van Gelderen P, de Vleeschouwer MH, DesPres D, Pekar J, van Zijl PC, Moonen CT. Water diffusion and acute stroke. Magn Reson Med 1994;31:154–163.
DWI Using Navigated Interleaved Multishot EPI with Realigned GRAPPA Reconstruction Wentao Liu,1,2 Xuna Zhao,1,2 Yajun Ma,1,2 Xin Tang,1,2 and Jia-Hong Gao1,2,3* Purpose: A novel k-space reconstruction method is proposed for generating diffusion-weighted imaging (DWI) using navigated interleaved multishot EPI (msEPI). Theory and Methods: In interleaved msEPI, each shot of data acquired from one coil channel is a subset of the full k-space of that channel. All the k-space subsets of one channel can be treated as an undersampled dataset of a virtual multichannel data, which can be reconstructed by the GRAPPA algorithm after k-space realignment. The intershot phase variations are directly compensated using navigator echoes as the autocalibrating data in GRAPPA reconstruction. In cases of multichannel msEPI data, all the virtual channels and actual channels can be integrated into a single GRAPPA reconstruction step. The proposed method is tested using both simulation and in-vivo data. The simulation results produced by the proposed method and a SENSE-based method are compared. Results: The simulated images generated by the proposed method exhibit less relative error compared with those generated by the SENSE method. Inconsistent shot-to-shot phase variation is naturally resolved by GRAPPA calibration without additional phase map processing. High-quality brain DWI with submillimeter resolution is obtained using our proposed reconstruction method. Conclusion: A novel k-space msEPI reconstruction method has been developed for generating high-quality diffusion imagC 2015 Wiley Periing. Magn Reson Med 75:280–286, 2016. V odicals, Inc. Key words: diffusion imaging; multishot EPI; navigator; realigned GRAPPA
INTRODUCTION Conventional diffusion-weighted imaging (DWI) is acquired using single-shot echo planar imaging (ssEPI) with a major advantage of time efficiency (1). However, the obtainable spatial resolution of DWI using ssEPI is limited by the acquisition window in a single shot (2). ssEPI is also very sensitive to the magnetic field inhomogeneities, including 1 Beijing City Key Lab for Medical Physics and Engineering, Institute of Heavy Ion Physics, School of Physics, Peking University, Beijing, China. 2 Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China. 3 McGovern Institute for Brain Research, Peking University, Beijing, China. Grant sponsor: China’s National Strategic Basic Research Program (973); Grant number: 2012CB720700; Grant sponsor: The Natural Science Foundation of China; Grant numbers: 81227003, 81430037, 31421003. *Correspondence to: Jia-Hong Gao, Ph.D., Center for MRI Research, Peking University, Beijing, China 100871. E-mail: [email protected]
Received 16 July 2014; revised 23 October 2014; accepted 26 November 2014 DOI 10.1002/mrm.25586 Published online 5 March 2015 in Wiley Online Library (wileyonlinelibrary. com). C 2015 Wiley Periodicals, Inc. V
those from gradient eddy currents, and often lead to severe image distortions and signal dropouts in ssEPI. Multishot EPI (msEPI) has been developed to alleviate the issues in ssEPI. Acquiring k-space in multiple excitations reduces the echo train length, so msEPI can provide images of high spatial resolution and less blurring. Moreover, for interleaved msEPI acquisitions, the increased bandwidth can reduce off-resonance effects such as susceptibility artifacts, eddy-current-induced distortion, and signal dropout (3). The major challenge of msEPI in DWI is that the image is typically corrupted by ghosting artifacts due to the phase variations from shot to shot. Even the effect of a tiny motion would be amplified by diffusion-sensitizing gradients and could produce intershot phase variations (4). The phase variations between different shots can be effectively probed by navigator techniques (5–9). Several methods have been proposed to correct for the shot-to-shot phase variations (4,10–12), which include both linear and nonlinear components (13). The linear phase variations are attributed to rigid motions (rotation and translation), while pulsing of cerebrospinal fluid produces irregular and nonlinear intershot phase shifts. Therefore, correction