FULL PAPER Magnetic Resonance in Medicine 00:00–00 (2014)

Parallel Imaging and Compressed Sensing Combined Framework for Accelerating High-Resolution Diffusion Tensor Imaging Using Inter-Image Correlation Xinwei Shi,1,2 Xiaodong Ma,2 Wenchuan Wu,2,3 Feng Huang,4 Chun Yuan,2,5 and Hua Guo2* vivo biological tissues. This unique ability has been widely explored in frontier studies and clinical applications, such as fiber tracking and diagnosis of various diseases in the brain (1). However, the difficulty of obtaining high quality diffusion images in reasonable scan time has constrained the practical usage of DTI. Because diffusion imaging demonstrates molecular displacement through signal diminishment in the presence of strong diffusion-weighting gradients, the resulted image has low signal-to-noise ratio (SNR) in nature. In addition, it requires at least six measurements of different diffusion directions and one non–diffusion-weighted baseline (i.e., b0 image) to calculate the diffusion tensor, which represents the three-dimensional diffusion process. Thus the scan time for DTI is usually longer than a typical MRI scan.

Purpose: Increasing acquisition efficiency is always a challenge in high-resolution diffusion tensor imaging (DTI), which has low signal-to-noise ratio and is sensitive to reconstruction artifacts. In this study, a parallel imaging (PI) and compressed sensing (CS) combined framework is proposed, which features motion error correction, PI calibration, and sparsity model using inter-image correlation tailored for high-resolution DTI. Theory and Methods: The proposed method, named anisotropic sparsity SPIRiT, consists of three steps: (i) motioninduced phase error estimation, (ii) initial CS reconstruction and PI kernel calibration, and (iii) final reconstruction combining PI and CS. Inter-image correlation of diffusion-weighted images are used through anisotropic signals for improved sparsity. A specific implementation based on multishot variable density spiral DTI is used to demonstrate the method. Results: The proposed reconstruction method was compared with CG-SENSE, CS-based joint reconstruction, and PI and CS combined methods with L1 and joint sparsity regularization, in brain DTI experiments at acceleration factors of 3 to 5. Both qualitative and quantitative results demonstrated that the proposed method resulted in better preserved image quality and more accurate DTI parameters than other methods. Conclusion: The proposed method can accelerate highresolution DTI acquisition effectively by using the sharable information among different diffusion encoding directions. Magn C 2014 Wiley Periodicals, Inc. Reson Med 000:000–000, 2014. V

Currently, there are two groups of acquisition techniques for diffusion-weighted imaging (DWI). Single-shot echo planar imaging (SSH-EPI) (2,3) is widely used in practice for its advantages of fast acquisition and robustness against bulk motion. But it has two main problems in image quality. First, off-resonance induced geometric distortion is severe, due to low acquisition bandwidth in phase encoding direction. Second, spatial resolution, determined by the acquisition window length, is confined to T2* value of imaged tissue, which constrains single-shot imaging from achieving high-resolution DWI. The other group is multishot acquisition techniques, such as multishot EPI (4,5), PROPELLER (6) and multishot variable density spiral (VDS) (7) sequences, which provide high-resolution diffusion images free from severe off-resonance induced distortions but at the expense of acquisition efficiency. Thus, acceleration methods are desired for both diffusion imaging techniques, which help solve the image quality problems of single-shot acquisitions (2,3) and improve the time efficiency of multishot acquisitions (4,8,9). But acceleration of diffusion imaging is highly challenging, considering the inherent low SNR problem of DWIs and sensitivity of DTI parameter estimation to image artifacts.

Key words: diffusion tensor imaging; variable density spiral; anisotropic sparsity; compressed sensing; parallel imaging

INTRODUCTION Diffusion tensor imaging (DTI) is a powerful tool for probing microstructures and physiological features of in 1 Department of Electrical Engineering, Stanford University, Stanford, California, USA. 2 Center for Biomedical Imaging Research, Department of Biomedical Engineering, Tsinghua University, Beijing, China. 3 Centre for Functional MRI of the Brain, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, United Kingdom. 4 Philips Healthcare, Gainesville, Florida, USA. 5 Department of Radiology, University of Washington, Seattle, Washington, USA. Grant sponsor: National Natural Science Foundation of China; Grant number: 61271132; Grant sponsor: National Key Technology R&D Program in the 12th Five-year Plan. *Correspondence to: Hua Guo, Ph.D., Center for Biomedical Imaging Research, Department of Biomedical Engineering, Tsinghua University, Beijing, China. E-mail: [email protected] Received 29 October 2013; revised 2 April 2014; accepted 23 April 2014 DOI 10.1002/mrm.25290 Published online 00 Month 2014 in Wiley Online Library (wileyonlinelibrary. com). C 2014 Wiley Periodicals, Inc. V

Parallel imaging (PI) has long been applied to DWI (2– 4,8,9), among its various applications in MRI. Specifically, sensitivity encoding (SENSE) (10,11) has been adopted in single-shot EPI to reduce echo train length, and thus to overcome the off-resonance induced image distortion and limitation of spatial resolution (2,3). And in multishot sequences for high-resolution DWI, SENSE, and generalized autocalibrating parallel acquisitions (GRAPPA) (12) are used for shortening the data 1

