Model-based reconstruction for simultaneous multislice and parallel imaging accelerated multishot diffusion tensor imaging

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1 Model-based reconstruction for simultaneous multislice and parallel imaging accelerated multishot diffusion tensor imaging Zijing Dong and Erpeng Dai Fuyixue Wang Harvard-MIT Health Sciences and Technology MIT, Cambridge, MA, USA Zhe Zhang and Xiaodong Ma Chun Yuan Department of Radiology, University of Washington, Seattle, WA, USA Hua Guo a) (Received 27 November 2017; revised 2 April 2018; accepted for publication 4 May 2018; published 1 June 2018) Purpose: Multishot interleaved echo-planar imaging (iepi) can achieve higher image resolution than single-shot EPI for diffusion tensor imaging (DTI), but its application is limited by the prolonged acquisition time. To reduce the acquisition time, a novel model-based reconstruction for simultaneous multislice (SMS) and parallel imaging (PI) accelerated iepi DTI is proposed. Materials and methods: DTI datasets acquired by iepi with SMS and PI acceleration can be regarded as 3D k-space data, which is undersampled along both the slice and phase encoding directions. Instead of reconstruction of individual diffusion-weighted image, diffusion tensors are directly estimated by the joint reconstruction of undersampled 3D k-space from all diffusion-encoding directions using a model-based formulation to exploit the correlation across different directions. DTI simulation and in vivo acquisition were used to demonstrate the superior performance of the proposed method. Results: The proposed method reduced the estimation errors and artifacts than traditional parallel imaging reconstruction in DTI simulation. In the in vivo DTI experiment, the acquisition time of 4- shot iepi was reduced from 11 min 7 s to 3 min 53 s with an acceleration factor of 4, and the image quality and precision of quantitative parameters were comparable with the fully sampled acquisition. Conclusions: The proposed model-based reconstruction for iepi DTI with SMS and PI can achieve fourfold acceleration while maintaining high accuracy for tensor measurements American Association of Physicists in Medicine [ Key words: diffusion tensor imaging, high-resolution DTI, interleaved EPI, model-based reconstruction, simultaneous multislice 1. INTRODUCTION Diffusion tensor imaging (DTI) is a powerful non-invasive tool to probe the microscopic properties in tissues by analyzing the diffusion anisotropy of water molecules. In DTI, six or more diffusion-encoding directions are applied to obtain the diffusion tensors using a Gaussian diffusion model. 1 Using the measured tensor from DTI, fiber tracking algorithms have been developed to investigate the white-matter connectivity of human brain, 2 spinal cord, 3 and skeletal muscle fibers. 4 Single-shot echo-planar imaging (SS-EPI) is a commonly used sequence in diffusion imaging, because of its fast acquisition speed and insensitivity to motion. Nevertheless, the low bandwidth along the phase encoding direction of SS-EPI results in severe geometric distortion and limited spatial resolution caused by the magnetic field inhomogeneity, 5 which hinder the detection of detailed structures. Parallel imaging (PI) techniques 6 9 can increase the bandwidth of SS-EPI by in-plane undersampling, to reduce the geometric distortion, but the reduction factor of PI is limited by the number of receiver coils and the 3196 Med. Phys. 45 (7), July /2018/45(7)/3196/ American Association of Physicists in Medicine 3196

2 3197 Dong et al.: Model-based reconstruction for iepi DTI 3197 g-factor. An alternative way to achieve high-resolution DTI is to use multishot echo-planar imaging sequences, 10,11 which can reduce the geometric distortion by acquiring the k-space through several excitations. However, multiple excitations and multiple diffusion-encoding directions prolong the acquisition time of DTI, which impedes its clinical application. To reduce the scan time of multishot EPI, in-plane PI methods 6,9 can be applied to reduce the number of excitations, but it will lead to signal-to-noise ratio (SNR) loss, especially at high acceleration factors. Compared with conventional PI, simultaneous multislice (SMS) with blipped CAPIRINHA 12 acquisition can reduce the volume scan time by a factor of MB p(where ffiffiffiffiffiffiffi MB is the SMS acceleration factor), but without MB