methods applicable to arbitrary phase variations are required for a robust msEPI reconstruction in DWI. Currently, the sensitivity encoding (SENSE) algorithm (14) has been considered as an effective method for phase correction in msEPI. In the case of an N-shot EPI, data acquired from each shot is a subset of full k-space that is modulated by a potential extra motion-induced phase variation. The SENSE-based method then uses the N fold undersampled data to reconstruct an unfolded diffusion image; and the intershot phase variations are compensated in the sensitivity maps by means of incorporating phase information extracted from navigators in the SENSE encoding matrix (8,12). A potential problem associated with the SENSE-based msEPI method is that the high accelerating acquisition is only performed on imaging-echoes, not on navigator-echoes. As a result, the acquisition bandwidths along the phase-encoding (PE) direction of navigator-echo and imaging-echo are different, which leads to different offresonance induced image distortion in the navigatorecho and imaging-echo, and hence impairs the direct use of phase information probed by navigator echoes in SENSE-based msEPI reconstruction. An accelerated navigator echo can be used to alleviate the inconsistency of image-echo and navigator-echo. To completely solve this problem, additional off-resonance measurements and phase map processing is needed (12). In this study, a novel k-space-based interleaved msEPI reconstruction method is developed to produce images of high quality in DWI. The intershot phase variations
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are conveniently and effectively compensated by directly using the navigator echoes as auto-calibrating signals (ACS) for coefficient-fitting in the generalized autocalibrating partially parallel acquisitions (GRAPPA) algorithm (15), so there are no additional measurements and phase map processing as in the SENSE-based method. Each coil channel data acquired after one excitation of an N-shot msEPI forms a subset of the entire k-space of that channel with a reduction factor N. All these N kspace subsets of one channel can be treated as N-channel undersampled data that are misaligned in the PE direction. After simple realignment in k-space, these data can be converted to virtual multichannel datasets. The virtual channels and actual channels can be integrated into a mixed channel dataset, which can be reconstructed by means of a single GRAPPA reconstruction. The final image can be combined from all the channels using the sum of squares (SOS) method (16). Simulation of phantom multishot data was performed to compare the reconstruction quality of the proposed method with the conventional SENSE-based method. Isotropic diffusionweighted msEPI of healthy volunteers at 1.5T was performed, and the DWI was reconstructed using the proposed method.
THEORY Realigned GRAPPA Reconstruction For brevity and clarity, the discussion in this part is based on the one channel situation. The case of multiple channels is to be discussed in a later section. In msEPI with an interleave factor of N, every imageecho acquired after an excitation is a subset of k-space with undersampling factor N, and the n-th image-echo signal has (n-1) k-space displacement along PE direction: Z ~ ~ Sn ð~ k img;n Þ ¼ rimg ð~ r Þeiwn ð~r Þ e-i½k img þðn-1ÞDk y ~r d~ r [1] where rimg ð~ r Þ denotes the msEPI image domain data at spatial position ~ r , and wn denotes the motion induced extra phase of excitation n. ~ k img is the k-space position of the image-echo data and D~ k y denotes the minimum step length in k-space along the PE direction. The navigatorecho is fully sampled in the k-space center: Z ~ Sn ð~ k nav Þ ¼ rnav ð~ r Þeiwn ð~r Þ e-ik nav ~r d~ r [2] where rnav ð~ r Þ denotes the navigator signal at spatial position ~ r , and ~ k nav is the k-space position of the navigatorecho data. Simple variable transformation is implemented for analogy with GRAPPA formalism: r Þ ¼ ei½wn ð~r Þ-ðn-1ÞDk y ~r Cn ð~ ~
[3]
where Cn ð~ r Þ are virtual coil sensitivity maps. According to the analysis in our previous work (17), both imageecho data and navigator-echo data can be synthesized by linear combination of neighboring k-space samples with the same set of fitting coefficients Wj; l; r .