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acquisition (4,8,9). However, both methods have disadvantages in accelerating DWI. In SENSE reconstruction, errors of coil sensitivity often compromise the quality of reconstructed images, which is a general shortcoming of PI methods using sensitivity maps explicitly (13). Especially in navigated multishot DWI, the low-resolution navigator images are usually used for estimation of sensitivity maps (8), which can be inaccurate due to low SNR and limited size of fully sampled k-space. While GRAPPA can be less sensitive to inaccurate sensitivity information (5,13), its adaptation to non-Cartesian trajectory is complicated and requires large set of calibration data for segment-varying kernel (14,15). Above all, both PI methods suffer from g-factor noise amplification and residual aliasing at high acceleration factors. In 2010, iTerative Self-consistent Parallel Imaging Reconstruction (SPIRiT) was introduced (16), as a new approach to autocalibrating, kernel-based PI reconstruction. SPIRiT is general for arbitrary k-space sampling patterns and improves the performance of traditional GRAPPA-like methods because the formulation of iteratively enforcing self-consistency is better conditioned (16). These features suggest SPIRiT is a better candidate for accelerating DWI acquisition. Furthermore, SPIRiT framework is flexible to incorporate priors such as sparsity-enforcing regularization, which enables synergistic combination with compressed sensing (CS) (17) and better preserved SNR (16,18). In recent years, there is an emerging trend of applying CS in DTI, and a variety of sparse models have been studied (19–26). CS exploits the sparsity of medical images to significantly undersample k-space. In the case of DTI, because the same field of view (FOV) is modulated by different diffusion weighting, the resulted images are highly correlated. Besides intra-image sparsity, inter-image correlation can also be used as prior in both image denoising (27,28) and data undersampling (20–26) of diffusion imaging techniques. In previous work (27,28), low rank and edge structure correlation constraints are applied in denoising DW datasets. For acceleration of data acquisition, CS methods exploiting low rank of x-q space (24), various diffusion models (22,23,25,26), and sparsity of principle component coefficients of DWIs (20) have been demonstrated with improved acceleration capacity than traditional CS. These acceleration methods above are generally intended for diffusion imaging techniques with a relatively large number of diffusion-weighting directions. For DTI with less diffusion-weighting directions such as 6, distributed CS (21,29,30), and mean-based CS (20) have been attempted in simulations or ex vivo experiments, and outperformed traditional CS in accuracy of reconstructed DTI parameters. However, their performance in multishot high-resolution DTI has not been investigated yet. Besides the intrinsic low SNR, motion-induced phase error among different shots can also affect the performance of reconstruction. Furthermore, diffusion gradient induced eddy current from different direction generates different distortion patterns in EPI, which inevitably complicate the process. The problems above have not been addressed by the aforementioned CS-based methods. In addition, the improved reconstruction perform-

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ance by combining PI and CS in other MRI applications (18,31) suggests that better reconstruction fidelity in high-resolution DTI should benefit from synergistically applying PI and CS. In this work, we propose a joint reconstruction framework for accelerating DTI acquisition combining CS and PI, for improved reconstruction fidelity and higher acceleration factor. In addition to intra-image sparsity, interimage correlation of DWIs is used by enforcing anisotropic sparsity. Based on the general SPIRiT framework, the proposed method, named anisotropic-sparsity SPIRiT (AS-SPIRiT), can be adopted in a variety of DTI acquisition techniques, including both single-shot and multishot acquisitions with different k-space trajectories. We addressed practical issues of phase correction and PI kernel calibration, and implemented the proposed methods in a special case of multishot VDS DTI. Apart from the aforementioned advantages of high-resolution DTI, VDS is an excellent choice for CS for its incoherent undersampling artifacts (32). Previously, conjugate gradient SENSE (CG-SENSE) (8) was used to accelerate multishot VDS-DTI, which combined motion-induced phase with coil sensitivity into dynamic sensitivity maps and adopted the reconstruction formulation of SENSE (10). And its acceleration factor was limited to 3. The proposed joint reconstruction method was compared with CG-SENSE, two CS-based joint reconstruction methods (20,21), L1-regularized SPIRiT (L1-SPIRiT) (16,18), and joint-sparsity (21) SPIRiT modified for multishot DTI in human brain. Both qualitative and quantitative results demonstrated that the proposed method improved the accuracy of reconstructed of DTI parameters and preservation of fine structures. THEORY Combing CS and PI for High-Resolution DTI The idea of SPIRiT (16,18) is adopted as the general formulation in this work, which is robust to imperfect sensitivity estimation and flexible for arbitrary k-space trajectories. Moreover, SPIRiT is better conditioned than traditional GRAPPA-like PI techniques, and can be easily combined with DWI and various regularization methods. The general reconstruction formulation is, X ^ i¼1;:::;L ¼ arg min ð m jjDi mi  yi jj2 m Xi¼1;:::;L þ l1 jjGi mi  mi jj2 þ l2 Rðmi¼1;:::;L ÞÞ; [1] i¼1;:::;L