SNR penalty, only g-factor. In addition to the long scan time, phase variation among different shots caused by the physiological motion during diffusion encoding must be corrected appropriately for multishot DTI. For such phase correction, extra navigator acquisition can provide reliable phase estimation, 11,13 however, the scan time will be further prolonged. In the contrast, navigator-free techniques 10,14 are more efficient as they estimate the phase variation using PI reconstruction for each excitation without extra sampling, and can work well if the number of shots is not very large (eg, 2 4). Recently, model-based reconstruction combined with compressed sensing (CS) 15 has been proposed for DTI acceleration The model-based methods can directly estimate diffusion tensors using the k-space signals from all diffusion directions, skipping the reconstruction of each single diffusion-weighted image. They have showed improved accuracy than PI and CS methods in spin-echo DTI for ex vivo specimens 17 and in vivo musculoskeletal imaging. 16 Random sampling with a higher sampling rate in the central of k-space can improve the performance of CS, however, it will increase the level of geometric distortion in EPI due to a low bandwidth of k-space center. Thus, to achieve less distorted EPI for high-resolution DTI, uniform undersampling should be applied, but this will limit the reduction factor of these model-based reconstruction. Here, we propose a novel model-based framework for high-resolution DTI using interleaved EPI (iepi) combined with SMS acquisition. The SMS-accelerated iepi sequence adopted in this study has been reported by our group recently. 19 It can achieve high-resolution diffusion imaging with through-plane acceleration. To further reduce the acquisition time, a model-based framework for iepi DTI is proposed to jointly reconstruct the diffusion tensor from all diffusion-encoding directions where each direction is undersampled with simultaneous in-plane (PI) and through-plane (SMS) acceleration. The effectiveness of the proposed method is validated by DTI simulations and in vivo brain experiments. To evaluate different methods under various acceleration factors, parameters of DTI, including fractional anisotropy (FA), mean diffusivity (MD) and fiber orientation are calculated and compared. 2. MATERIALS AND METHODS If a Gaussian diffusion model is assumed for DTI, the k-space signal of m-th diffusion-encoding direction at i-th location can be represented by: K i;m ðdþ ¼ XN p j¼1 e ik ix j ðf xj p xj ;mþe B md xj (1) j¼1 where N p is the number of pixels, f xj is the magnitude of nondiffusion-weighted (b0) image at location x j (j = 1,2... N p ), D is a rank-2 symmetric diffusion tensor with six independent elements (D xx, D yy, D zz, D xy, D yz, D yz ). B m is the B-matrix of m-th diffusion-encoding direction, and B m ¼ bg m g T m where b is the b value and g m is the diffusion gradient vector. The diffusion-weighted image along m-th direction can be obtained by multiplying the b0 image with p xj ;m, the motion-induced phase of the corresponding diffusion image, and with exponential attenuation e B md xj. PN p e ik ix j is the Fourier Transform operator to transform the diffusion-weighted image to k-space signals. Note that the channel dimension is omitted in the equation, where f, p and K all include multi-channel information. In the proposed method, the image phase of each direction and each shot can be estimated by PI-based methods, and the b0 image f is fully sampled. Thus, if the k-space data K in Eq. (1) are acquired, the diffusion tensor D is the only unknown variable, which can be estimated by solving the following optimization problem using undersampled k-space data: 1 arg min D 2 k K0 RKðDÞ k 2 2 þ ktvðdþ (2) Here, the first term is data fidelity and second term is a total variation constraint. K 0 is the acquired undersampled k- space data along all diffusion-encoding directions. K(D) is the k-space data calculate by Eq. (1) using the estimated D. R is an operator to select data of K(D) at the same location as K 0. TV(D) is the sum of L 1 norm total variation (TV) 20 of six tensor elements. k is the control parameter for the contribution of TV. To solve this non-linear optimization problem, a non-linear conjugate gradient algorithm 21 is used. For multishot iepi, different shots with the same diffusion-encoding direction can be regard as independent directions in model-based reconstruction with the same B-matrices. For instance, a 32-direction DTI dataset acquired by 4-shot iepi can be regard as a 128-direction DTI data with 49 in-plane undersampling. Without SMS acceleration, the acquired k-space are 2D datasets, and the tensor D can be estimated slice by slice. When SMS is applied (MB >1), the k-space can be described as an undersampled 3D k-space for more straightforward reconstruction as reported. 