8 L X > > ~ > S ð k Þ ¼ Sl ð~ k img;l Þ Wj; l; r > j img;j > < l¼1 > L X > > > ~ ~ ~ ~ > S þ ðj-1ÞD k S þ ðl-1ÞD k k ¼ k Wj; l; r j nav y nav y l : l¼1
[4] where l denotes the l-th channel, L is the total number of channels, R is the acceleration factor and r (r R) is the index of the skipped lines in a block. Therefore, the navigator-echoes can be used as ACS to calculate the fitting coefficients, and then these fitting coefficients are used to reconstruct the N undersampled image-echoes using the GRAPPA algorithm. According to Eq. [4], only realigning of the misaligned image-echoes and shifting of navigator-echoes with corresponding displacements are required before the GRAPPA reconstruction. The principal procedure of the realigned GRAPPA method is shown schematically in Figure 1. Adjustment of Navigator Acquisition Window The navigator-echo used as ACS data is fully sampled at k-space center, whereas the image-echo is acquired with an acceleration factor N. Due to the off-resonance effects r Þ, the phase processions are incoherent between of DB0 ð~ navigator-echo signals and image-echo signals. The incoherence will lead to errors in GRAPPA coefficient fitting, which may lead to residual artifacts in the final reconstructed images. To address this problem, the echo spacing of the navigator-echo should be reduced by N times to make the acquisition BWs along the PE direction of the navigator-echo and image-echo consistent. If the navigator echo and image-echo are acquired with the same sampling interval t and gradient ascending/descending ramp time tramp , number of samples along the readout (RO) direction for the navigator echo should be reduced 0 from nx to nx : 0
nx ¼
nx -2ðN-1Þtramp =t : N
[5]
The acquisition window of navigator-echoes is reduced to accelerate the sample rate along the PE direction (as shown in Figure 2b), so the effective phase procession of navigator-echo signals is sampled at the same rate as the image-echo signals. Integrated Reconstruction of Virtual-Actual-Mixed Channels For multiple channels case, each individual channel can be processed separately and combined together using the SOS method. Alternately, all the virtual channels and actual channels can be integrated into a single GRAPPA reconstruction framework. For example, the eight-shot DWI data of eight coil elements can be formed as a combination of 64 virtual-actual mixed channels. The data processing will be more convenient and clearer in this manner because only a single GRAPPA reconstruction of the mixed channels is needed. Additional advantage of
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FIG. 1. The proposed realigned GRAPPA reconstruction of a typical four-shot interleaved msEPI k-space data set is shown schematically. Red, green, blue, and purple circles denote k-space lines acquired by the 1st, 2nd, 3rd, and 4th shot, respectively. White circles denote unacquired lines and gray circles are the reconstructed lines by GRAPPA algorithm. Left–right direction is the phase encoding direction, only the first 8 and the last 8 lines of total 256 lines in PE direction are shown and other lines are omitted and represented by ellipses. In the first stage, multishot EPI data are converted to multichannel data, and then the lines of the n-th excitation are shifted (n-1) steps backward along the PE direction to form realigned data, which are reconstructed by the GRAPPA algorithm in the third stage. Dashed arrows indicate the data moving paths and solid arrows denote an example fitting process in GRAPPA reconstruction.
using virtual-actual-mixed channels reconstruction is that it enables the acceleration of the proposed multishot DWI approach. METHODS Simulation of multishot k-space data reconstruction was performed to compare the proposed method with the conventional SENSE-based method. The simulated eightshot data were generated using the Shepp-Logan phantom that is modulated by sensitivity maps of a simulated eight-channel head coil. Random Gaussian noise with mean ¼ 0 and standard deviation SD ¼ 0.1 was added to the simulated phantom data and different nonlinear extra phases were added to the each shot image to simulate the motion-induced phase variations. Only a 1/8 subset of k-space samples from each image was used to form an eight-shot raw data set. The simulated raw data were then used in msEPI reconstruction both using the SENSE-based method (9,12,18) and the proposed GRAPPA-based method. A quantitative measure of the reconstruction performance was evaluated by calculating the relative errors between the reference and
reconstructed images: Er ¼
P
jIref ðrÞ-Irecon ðrÞj
P
jIref ðrÞj
100%, where
Iref (r) and Irecon (r) denote the intensity of the reference and P the reconstructed images at position r, respectively, denotes the sum over all the pixels across the entire field of view (FOV) in the images. The simulation data were constructed at an acceleration factor of 2 by only using the 2nd, 4th, 6th, and 8th shot data, and the data were processed by the integrated approach to form a 32 virtual-actual mixed channel undersampled dataset. Then the proposed realigned GRAPPA algorithm was performed to reconstruct the 32 channel data. To test the proposed method with different levels of motion-induced phase, extra nonlinear phases variations with different amplitude levels were added to the simulated eight-shot dataset. The amplitude level was defined by the standard deviation of the phase variations, denotes as SD(f). To test the utility of the proposed GRAPPA-based method for msEPI reconstruction in in vivo DWI, isotropic diffusion-weighted (19) brain imaging data were acquired from healthy volunteers on an Anke 1.5 Tesla
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FIG. 2. A typical dual refocusing SE diffusion-weighted msEPI sequence diagram (a) and the corresponding k-space trajectory of image-echo and navigator-echo of an eight-shot msEPI (b). The diffusion-sensitizing gradients are represented by dotted lines. The acquisition window of navigator-echo is adjusted to maintain the phase procession coherent with image-echo.