where mi¼1;:::;L are coil-by-coil DWIs to be reconstructed and the matrix size is L  C  N. L is the number of diffusion directions; C is the number of coils; N is the number of pixels in a single image. yi¼1;:::;L are partially sampled k-space data. Di is an operator transforming image space to acquired k-space, which includes sampling-mask, Fourier transform (FT) for Cartesian trajectory or nonuniform Fourier transform (nuFT) for nonCartesian trajectory. For multishot DWI, motion-induced phase correction is also incorporated into operator Di , rendering phase-corrected and interleaf-combined images mi¼1;:::;L . Gi is the SPIRiT operator implemented in image

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FIG. 1. Demonstration of anisotropic sparsity of diffusion weighted images. The top row shows diffusion weighted images of six different diffusion directions in DTI, and the second row shows corresponding images after removing isotropic signals (scaled by a factor of 2).

domain, which is a multiplication operation with inverse FT of the k-space convolution kernels. Because data consistency and calibration consistency are enforced in separate terms in the reconstruction formulation, operator Gi is free from effects of different sampling trajectories and interleaf-varying phase errors, thus making the calibration process highly flexible. Rðmi¼1;:::;L Þ is the regularization term using prior information as additional constraints. Adopting sparsity-enforcing regularization enables synergistic combination with CS and better preserved SNR (16,18). In the case of DTI, both intra-image sparsity and inter-image correlation can be pursued by CS-based regularization. l1 and l2 are nonnegative weights for calibration consistency and regularization respectively, making this method more adaptable. Setting l1 to zero makes Eq. [1] a formulation of CS, and setting l2 to zero leads to SPIRiT without regularization. Anisotropic Sparsity Prior DWIs are sparse in some transform domain, and they can be further sparsified by removing the isotropic signals. In DWIs of multiple diffusion directions, diffusion anisotropy results from constraints of molecular movement in some directions or special physical structure of the medium (1). For tissues without such directional constraints or special structure, such as cerebrospinal fluid (CSF), the diffusion process is isotropic, resulting in similar signal levels in images of different diffusion directions. The isotropic signals can be represented P by averaging  ¼ L1 i¼1;::::;L mi . In across the diffusion directions: m this study, our hypothesis is: for the brain DWIs espe from the cially at low b values, after subtracting m overall signal m, the signals of isotropic tissues are suppressed, and the resulted anisotropy images are sparser than the original DW images. As demonstrated in Figure 1, the different diffusion directional images in the first row appear similar. After removing the isotropic signals, only structures with anisotropic diffusion character have strong signals; hence, the images are sparsified, as shown in the second row. The anisotropic sparsity regularization is formulated as,

 1 RAS ðmi¼1;:::;L Þ ¼ ljCfm  mgj  X X X   Cfmi;c;n  m ;  ¼l g c;n   i¼1;::::;L c¼1;:::C n¼1;:::;N

[2] where C is a sparsifying transform, i, c, and n count through diffusion direction, coil, and image space dimension respectively. A combination of wavelet (Daubechies 4) and finite-difference transforms is adopted and RAS ðmi¼1;:::;L Þ consists of two terms, because the combination is reported to be useful in basic CS (17). The  is determined before the reconstruction, average value m as described in the next section. Joint Reconstruction Framework The whole reconstruction process of the proposed method is described in this section, and the implementation for multishot VDS-DTI is used as an example. As demonstrated by Figure 2, the framework is composed of three main steps: motion-induced phase estimation, initial reconstruction and calibration, and final reconstruction. The motion-induced phase error is estimated in the same way as introduced in (8). In in vivo multishot DWI, this phase error is varying from shot to shot, and needs to be estimated from navigator data. In multishot VDS, the k-space center of each shot, close to fullysampled, is extracted by applying a Gaussian window, and the phase of the reconstructed low-resolution image can be used for motion-induced phase removal. Di operates by first multiplying the image m with the estimated shot-by-shot varying motion-induced phase, and then applying nuFT (33). Operator Gi represents k-space convolution with the SPIRiT kernel and is implemented by multiplication in image space, which is more convenient for non-Cartesian sampling. In general, the kernel weights are calibrated with the fully-sampled center k-space, which is gridded to Cartesian in the case of non-Cartesian sampling. For multishot VDS-DTI, different shots for the same image should be phase corrected and combined before calibration. In addition, at high reduction factors, the fully

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FIG. 2. Block scheme of the proposed method. First, motion-induced phase is estimated and integrated into an operator D. Then initial reconstruction is conducted, which provides shot-combined data for kernel calibration and isotropic signals for AS-SPIRiT. The final step is SPIRiT-like reconstruction, which synergistically combines PI and AS-CS. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

sampled portion of the combined k-space is still too small for kernel calibration. Thus after motion-induced phase estimation, an initial reconstruction is performed to generate shot-combined multicoil images for calibration. In this study, CS reconstruction with phase correction is adopted, by simply setting l1 to zero in Eq. [1]. CS regularization helps to resolve aliasing and increase SNR of the initial reconstructed images, which increases the size of fully sampled k-space for kernel calibration. A small number of iterations, such as five, is sufficient for generating calibration data. The initial results are  for anisoalso used to calculate the isotropic signals m tropic sparsity regularization in the final reconstruction.  are determined in previAfter operators Di , Gi , and m ous steps, the final step is a SPIRiT-like reconstruction with phase correction and anisotropic sparsity regularization, formulated as Eq. [1].