22 The undersampling of SMS-accelerated data is along the slice direction. Thus, SMS-accelerated iepi acquires 3D k-space data K 0 along each diffusion-encoding direction with undersampling in both slice and phase encoding directions. In addition,

3 3198 Dong et al.: Model-based reconstruction for iepi DTI 3198 FIG. 1. Pipeline of the model-based reconstruction for SMS-accelerated iepi DTI. N-direction DTI with MB = 2 are shown as an example. Firstly, 2D GRAPPA performs on each direction to unfold images of the two slices. Next, the image phases are filtered by Tukey windowing for phase estimation. Using an estimated tensor D, diffusion-weighted image of each direction can be calculated by multiplying b0 images with image phases and exponential attenuations. Then, the cost function including the data fidelity and TV term is calculated. If the stop criterion is met, D in this iteration will be the final reconstruction. Otherwise, the gradient of D in the objective function will be calculated to update D and reduce the cost until meeting stop criterion. [Color figure can be viewed at wileyonlinelibra ry.com] tensor D, b0 image f, and phase p in Eq. (1) are multi-slice 2D images, thus a 3D Fourier Transform operator should be used for SMS datasets. Figure 1 illustrates the computation process of the model-based reconstruction for such an acquisition. At first, when the number of shots is not very large (eg, 4), PI methods like 2D GRAPPA 9 can be applied to estimate the image phase of each direction and each slice using the undersampled data K prime. Next, K can be reconstructed by Eq. (1) using the low-pass filtered phase, fully sampled b0 image and estimated diffusion tensor D. Then, the cost of objective function (Eq. 2) is calculated using the acquired undersampled data of all diffusion directions. If it does not converge, the gradient of D will be calculated to determine the search direction, and an updated D can be obtained with an estimated step size in this iteration. The gradient of D of the objective function can be ¼XNdir m¼1 X i¼1 2bg m g T m fpe bgt m Dg m Realfp ð ek i K i ðdþþe ix~k~ This non-linear conjugate algorithm is performed iteratively to update D until convergence. 21 In this study, the (3) initial estimation of D was set to 0. The stop criterion is that the reduction in cost is smaller than 1% in one iteration or the number of iteration is larger than 50. In the model-based reconstruction, undersampled data from all directions are used to directly estimate D instead of reconstructing each diffusion-weighted image. In addition, the b0 images are fully sampled along the phase encoding direction in our method using multishot iepi with SMS acceleration. They have the same bandwidth and distortion levels as the undersampled data. Thus, the unknowns are only six tensor elements with total variation constraint, which should achieve better performance than conventional methods due to a reduced number of unknowns. Moreover, the proposed method is also compatible with partial Fourier acquisition for reduced TE and high SNR. 2.A. Numerical simulations To evaluate the proposed method quantitatively, DTI simulation was designed. A diffusion scan was performed following a non-diffusion-weighted scan, and a set of diffusion tensor D was calculated from it as a gold standard. The D matrices of two slices were used to simulate the SMS data with a MB factor of 2. The non-diffusion-weighted images