(T) MRI Scanner (SuZhouAnke Medical System, China) using a dual refocusing spin-echo (SE) diffusionweighted msEPI sequence (as shown in Figure 2a) with acquisition parameters as follows: repetition time/echo time (TR/TE) ¼ 3200 ms/92 ms, matrix size ¼ 256 256, field of view (FOV) ¼ 240 240 mm2, number of slices ¼ 15, slice thickness ¼ 6 mm. The imaging data were acquired with an 8-channel head coil. The acquisition of the navigator-echo was after the second refocusing radiofrequency pulse, and the acquisition central time of the navigator-echo was 144 ms. The crusher gradients implemented along slice selective (SS) direction were different in magnitude to eliminate the effect of stimulated echoes. An interleave factor of 8 was used in msEPI, the echo train length of both image-echo and navigator-echo was 32. Three orthogonal diffusion gradient direction imaging with b-value ¼ 1000 s/mm2 was performed with three averages for each direction, and the final image was combined using the geometric mean of three diffusion direction images. This study was approved by institutional internal reviewed board at Peking University. Informed written consent was obtained from volunteers. For image reconstruction, the integrated realigned GRAPPA method was applied to the multichannel MR data. k-space position shifting of both image-echo and navigator-echo was implemented first, data of the n-th excitation was shifted (n-1) steps backward along PE direction. The GRAPPA fitting kernel size was of four blocks and three columns, and 32 lines of navigator echoes were used as ACS for calibrating the GRAPPA algorithms. After the integrated GRAPPA reconstruction of
virtual-actual-mixed channels, the final image was the combination of all the channels using the SOS method. RESULTS The simulation results are shown in Figure 3. No obvious residual artifacts were present in either images reconstructed using the SENSE-based method or the proposed method, and the noise level increased in both images as compared to the reference image. However, the relative reconstruction error of the proposed method was 10.1% and was less than 11.6% of the SENSE-based method. Also the signal-to-noise ratio of the proposed method is no less than the conventional SENSE-based method. The result of the simulation data with acceleration factor R ¼ 2 was shown at the rightmost of the first row in Figure 3 with a relative reconstruction error of 14.8%. The results of the simulation data with different phase variation levels SD(f) ¼ 0, 1.4, 2.8, and 4.2 rad are shown in the second row in Figure 3 with relative errors of 9.9%, 10.1%, 10.7%, and 12.2%, respectively. An example of eight-shot DWI is shown in Figure 4. The first row shows the images directly reconstructed by means of Fast Fourier Transform (FFT) without motion correction, severe ghosting artifacts are present due to the random motion-induced phase errors. The second row shows the results using the proposed method; the phase errors are naturally compensated by using navigator-echo signals as ACS in GRAPPA reconstruction. No residual ghosting artifacts were visible in these images. From left to right columns, images are diffusion encoded along the RO, PE, and SS
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FIG. 3. In the first row, simulation eight-shot images were reconstructed using both conventional SENSE-based method (12) and the proposed GRAPPA-based method with acceleration factor R ¼ 1 and R ¼ 2, respectively. In the second row, simulation images were reconstructed using the proposed method with different phase variation levels SD(f) ¼ 0, 1.4, 2.8, and 4.2 rad. The relative reconstruction errors comparing to the reference image are shown in the top-right corner of each image.
directions respectively, and the rightmost column shows isotropic diffusion weighted images combined from the geometric mean of the left three images. The average phase variation (SD(f)) in vivo was found to be around 1.35 rad.
To demonstrate the robustness of the proposed method, additional results of the isotropic DWI images are shown in Figure 5. Different slices from top to bottom of the brain (as shown in Figures 5a–h) are reconstructed using
FIG. 4. Images reconstructed using direct FFT (a–d) and our proposed method (e–h). (a) and (e) are the msEPI data with diffusion encoded along RO direction, (b) and (f) are diffusion encoded along PE direction, (c) and (g) are diffusion encoded along SS direction, and (d) and (h) are the geometric average combined images with isotropic diffusion weighted.