METHODS Data Acquisition The proposed methods were evaluated in a series of in vivo DTI studies of human brain. Informed written consent forms were signed by the volunteers. The scans were performed on a Philips 3 Tesla (T) system (Philips Healthcare, Best, The Netherland) using an eight-channel head coil. All experiments used multishot VDS sequence (7) with a ¼ 4, FOV ¼ 220 mm  220 mm, slice thickness ¼ 5 mm, number of diffusion direction ¼ 6, acquisition matrix ¼ 256  256, image resolution ¼ 0.86 mm  0.86 mm. Other parameters include: Experiment 1: b ¼ 1000 s/mm2, TR/TE ¼ 2000/67 ms, number of VDS interleaves ¼ 24, Number of Signal Averages (NSA) ¼ 1; Experiment 2: b ¼ 1600 s/mm2, TR/TE ¼ 2506/64 ms, number of VDS interleaves ¼ 24, NSA ¼ 2; Experiment 3: b ¼ 800 s/mm2, TR/TE ¼ 2500/65 ms, number of VDS interleaves ¼ 26, NSA ¼ 4; Experiment 4: b ¼ 800 s/mm2, TR/TE ¼ 2506/65 ms, number of VDS interleaves ¼ 24, NSA ¼ 2. For experiment 3 and 4, high SNR reference images were obtained by averaging over the repeated acquisitions, and were used as gold standard.

Fully-sampled data were artificially undersampled by reduction factors ranging from R ¼ 3 to 5. To obtain a reduction factor of R, one in every R spiral interleaves was sampled. In the diffusion direction dimension, interleaved sampling pattern was adopted to maximize complementary information. Data Processing The proposed PI and CS combined reconstruction framework was compared with the traditional method CGSENSE and CS-based reconstruction. The CS-based methods included joint sparsity CS (JS-CS) and anisotropic sparsity CS (AS-CS), which demonstrated superior performance compared with traditional L1 regularized CS in accelerated DTI in previous work (20,21). Furthermore, the proposed AS-SPIRiT was compared with two SPIRiT-based methods using other sparsity models, including L1-SPIRiT (18) and joint sparsity SPIRiT (JSSPIRiT). In summary, the undersampled in vivo DTI data were reconstructed by (i) AS-SPIRiT, (ii) CG-SENSE, (iii) JS-CS, (iv) AS-CS, (v) L1-SPIRiT, and (vi) JS-SPIRiT. Except for CG-SENSE, their procedures follow the same framework as shown in Figure 2. The methods’ ability to preserve details in diffusion images and DTI parameter maps was particularly examined based on the data from experiment 1 and 2. Due to the low SNR nature of high-resolution DWI, faithful gold standard for quantitative evaluation was obtained in experiment 3 and 4 which had more signal averages. And then reconstructed diffusion images and DTI parameter maps were evaluated and compared numerically based on these two sets of data. All the methods adopted the same undersampling scheme. For experiment 2, VDS interleaves from two acquisitions (NSA ¼ 2) were combined in the reconstruction, to compensate for the low SNR at a relatively high b-factor. For other experiments, the undersampled data from different acquisitions were processed separately. For JS-SPIRiT and JS-CS, the undersampled b0 image was included in the joint reconstruction process and treated in the same way as DWIs. For AS-SPIRiT and AS-CS, because b0 image is not modulated by diffusion

