Ghost Reduction in Echo-Planar Imaging by Joint Reconstruction of Images and Line-to-Line Delays and Phase Errors
aa r X i v : . [ phy s i c s . m e d - ph ] J un Ghost Reduction in Echo-Planar Imaging by JointReconstruction of Images and Line-to-Line Delays andPhase Errors
Julianna D Ianni , , E Brian Welch , , William A Grissom , , , Vanderbilt University Institute of Imaging Science, Department of Biomedical Engineering, Department of Radiology, Department of Electrical Engineering, Vanderbilt University,Nashville, TN, United States
Submitted to Magnetic Resonance in Medicine
Abstract
Purpose:
To correct line-to-line delays and phase errors in echo-planar imaging (EPI).
Theory and Methods:
EPI- trajectory auto-corrected image reconstruction (EPI-TrACR)is an iterative maximum-likelihood technique that exploits data redundancy provided bymultiple receive coils between nearby lines of k-space to determine and correct line-to-linetrajectory delays and phase errors that cause ghosting artifacts. EPI-TrACR was appliedto in vivo data acquired at 7 Tesla across acceleration and multishot factors, and in a dy-namic time series. The method was efficiently implemented using a segmented FFT andcompared to a conventional calibrated reconstruction.
Results:
Compared to conventional calibrated reconstructions, EPI-TrACR reduced ghost-ing up to moderate acceleration factors and across multishot factors. It also maintained ow ghosting in a dynamic time series. Averaged over all cases, EPI-TrACR reducedroot-mean-square ghosted signal outside the brain by 27% compared to calibrated recon-struction. Conclusion:
EPI-TrACR is effective in automatically correcting line-to-line delays andphase errors in multishot, accelerated, and dynamic EPI. While the method benefits fromadditional calibration data, it is not a requirement.
Key words: image reconstruction; EPI; parallel imaging; phase correction; eddy currents;ghosting
Introduction
Echo-planar imaging (EPI) is a fast imaging technique in which multiple Cartesian linesof k-space are measured per excitation. It is widely used in functional magnetic resonanceimaging (fMRI) and diffusion weighted imaging (DWI). However, EPI images containghosting artifacts due to trajectory delays and phase errors between adjacent k-space linesthat result from eddy currents created by rapidly switched readout gradients.The most common methods to correct EPI ghosting artifacts are based on the collec-tion of calibration data from which delays and phase shifts can be estimated and applied inimage reconstruction [1–6]. Usually this data comes from a separate acquisition withoutphase encoding gradient blips, acquired before the imaging scan. Corrections can alsobe made by re-acquiring EPI k-space data that is offset by one k-space line so that oddk-space lines become even and vice versa [1, 7]. The gradient impulse response functioncan also be measured and applied to predict errors [8]. However, these methods cannotcorrect dynamic errors caused by effects such as gradient coil heating. Dynamic errorscan be compensated by measuring calibration data within the imaging sequence itself, forexample by reacquiring the center line of k-space within a single acquisition [9]. However,these approaches result in a loss of temporal resolution. Alternatively, dynamic errors can e measured during a scan without modifying the sequence using field-probe measure-ments [10–12]. However, the hardware required to make those measurements can take upvaluable space in the scanner bore and is not widely available at the time of writing.As an alternative to separate calibration measurements, many retrospective methodsattempt to correct ghosting based on the EPI data or images themselves. The image-basedmethods [13–16] rely on the assumption that some part of the initial image contains noghosted signal. Another group of methods makes corrections based on finding phasedarray combinations that cancel ghosts [17–21]. Several methods use parallel imaging toseparately reconstruct images from odd and even lines and then combine them, and thesehave further been combined with a dynamically alternating phase encode shift or direction[18–20, 22, 23]. However, relying on undersampled data for calibration weights may makethese approaches unstable, and some methods reduce temporal resolution. Importantly,almost all these retrospective methods are either incompatible or have not been validatedwith multi-shot EPI, and most are either incompatible with parallel imaging accelerationor have only been implemented and validated with small acceleration factors.In this work, a flexible EPI- trajectory auto-corrected image reconstruction (EPI-TrACR)is proposed that alleviates ghosting artifacts by exploiting data redundancy between ad-jacent k-space lines in multicoil EPI data. It is an extension of a previously-describedmethod for automatic non-Cartesian trajectory error correction (TrACR-SENSE) [24] tothe joint estimation of images and line-to-line delays and phase errors in EPI. In the fol-lowing we describe the method, including an efficient segmented FFT algorithm for de-layed EPI k-space trajectories. The method is then validated in vivo at 7 Tesla, at multipleacceleration and multishot factors and in a dynamic time series. It is demonstrated thatEPI-TrACR reduces dynamic ghosting and is compatible with multishot EPI and acceler-ation. Furthermore, the method benefits from initialization with calibration data but doesnot require it at moderate acceleration and multishot factors. heory Problem Formulation