4 3199 Dong et al.: Model-based reconstruction for iepi DTI 3199 were duplicated and multiplied by the exponential attenuation term calculated from D to generate multi-direction diffusion-encoded images. Then, spatially varying random phases (2nd-order) were multiplied to the images, and spatially uncorrelated Gaussian noise was added into k-space (SNR = 10). To mimic the undersampled 3D k-space data using SMS and in-plane PI acceleration, the synthesized images were first transformed to full 3D k-space and then manually undersampled along the slice and phase encoding directions. Here, the undersampling factors of SMS and inplane PI were denoted by MB and R PE, respectively. For iepi, R PE is equal to the reduction in shots, for example, R PE = 2 for 4-shot iepi means that only two of four shots are acquired for acquisition acceleration. The net acceleration factor (AF) equals to MB 9 R PE. The b0 data for all methods were fully sampled along PE but accelerated by SMS. In this test, two iepi DTI datasets with 16-direction and 32-direction diffusion encoding were simulated using the same D. The scan time is proportional to the number of diffusion-encoding directions, so here, the AF of 16-direction acquisition is 2 times larger than that of 32-direction data under the same undersampling. The performance of the proposed method was compared with conventional 2D GRAPPA. 23 The imaging parameters were: number of shots = 4, MB = 2, number of channels = 32, b value = 800 s/mm 2, number of signal average (NSA) = 1, matrix size = , in-plane resolution = 1 9 1mm 2. Three quantitative parameters were used to assess the performance of the different algorithms: mean error of FA, mean error of MD and the mean angular deviation of the principal eigenvector V1 (V1). The normalized root mean squared error (nrmse) of FA and MD were also calculated to evaluate the estimation of tensor quantitatively: 1 nrmse ¼ maxðx ref Þ minðx ref Þ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (4) u 1 X t Np 2 x ref ðþ xðiþ i 100% N p i¼1 where x ref is the reference value of the gold standard, x is the reconstructed result and N p is the number of pixels in a region of interest (ROI). ROIs were selected in the brain parenchymal tissues within the skull. 2.B. In vivo experiments In vivo experiments were carried out on a Philips 3T Achieva TX scanner (Philips Healthcare, Best, the Netherlands) on three healthy volunteers, following the approval by an Institutional Review Board and after obtaining written informed consent. Brain DTI data were acquired using SS-EPI and iepi with 32 diffusion-encoding directions. The detailed imaging parameters were listed in Table I. In particular, SS-EPI with a SENSE factor R PE = 2 was acquired as a low-resolution reference. SMS acquisition with MBs of 1 and 2 were both acquired using iepi to evaluate the performance of multiband acceleration. The corresponding data were then reconstructed by 2D k- space 13 and 3D k-space 19 multishot reconstruction methods, using 2D navigators for shot-to-shot phase correction. The last three datasets in Table I (iepi with AF = 2, 4, 8) with different R PE (1, 2, 4) were retrospectively undersampled from the iepi with MB = 2, and the navigators were not used in the proposed model-based reconstruction and 2D GRAPPA. In such 4-shot iepi acquisitions, each shot has a reduction factor of four along the phase encoding direction with the same effective echo spacing and bandwidth. Even if only one or two shots are used for image reconstruction, the distortion level is the same as the fully sampled four-shot data. Thus, the retrospectively undersampled data has the same distortion level as the actual undersampling, and it was used to compare the performance with the fully sampled data. By doing this, interscan motion can be avoided between the reference image and undersampled reconstruction. 10 These datasets were reconstructed by 2D GRAPPA, 23 3D k-space multishot reconstruction, 19 and the proposed model-based method respectively. The corresponding acquisition times of these three acquisitions were estimated based on the actual scan parameters of iepi with MB = 2. Other scan parameters for both SS-EPI and iepi were: number of channels = 32, FOV = mm 3 (RL 9 AP 9 FH), b value = 800 s/mm 2. For SMS reconstruction, a 40 s calibration scan was acquired to provide 3D autocalibrating signals (ACS) for 2D GRAPPA. A prospectively undersampled 4-shot dataset was also acquired with acceleration (MB 9 R PE ) without navigator acquisition to evaluate the proposed method. Both 3D TABLE I. Imaging parameters for in vivo human brain DTI. Name Shots MB 9 R PE NSA 2D Navigator Voxel size (mm 3 ) TE(ms) TR(ms) Partial fourier T ACQ * (min:sec) SS-EPI N :28 iepi-mb Y :07 iepi-mb Y :10 iepi-af N :10 iepi-af N :52 iepi-af N :13 *Last three datasets were generated by retrospective undersampling using iepi-mb2, from which the acquisition times of these datasets were estimated.