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weighting and cannot be included in the anisotropic sparsity model, it was separately reconstructed by L1SPIRiT or L1-CS. Reference images were reconstructed from fully sampled k-space of each acquisition and averaged when there were multiple acquisitions. The reconstruction of fully sampled k-space included iterative gridding and phase correction, i.e., using Eq. [1] with l1 ¼ 0, l2 ¼ 0, until convergence, which usually took 15 iterations. All the methods used the same procedure for motioninduced phase estimation. For each interleaf, a 12  12 Cartesian k-space center was extracted for phase error estimation. Conjugate gradient (CG) algorithm was used to solve nonlinear reconstruction problem in all the methods. Weights for regularization based on wavelet and finite-difference transform were determined by numerical trials to minimize root-mean-square error (RMSE) of reconstructed DWIs with regard to the fully sampled reference images, for each method and each dataset at different acceleration factors. The CS initial reconstruction step used the same regularization weights as the final reconstruction. CG-SENSE followed the reconstruction process exactly as described in Liu et al (8), and number of iterations was set to 6 accordingly. JS-CS and AS-CS reconstructions were the same to distributed CS (21) and mean-based CS (20) in idea, while in the previous work they were implemented only for simulated or ex vivo tissue data. For comparison on in vivo DTI data, they were implemented in the same reconstruction framework as AS-SPIRiT, except that there was no PI kernel calibration step and no calibration-consistency term in the final reconstruction formulation. L1-SPIRiT, JS-SPIRiT, and AS-SPIRiT adopted the framework introduced in the theory part, and the only difference was the regularization term. The initial reconstruction took 5 iterations, and finial reconstruction took 10 iterations. For R ¼ 3, a 32  32 k-space center after initial reconstruction was used for PI kernel calibration. For R ¼ 4 or 5, the calibration data size was reduced to 16  16, because the size of high fidelity k-space reconstructed by initial reconstruction was smaller as R increased. All the reconstruction methods were implemented in Matlab (Matlab7, Mathworks) on a Linux workstation with 3.47 GHz CPU and 96 GB RAM. The reconstruction time of the proposed reconstruction framework for one slice was approximately 5 min. Except for CG-SENSE, other reconstruction methods resulted in coil-by-coil images, which were combined by sum-of-squares method afterward. After the DWIs were recovered, DTI parameters were calculated by DTI studio (34). Normalized RMSE (nRMSE) and SNR were used to assess the reconstructed results in experiment 3. nRMSE was calculated as, ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX  2 u ^ m ðrÞ  mðrÞ ref u ur2ROI X  nRMSE ¼ u 2 t m ðrÞ

[3]

ref

r2ROI

where mref is the reference image (averaged across the ^ is the image reconstructed from underfour scans), m sampled data of one scan, r represents spatial location.

SNR was calculated using signal statistics in a difference image of two identical acquisitions (35,36), meanr2ROI ðSðr; k1 Þ þ Sðr; k2 ÞÞ SNRðk1 ; k2 Þ ¼ pffiffiffi 2 stddev r2ROI ðSðr; k1 Þ  Sðr; k2 ÞÞ

[4]

where k1 ; k2 are two identical acquisitions, Sðr; ki Þ refers to signal intensity of voxel at spatial location r in acquisition ki . In experiment 3, four repeated acquisitions were denoted by I1, I2, I3, I4, respectively. The whole brain in all six directional DWIs was selected as the region of interest (ROI). Four values of nRMSE were calculated using Eq. [3] with the results of the four acquisitions respectively. Four values of SNR were calculated using Eq. [4] based on I1 and I2, I2 and I3, I3 and I4, I1 and I4. Final nRMSE and SNR were obtained by averaging the four values. RESULTS Qualitative Comparison Figure 3 shows the DWIs reconstructed by the proposed method and CG-SENSE, L1-SPIRiT, and JS-SPIRiT in experiment 1 at R ¼ 5. Figure 4 shows corresponding FA maps and color-coded FA maps. In the second column of Figure 3, the DWI reconstructed by CG-SENSE is severely degraded by amplified noise, and apparent residual aliasing appears in various areas of the brain. In the second column of Figure 4, the noise level of CGSENSE reconstructed FA map is also relatively high, which hinders the accurate delineation of directionality in most areas of the brain in the color-coded FA map. With the proposed reconstruction framework and CS regularization, the DWIs reconstructed by L1-SPIRiT, JSSPIRiT, and AS-SPIRiT have lower noise level, as shown in the three rightmost columns of Figure 3. And in their corresponding FA maps in Figure 4, the general directionality is consistent with the reference. Furthermore, AS-SPIRiT results in lower error level in DWIs than L1SPIRiT and JS-SPIRiT, as demonstrated by the difference maps in the second row of Figure 3. And in the enlarged portion of FA maps in Figure 4, the result of AS-SPIRiT has best-defined details in FA maps among all the methods, which follows the reference result most closely. Figure 5 compares the reconstructed DWIs of ASSPIRiT and CS-based methods exploiting the same sparsity models in experiment 1 at R ¼ 5. As observed from the difference maps in the lower row, the error levels of images reconstructed by all the three methods are approximately the same in areas where signal intensity change is relatively smooth. Both JS-CS and AS-CS reconstructed images are blurred in areas rich of fine structures, where high error level appears in the difference maps. The blurring effect can be observed more clearly from the enlarged parts of images in the bottomright corner of each image. AS-SPIRiT reconstructed images have sharper and more accurate image features in these regions, and their error distributions are more uniform inside the brain than the CS alone based methods. FA maps computed by CG-SENSE, L1-SPIRiT, JSSPIRiT, and AS-SPIRiT at R ¼ 3 in experiment 2 (b ¼ 1600 s/mm2) are compared in Figure 6. Although

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FIG. 3. Representative diffusion weighted images in experiment 1. The upper row shows one of the representative images, and the lower row shows corresponding difference images (scaled by a factor of 5). The columns, from left to right, are reference image and results of CG-SENSE, L1-SPIRiT, JS-SPIRiT, and AS-SPIRiT at R ¼ 5.