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FIG. 5. Isotropic diffusion weighted images for b-value ¼ 1000 s/mm2 using the proposed msEPI method on different slice positions in human brain from top to bottom (a–h), respectively.
isotropic diffusion-weighted msEPI data with b-value ¼ 1000 s/mm2 by the proposed method. High quality DWI images of submillimeter in-plane resolution were obtained, and no obvious geometric distortion or artifacts were seen in the images. DISCUSSION A k-space GRAPPA algorithm based reconstruction method for multishot diffusion-weighted EPI reconstruction was proposed. The subsets of k-space data of each coil channel acquired by means of multi-excitations are treated as multichannel undersampled data in parallel imaging, and only simple k-space position realignment is needed before the reconstruction of these k-space data using the standard GRAPPA method. The key processing of the proposed method is to convert multishot data to virtual multichannel data (as shown in Figure 1: stages 1 and 2). N-shot DWI data form N undersampled k-space subsets. There are two distinctions between these and Nchannel undersampled data: (i) the n-th shot data has kspace displacement of (n-1)*dky along the PE direction compared with the first shot data and (ii) different motion-induced phases exist in each shot’s data. To convert the N-shot data to a N-channel data, the n-th shot data were shifted -(n-1) steps in k-space along the PE direction to align to the first shot, this consequently introduces an extra image-domain linear phase to each shot (n > 1) of data. This extra linear phase together with the motion-induce phase can be represented by a virtual coil sensitivity map (as expressed in Eq. [3]). Therefore, when the virtual coil sensitivity was regarded as coil sensitivity in multichannel data, the realigned multishot data can be identically treated as multichannel data. In this method, the intershot phase variations are directly compensated by using the navigator-echo as ACS
data for calculating the fitting coefficients in a GRAPPA reconstruction, and the incoherence between the imageecho and navigator-echo can be alleviated by adjustment of the navigator-echo acquisition window. Therefore, no additional measurement or process is necessary to extract and correct the intershot phase information as in the SENSE-based multishot reconstruction method. The adjustment of the navigator-echo acquisition window can be integrated with an accelerated navigator to increase the spatial resolution of navigator echo while keeping the appropriate phase-encoding bandwidth. However, this approach needs additional calibration data acquisition and parallel imaging reconstruction of the navigator echo. To test the benefits of a high resolution navigator echo, the simulated multishot data described in the Methods section have been reconstructed by realigned GRAPPA reconstruction with navigator echoes of high resolution (128 64) and low resolution (32 32). The resulting relative reconstruction errors were 9.9% and 10.1%, respectively. Hence the improvement of realigned GRAPPA reconstruction with high-resolution navigator echo is not significant. The usage of msEPI in DWI offers significant advantages compared with the conventional ssEPI approach: high spatial resolution, reduced image blur, and image distortions due to static off-resonance and eddy-current effects. The proposed method provides a unique and relatively simple approach to reconstruct multishot diffusion-weighted EPI data using the GRAPPA algorithm, and the nature of the intrinsic compensation of the motion-induced phase errors makes the proposed method robust and convenient. The reconstruction algorithm proposed in this work was applied to PE interleaved multishot EPI data, but highresolution DWI can also be achieved with other pulse sequences such as multishot spiral imaging, readout
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segmented EPI, and PROPELLER imaging. The core idea of the algorithm is to treat multishot data as multichannel data, so if an appropriate conversion of multishot sequence data to multichannel data exists, the proposed algorithm may be applied to other multishot DWI sequences. CONCLUSIONS In this note, a novel msEPI reconstruction method based on k-space GRAPPA for DWI is presented. Isotropic diffusion-weighted human brain imaging of healthy volunteers demonstrates that the proposed method provides robust reconstruction with excellent quality of high spatial resolution, no obvious residual artifacts, and no apparent distortion. REFERENCES 1. Turner R, Le Bihan D, Maier J, Vavrek R, Hedges LK, Pekar J. Echoplanar imaging of intravoxel incoherent motion. Radiology 1990;177: 407–414. 2. Farzaneh F, Riederer SJ, Pelc NJ. Analysis of T2 limitations and offresonance effects on spatial resolution and artifacts in echo-planar imaging. Magn Reson Med 1990;14:123–139. 3. Bernstein MA, King FK, Zhou XJ. Handbook of MRI pulse sequences. Burlington, MA: Elsevier Academic Press; 2004. 4. Butts K, de Crespigny A, Pauly JM, Moseley M. Diffusion-weighted interleaved echo-planar imaging with a pair of orthogonal navigator echoes. Magn Reson Med 1996;35:763–770. 5. Ordidge RJ, Helpern JA, Qing ZX, Knight RA, Nagesh V. Correction of motional artifacts in diffusion-weighted MR images using navigator echoes. Magn Reson Imaging 1994;12:455–460. 6. de Crespigny AJ, Marks MP, Enzmann DR, Moseley ME. Navigated diffusion imaging of normal and ischemic human brain. Magn Reson Med 1995;33:720–728.
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