5 3200 Dong et al.: Model-based reconstruction for iepi DTI 3200 k-space multishot reconstruction and the proposed method were used to reconstruct the undersampled data for comparison. Since there was no navigator acquisition, phase information from each shot was estimated by 2D GRAPPA, then the b0 image combined with the calculated phase was used in kernel training for 3D k-space reconstruction. Diffusion data with 32 diffusion directions were acquired at b value = 800 s/mm 2, FOV = mm 3 (RL 9 AP 9 FH), voxel size = mm 3, TR/TE = 3100/75 ms, partial Fourier = 0.7. The total scan time of this accelerated acquisition was 3 min and 46 s. 2.C. Data processing The computation was conducted in Matlab (Mathworks Inc., Natick, MA, USA) on a personal computer with a 3.30 GHz quad-core CPU and 128 GB of RAM. The fractional anisotropy (FA), mean diffusivity (MD) and principal eigenvectors (V1) in the simulation and in vivo experiments were calculated from the reconstructed images using DTIStudio. 24 k in the model-based reconstruction was set to 0.5 for all experiments. 3. RESULTS 3.A. Numerical simulations Figure 2 shows reconstructed MD, FA and color-coded FA maps from the gold standard, 2D GRAPPA and modelbased reconstruction. The data used in 2D GRAPPA and model-based reconstruction was simulated with 32 diffusion directions, and the AF was 8 (MB = 2, R PE = 4). Since DTI data were simulated using the known tensors, the reference maps calculated by such gold standard tensors were accurate. In comparison, severe noise occurred in the center of images reconstructed by 2D GRAPPA, while the proposed method showed more accurate images, which were closer to the FIG. 3. Mean errors of FA, MD and angular deviation of V1 in the simulation test. Results of different reconstruction methods with 16- or 32-direction DTI data are grouped according to acceleration factors (AFs). In all cases, model-based method shows reduced errors compared to 2D GRAPPA. FIG. 2. Results of the DTI simulation. References are diffusion parameters calculated by the gold standard D. MD, FA and color-coded FA maps reconstructed by 2D GRAPPA and model-based method using 32-direction data with AF = 8(29 4) are shown. NRMSEs of MD and FA as well as mean angular deviation of V1 are listed at the bottom right of images. [Color figure can be viewed at wileyonlinelibrary.com]

6 3201 Dong et al.: Model-based reconstruction for iepi DTI 3201 reference. Moreover, nrmses of MD and FA, as well as mean angular deviations of eigenvector V1 from the proposed method were all smaller than those from 2D GRAPPA (Fig. 2). More quantitative errors are shown in Figure 3. Different datasets reconstructed by 2D GRAPPA and model-based methods were grouped according to AFs. Strategies with the same AF indicate close scan times. As all strategies were accelerated by SMS with MB = 2, the differences in AFs were determined by R PE (1, 2, 4) and the number of encoding directions (16 or 32). For all these simulations, model-based reconstruction achieved smaller errors than 2D GRAPPA consistently. In addition, the error increased when a higher AF was used, especially for FA and angular deviation of V1. FIG. 4. MD, FA and color-coded FA maps from the in vivo DTI experiment. The protocols of different datasets are listed in Table I. Here, images of one slice reconstructed by the model-based method, 2D GRAPPA and 3D k-space multishot reconstruction with different AFs are shown. The results of the proposed model-based method show less noise and fewer artifacts at AF = 4 and 8. [Color figure can be viewed at wileyonlinelibrary.com] FIG. 5. FA and color-coded FA maps from the in vivo experiment. Results shown here using iepi-af4 were reconstructed by the model-based method. The zoomed-in regions from the yellow squares show that iepi with higher resolution provided more detail structures (yellow arrows) compared with SS-EPI. IEPI-AF4 achieved comparable image quality to iepi-mb2 (AF = 2) and iepi-mb1 (AF = 1). [Color figure can be viewed at wileyonlinelibrary.com]