anisotropic signals are more dominant in this dataset than in the lower b value cases, AS-SPIRiT still has the best result among these methods with lowest error level, especially in the center of the brain. Quantitative Comparison In Figure 7, reconstruction performance of CG-SENSE, L1-SPIRiT, JS-SPIRiT, and AS-SPIRiT from R ¼ 3 to 5 is compared quantitatively on nRMSE and SNR of reconstructed images, based on the data from experiment 3. Results show that AS-SPIRiT yields the lowest nRMSE and highest SNR in this range of reduction factors except

that for R¼3, result of JS-SPIRiT has higher SNR than that of AS-SPIRiT. While L1-SPIRiT and JS-SPIRiT show improved reconstruction compared with CG-SENSE, ASSPIRiT maintains significantly better reconstruction quality with very small nRMSE increment and SNR decrement as reduction factor increases. Representative FA and color-coded FA maps reconstructed by CG-SENSE, L1-SPIRiT, JS-SPIRiT, and ASSPIRiT from experiment 3 at R ¼ 3 are compared in Figure 8. In consistency with the quantitative comparison of results in Figure 7, the resultant FA maps of CG-SENSE are severely degraded by noise and have the highest error level, compared with the methods using the

FIG. 4. Comparison of reconstructed DTI FA maps in experiment 1. The upper row shows color-coded FA maps (red: right-left, green: anterior–posterior; blue: dorsal–ventral). The lower row shows FA maps. The columns, from left to right, are gold standard and results of CG-SENSE, L1-SPIRiT, JS-SPIRiT, and AS-SPIRiT at R ¼ 5. An enlarged portion of the images are displayed at the bottom right corner of each image.

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FIG. 5. Comparison of CS-based and proposed reconstruction results in experiment 1 at R ¼ 5. The upper row shows the diffusion weighted images, and the lower row shows corresponding difference (scaled by a factor of 5). The columns, from left to right, shows reference image and results of JS-CS, AS-CS, and AS-SPIRiT. An enlarged portion of the images are displayed at the bottom-right corner of each image.

proposed reconstruction framework and CS regularization. AS-SPIRiT has the closest results to the reference among all methods. For example, as pointed by the arrows in Figure 8, severe false directionality appears in the results of L1-SPIRiT and JS-SPIRiT, and this error is reduced in the results of AS-SPIRiT.

The accuracy of reconstructed FA maps in experiment 3 is further compared quantitatively in Figure 9, which displays whole brain FA error histograms of CG-SENSE, L1SPIRiT, JS-SPIRiT, and AS-SPIRiT at R ¼ 3 and 5. FA error is calculated as the difference of reference FA and reconstructed FA. Mean value and two times standard

FIG. 6. Comparison of reconstructed DTI FA maps in experiment 2 (b ¼ 1600 s/mm2). The rows from top to bottom, are color-coded FA, FA error (scaled by a factor of 2) and FA maps at R ¼ 3. The columns, from left to right, are gold standard and results of CG-SENSE, L1-SPIRiT, JS-SPIRiT, and AS-SPIRiT. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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FIG. 7. Quantitative comparison of the results from R ¼ 3 to 5 in experiment 3. Plot and compare nRMSE (a) and SNR (b) of diffusion weighted images reconstructed by CG-SENSE(stars), L1-SPIRiT (triangles), JS-SPIRiT (dots), and AS-SPIRiT (circles), respectively.

deviation of FA error is labeled in each histogram. ASSPIRiT reconstruction errors have the mean values closest to zero and the smallest standard deviation at both reduction factors, which means the proposed method resulted in the least bias in FA maps. The quantitative performance of the methods is also illustrated in Table 1, which summarizes the average RMSE of reconstructed FA maps from experiment 3 and 4 at R ¼ 3, 4, 5. RMSE is calculated as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi uX  u ^ m ðrÞ  mðrÞ ref t RMSE ¼ r2ROI , where ROI is selected Nr2ROI to be the whole brain, and Nr2ROI is the number of pixels in the ROI. The table again demonstrates that the

proposed reconstruction, AS-SPIRiT, yields FA maps with better fidelity than other methods. DISCUSSION While high-resolution DTI is a useful and promising technique in scientific studies and clinical diagnosis, SNR and acquisition time have always been obstacles in its practical applications. Improving spatial resolution while maintaining SNR and time efficiency in DTI is always desired. Traditional PI methods, such as CGSENSE and GRAPPA, have long been attempted in accelerating high-resolution DTI (4,8,9), but reached their bottleneck in acceleration capability due to noise

FIG. 8. Representative color-coded FA (upper row), FA error (scaled by a factor of 2) (middle row) and FA maps (lower row) at R ¼ 3 in experiment 3. The columns, from left to right, are gold standard and results of CG-SENSE, L1-SPIRiT, JS-SPIRiT, and AS-SPIRiT. The yellow arrows point out where large error appears in the FA maps of L1-SPIRiT and JS-SPIRiT, and the error is reduced by AS-SPIRiT. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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FIG. 9. Histograms of FA error (reference FA - reconstructed FA) in experiment 3. The columns, from left to right, are results of CGSENSE, L1-SPIRiT, JS-SPIRiT, and AS-SPIRiT. The number in the upper-right corner of each histogram is mean FA error 6 two standard deviations. The upper row shows results at R ¼ 3, and the lower row shows results at R ¼ 5. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

amplification and residual aliasing at high acceleration factors. In the meantime, recent published work has demonstrated great potential of CS based techniques (19–26), which apply various sparsity models to optimally use inter and intra-image correlations of DWIs. Success in combining PI and CS in other MRI applications (18,31) suggests that better reconstruction fidelity and higher acceleration factor in high-resolution DTI should result from synergistically applying PI and CS. To be best of our knowledge, it is the first time to the best knowledge that a PI-CS combined framework was implemented for accelerating in vivo high-resolution diffusion imaging by using the just appropriate VDS sampling trajectory. In this study, the proposed method was compared with one traditional PI method, CG-SENSE, which had only been tried with acceleration factor of 3 for highresolution VDS-DTI (8). In the perspective of reconstruction process, CG-SENSE combines motion-induced phase error with coil sensitivity maps into dynamic composite sensitivity maps, which are obtained from the limited navigator data of each shot. In our new reconstruction, phase error and sensitivity information are used in two separate terms of the objective function, which makes it more convenient to adapt either one of them. The calibration information for PI is not limited to navigator data, but based on coil-by-coil phase-corrected data after initial reconstruction, which Table 1 RMSE of FA Maps at R ¼ 3, 4, 5 in Experiment 3 and 4 R¼3 R¼4 R¼5

CG-SENSE

L1-SPIRiT

JS-SPIRiT

AS-SPIRiT

0.1419 0.1605 0.1631

0.0894 0.1091 0.1206

0.0885 0.1069 0.1155

0.0826 0.0891 0.1026

have a larger portion of k-space than the originally fully sampled navigator. In addition, integration of CSbased regularization suppressed noise amplification and further enhances the reconstruction fidelity. Based on the data from experiment 3, we compared the accuracy of calibration data obtained from CS initial reconstruction and direct phase subtraction (DPS) method (7). nRMSE of the low resolution images corresponding to the calibration data in center k-space was used as the metric in comparison, and the reference low resolution image was obtained from averaging over the four repeated acquisitions. The comparison showed that the accuracy of the calibration data is improved by the initial reconstruction process. For example, when R ¼ 5, nRMSE was 0.8077 for DPS but was only 0.1995 for CS initial reconstruction. In the in vivo DTI experiments, superior reconstruction results with higher SNR and reduced aliasing artifacts were demonstrated by the new ASSPIRiT framework, in comparison with CG-SENSE. The proposed reconstruction was also explored at a high b value of 1600 s/mm2 in this study. Due to limited SNR at high b values with the high resolution used, the acceleration factor R was reduced accordingly. In such a scenario, our proposed method still showed improved performance than the compared ones (Fig. 6), although the difference was not as strong as at lower b values. One possible cause is that the anisotropic signal might be more dominant at higher diffusion weighting than the isotropic signal, and, therefore, the effectiveness of subtracting the isotropic signal is reduced. For highresolution diffusion imaging, when b value becomes even higher than the tested values in this study, the limited SNR does not allow further down-sampling. Instead, the proposed method could be considered for denoising the DWIs.

10

Another feature of AS-SPIRiT was the usage of correlation, or sparsity in inter-image diffusion dimension. Previous work in CS accelerated DTI had used a similar inter-image sparsity model (20). In this work, anisotropic sparsity was integrated into a PI and CS combined framework and used in accelerating in vivo high-resolution DTI. Improvement in reconstruction performance by ASSPIRiT was observed in the experiments, compared with L1-SPIRiT, which only uses intra-image sparsity information alone. JS-SPIRiT, which uses the direct inter-image joint sparsity, was also explored as a comparison with AS-SPIRiT. Although it also showed better performance than all other methods, its improvement was less significant when compared qualitatively and quantitatively with AS-SPIRiT. The reason is that the removal of the isotropic signals among DWIs boosts the sparsity. Furthermore, to compare the CS-based methods with ASSPIRiT, we implemented JS-CS and AS-CS under the same reconstruction framework with motion-induced phase correction. The results demonstrated CS-based methods showed stronger blurring in reconstructed DWIs at high reduction factors such as 5, while fine structures and image resolution was better preserved in the proposed method (Fig. 5). Therefore, AS-SPIRiT gave the best reconstruction results among all methods, with lowest error level and highest SNR of DWIs, and smallest deviation of FA maps from gold standard. By using VDS based acquisition technique, there is no severe image distortion among different diffusion directions. Thus image registration is not required in using anisotropic sparsity model. This is another reason we chose VDS, in addition to its self-navigating and selfcalibration capacity and incoherent undersampling artifacts. Besides, the reconstruction framework is highly flexible in terms of its adaptive separate steps and the general PI formulation of SPIRiT. So the proposed reconstruction method has the potential to be extended to other diffusion imaging techniques, including DTI using multishot EPI trajectories. One limitation of the current work is that the effect of motion and pathologies on reconstruction performance has not been investigated. While self-navigation is leveraged to correct for image phase induced by both rigid and nonrigid motion of different shots, inter-scan motion is still a concern for joint reconstruction schemes. The 3 to 5 times acceleration provided by the proposed method is beneficial for reducing bulk motion during the whole scan. But when inter-image motion does happen, it is intuitively expected that the performance of AS-SPIRiT might be degraded because the isotropic signals cannot be extracted accurately. However, it is also reasonable to speculate that AS-SPIRiT will not introduce additional artifacts in case of moderate inter-scan motion, because images from different scans are reconstructed separately and their individual sparsity is not destroyed by removing the averaged signals. The reasoning is similar with regard to disorder-related changes in diffusion anisotropy. And as current results on healthy volunteers with different b values suggest, the proposed reconstruction framework can handle various anisotropy levels. These assumptions still need to be fully investigated in future work.