7 3202 Dong et al.: Model-based reconstruction for iepi DTI B. In vivo experiments For in vivo DTI acceleration, DTI maps with different AFs by the three reconstruction methods are shown (Fig. 4). Note that when only one shot is used for reconstruction (AF = 8), phase correction is not required and 3D k-space method is the same as 2D GRAPPA. The model-based method provided more reliable and accurate images at both AF = 4 (MB 9 R PE = 2 9 2) and AF = 8 (MB 9 R PE = 294) compared to 2D GRAPPA and 3D k-space multishot reconstruction. Figure 5 shows the FA and color-coded FA maps from the four acquisition schemes. The images acquired by 4-shot iepi with higher resolution show more details (yellow arrows) than those by SS-EPI, which demonstrates the improvement of high-resolution DTI. The proposed method for iepi with AF = 4 achieved 49 acceleration than the fully sampled four-shot iepi while maintaining similar image quality. The results from prospectively undersampling in vivo experiments at AF = 4 (MB 9 R PE = 2 9 2) are shown in Fig. 6. The proposed model-based reconstruction shows improved image quality and SNR than the 3D k-space multishot reconstruction. 4. DISCUSSION Although more detailed information can be obtained by high-resolution DTI with multishot acquisition than conventional SS-EPI, 13,14 its acquisition time is usually multiple times longer. Moreover, DTI needs an even longer scan time due to a large number of diffusion-encoding directions (ie, >20 30), which is required for robust DTI measurements. 25,26 Thus, the acquisition of multishot DTI can be too long for clinical applications. In addition, scans with longer sampling time are more susceptible to subject motion, which results in bias of tensor calculation. To solve these problems, in this study, we proposed a model-based reconstruction for SMS-accelerated iepi DTI. Both through-plane acceleration by SMS and in-plane acceleration by PI were adopted to improve the acquisition efficiency. The joint model-based reconstruction of all diffusion directions can directly estimate tensors using undersampled k-space data. The improved accuracy of tensor quantification facilitated by the reduced number of unknowns and the total variation constraint has been demonstrated through numerical simulations and in vivo DTI experiments. The model-based reconstruction can achieve superior image quality using SMS and PI accelerated iepi. Results from the simulation (Figs. 2 and 3) and in vivo DTI (Figs. 4 6) demonstrated that the proposed method can reduce artifacts and noise in DTI metric maps at various acceleration factors. The results reconstructed by the proposed navigator-free method at AF of 4 show similar image quality to those at MB = 1 (AF = 1) and MB = 2 (AF = 2) (Fig. 5), but with reduced acquisition time. However, higher acceleration factors could still result in more noise and errors. For example, when a high AF of 8 was applied, noise and artifacts occurred in the in vivo experiment (Fig. 4). Thus, to maintain the image quality and accuracy of DTI metrics, AF = 4 (MB 9 R PE = 2 9 2) was a safe acceleration for the proposed method. For iepi with AF = 4, the acquisition time was 3 min 52 s (Table I), reducing more than 6 min than the acquisition without acceleration (11 min 7 s). The efficiency of iepi with AF = 4 can be further improved using optimized imaging parameters (eg, shorter TR, increased acquired slices). The scan time of the accelerated iepi at FIG. 6. Reconstructed color-coded FA maps of the prospectively undersampling in vivo experiments at AF = 4 (MB 9 R PE = 2 9 2). [Color figure can be viewed at wileyonlinelibrary.com]