Shi et al.

CONCLUSIONS In this work, a reconstruction chain for accelerating high-resolution DTI was developed, which combined PI and CS, and used anisotropic sparsity of DWIs to enhance reconstruction fidelity. The proposed ASSPIRiT was evaluated and compared with traditional methods qualitatively and quantitatively in in vivo DTI experiments of human brain. In comparison with CGSENSE, the PI-CS combined framework demonstrated superior reconstruction results with higher SNR and reduced aliasing artifacts in resultant DWIs and DTI parameter maps. And compared with CS alone based methods, the proposed method preserved better delineation of structures. In addition, the benefits of using anisotropic sparsity of DWIs in improving the accuracy of reconstructed DTI parameters were also validated by the experiment results, where AS-SPIRiT had improvement in comparison with L1-SPIRiT. In summary, the proposed method provides an effective way for enhancing the reconstruction fidelity in accelerated high-resolution DTI. REFERENCES 1. Le Bihan D, Mangin JF, Poupon C, Clark CA, Pappata S, Molko N, Chabriat H. Diffusion tensor imaging: concepts and applications. J Magn Reson Imaging 2001;13:534–546. 2. Bammer R, Auer M, Keeling SL, Augustin M, Stables LA, Prokesch RW, Stollberger R, Moseley ME, Fazekas F. Diffusion tensor imaging using single-shot SENSE-EPI. Magn Reson Med 2002;48:128–136. 3. Bammer R, Keeling SL, Augustin M, Pruessmann KP, Wolf R, Stollberger R, Hartung HP, Fazekas F. Improved diffusion-weighted single-shot echo-planar imaging (EPI) in stroke using sensitivity encoding (SENSE). Magn Reson Med 2001;46:548–554. 4. Holdsworth SJ, Skare S, Newbould RD, Guzmann R, Blevins NH, Bammer R. Readout-segmented EPI for rapid high resolution diffusion imaging at 3T. Eur J Radiol 2008;65:36–46. 5. Skare S, Newbould RD, Clayton DB, Albers GW, Nagle S, Bammer R. Clinical multishot DW-EPI through parallel imaging with considerations of susceptibility, motion, and noise. Magn Reson Med 2007;57: 881–890. 6. Pipe JG, Farthing VG, Forbes KP. Multishot diffusion-weighted FSE using PROPELLER MRI. Magn Reson Med 2002;47:42–52. 7. 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. 8. 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. 9. Holdsworth SJ, Skare S, Newbould RD, Bammer R. Robust GRAPPAaccelerated diffusion-weighted readout-segmented (RS)-EPI. Magn Reson Med 2009;62:1629–1640. 10. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn Reson Med 1999;42:952–962. 11. Pruessmann KP, Weiger M, B€ ornert P, Boesiger P. Advances in sensitivity encoding with arbitrary k-space trajectories. Magn Reson Med 2001;46:638–651. 12. 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. 13. Blaimer M, Breuer F, Mueller M, Heidemann RM, Griswold MA, Jakob PM. SMASH, SENSE, PILS, GRAPPA: how to choose the optimal method. Topics in Magn Reson Imaging 2004;15:223–236. 14. Heberlein K, Kadah Y, Hu X. Segmented spiral parallel imaging using GRAPPA. In Proceedings of the 12th Annual Meeting of ISMRM, Kyoto, Japan, 2004. Abstract 328. 15. Heidemann RM, Griswold MA, Seiberlich N, Kruger G, Kannengiesser SA, Kiefer B, Wiggins G, Wald LL, Jakob PM. Direct parallel image reconstructions for spiral trajectories using GRAPPA. Magn Reson Med 2006;56:317–326.

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Parallel imaging and compressed sensing combined framework for accelerating high-resolution diffusion tensor imaging using inter-image correlation.

Increasing acquisition efficiency is always a challenge in high-resolution diffusion tensor imaging (DTI), which has low signal-to-noise ratio and is ...
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