8 3203 Dong et al.: Model-based reconstruction for iepi DTI 3203 AF = 4 with optimized parameters is only slightly longer than SS-EPI with the same NSA and diffusion-encoding directions. For example, to acquire 40 slices images with the shortest TR (2882 ms for iepi with AF = 4, and 4177 ms for SS-EPI) and 32-directions, the acquisition time for iepi is 3 min 36 s, only 1 min longer than 2 min 26 s of SS-EPI (SENSE = 2). Nevertheless, the in-plane image resolution of iepi (1 9 1mm 2 ) is higher than that of SS-EPI (2 9 2mm 2 ), which can provide more image details as shown in Fig. 5. In Fig. 2 at AF = 8, the proposed modelbased method shows elevated image errors near the ventricle region, the reason could be that the low signal intensity and intense phase variation in the ventricle area, which makes phase estimation harder and compromises the accuracy of model-based reconstruction. In this study, 2D GRAPPA was used to estimate the phase of each diffusion image for navigator-free phase correction. When a large number of shots (eg, 8) of iepi is applied for further distortion reduction, 2D GRAPPA is unable to unfold the images. In this case, 2D navigators can be acquired for phase estimation, and the proposed method is also compatible with such navigated phase correction. In navigated phase correction methods, the mismatch between 2D navigators and image echoes should be considered and corrected for accurate phase estimation. 19 The fully sampled b0 data used in the proposed method is critical to achieve accurate reconstruction, but this would reduce the effective acceleration of the whole data acquisition. This effect is not large especially for large number of directions. For example, the effective acceleration for the 32-direction 4-shot in vivo acquisition at AF = 4 (MB 9 R PE = 2 9 2) was 3.88, about 3% loss in efficiency. The selection of the control parameter k for total variation constraint is a tradeoff. A high value of k can reduce the image noise but result in smoothness of the tensors, and a low value will result in low SNR when a high acceleration factor is used. In all tested cases, k was set to 0.5, which preserved detailed structures well without obvious smoothness effects (Fig. 5), and maintained good image SNR. In the in vivo experiment, b value was 800 s/mm 2, thus the diffusion process can be characterized well by Gaussian distribution. However, for higher b values, the diffusion in white matters was found to be non-gaussian, 27 where advanced models should be applied. 28 The proposed modelbased framework using joint reconstruction can be extended to other models with modified formulism. 29 In this study, data rejection was not used, but it can be applied before reconstruction to remove corrupt data due to motion. One limitation of the propose method is that the computation load is heavier than conventional parallel imaging reconstruction. In current study, the computational time of model-based reconstruction for 32-direction data is about 1 h per slice, while the reconstruction time of 3D k-space multishot reconstruction is about 15 min per slice. For computation acceleration, coil compression algorithms 30 can be applied to reduce the number of channels, and parallel computation can further speed up the reconstruction. 5. CONCLUSIONS In this study, we proposed a novel model-based reconstruction for SMS-accelerated iepi DTI. The proposed method can achieve 49 acceleration while maintaining similar image accuracy and quality compared with the fully sampled iepi. Whole brain 32-direction DTI with 1 9 1mm 2 in-plane resolution can be acquired in 4 min by the proposed method. Thus, the proposed model-based reconstruction allows efficient acquisition of DTI when high-resolution is desired. ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of ( and ) and Tsinghua University Initiative Scientific Research Program ( ). CONFLICTS OF INTEREST The authors have no relevant conflicts of interest to disclose. a) Author to whom correspondence should be addressed. Electronic mail: huaguo@tsinghua.edu.cn; Telephone: REFERENCES 1. Basser PJ, Mattiello J, LeBihan D. MR diffusion tensor spectroscopy and imaging. Biophys J. 1994;66: Mori S, Crain BJ, Chacko V, van Zijl P. Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann Neurol. 1999;45: Thurnher MM, Law M. Diffusion-weighted imaging, diffusion-tensor imaging, and fiber tractography of the spinal cord. Magn Reson Imaging Clin N Am. 2009;17: Filli L, Piccirelli M, Kenkel D, et al. 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