EPI-TrACR jointly estimates images, delays and phase shifts by fitting an extension of theSENSE MR signal model [25] to EPI k-space data: y c [ m, n ] = N s X i =1 e − ı π (( k xm +∆ k xn ) x i + k yn y i ) e ı ∆ φ n s ci f i , (1)where y c [ m, n ] is the signal measured in coil c at the m th time point of the n th phase-encoded echo, k xm is the k-space coordinate in the readout/frequency encoded dimensionand ∆ k xn is the trajectory delay in that dimension for the n th echo (out of N echoes), k yn isthe n th echo’s k-space coordinate in the phase-encoded dimension, ∆ φ n is the phase shiftof the n th echo resulting from zeroth-order eddy currents, s ci is coil c ’s measured sensitiv-ity at ( x i , y i ) , f i is the image at ( x i , y i ) , and N s is the number of pixels in the image. Thevariables in this model are the image f and the delays and phase shifts { (∆ k xn , ∆ φ n ) } Nn =1 ,and it is fit to measured data ˜ y c [ m, n ] by minimizing the sum of squared errors betweenthe two. This is done while constraining the delays and phase shifts so that a single delayand phase shift pair applies to all of a shot’s odd echoes and another pair applies to all ofits even echoes, with separate parameters for each shot. The first shot’s odd echoes serveas a reference and are constrained to have zero delay and phase shift. Overall, a total of N shot − delay and phase shift parameters are fit to the data along with the image. Algorithm
The EPI-TrACR algorithm minimizes the data-model error by alternately updating theestimated image f , the k-space delays { ∆ k xn } Nn =1 , and the phase shifts { ∆ φ n } Nn =1 . Theimage is updated with a conjugate-gradient (CG) SENSE reconstruction [26]. The delayand phase shift updates are both performed using a nonlinear Polak-Ribi`ere (CG) algo- ithm [27], which requires computation of the derivative of the squared data-model errorwith respect to those parameters.This CG algorithm was chosen for its efficiency in min-imizing the data-model error in similar problems; other optimization algorithms, such asgradient descent, may be applied alternatively. Denoting the sum-of-squared errors as thefunction Ψ , the derivative with respect to each delay ∆ k xn is: ∂ Ψ ∂ ∆ k xn = N c X c =1 M X m =1 N s X i =1 ℜ n − ı πx i e − ı ∆ φ n e ı π (( k xm +∆ k xn ) x i + k yn y i ) s ∗ ci f ∗ i r cmn o , (2)and the derivative with respect to each phase shift ∆ φ n is: ∂ Ψ ∂ ∆ φ n = N c X c =1 M X m =1 N s X i =1 ℜ n ıe − ı ∆ φ n e ı π (( k xm +∆ k xn ) x i + k yn y i ) s ∗ ci f ∗ i r cmn o , (3)where ℜ denotes the real part, ∗ is complex conjugation, and r cmn is the residual errorbetween the measured data and the model given the current parameter estimates, ˆ f , ∆ˆ k xn ,and ∆ ˆ φ n : r cmn = ˜ y c [ m, n ] − N s X i =1 e − ı π (( k xm +∆ˆ k xn ) x i + k yn y i ) e ı ∆ ˆ φ n s ci ˆ f i . (4)To constrain the delays and phase shifts to be the same for the set of odd or even echoesof each shot, the derivatives above are summed across the echoes in that set, and a singledelay and shift pair is determined for the set each CG iteration. The updates are alternateduntil the data-model error stops changing significantly. Segmented FFTs
Since a delayed EPI trajectory is non-Cartesian, the model in Equation 1 corresponds toa non-uniform discrete Fourier transform (DFT) of the image. Non-uniform fast Fouriertransform (FFT) algorithms (e.g., Ref. [28]) are typically used to efficiently evaluate non-uniform DFTs, but they use gridding, which would result in long compute times in EPI-TrACR, since Equation 1 is repeatedly evaluated by the algorithm. Figure 1 illustrates rajectory Magnitude Phase x Hybrid-Space Data k y k x k y Segment 1D IFT PhaseShiftsIFT acrosssegmentsImage
Figure 1: Illustration of the inverse segmented FFT, starting with 2-shot x - k y EPI data corruptedby line-to-line delays and phase errors. First the data are segmented into 2 N shot submatrices andindividually inverse Fourier transformed. Then each image-domain submatrix is phase shifted toaccount for its offset in k y , its phase error, and its delay. Finally, an inverse Fourier transform iscalculated across the segments, and the result is reshaped into the image. a segmented FFT algorithm that applies the delays as phase ramps in the image domain,instead of gridding the delayed data in the frequency domain. In addition to eliminatinggridding, this also enables the data to be FFT’d in the frequency-encoded dimension beforestarting EPI-TrACR, so that the algorithm only needs to compute 1D FFTs in the phase-encoded dimension. The figure shows an inverse segmented FFT (k-space to image space)for a 2-shot dataset with delays and phase shifts, which comprises the following steps:1. The data in each set of odd or even echoes of each shot are collected into N shot submatrices of size M × ( N/ (2 × N shot )) , and the 1D inverse FFT of each submatrixis computed in the phase-encoded dimension. . The estimated phase shifts are applied to each submatrix.3. A phase ramp is applied in the phase-encoded spatial dimension of each submatrixto account for that set’s relative position in the phase-encoded k-space dimension.This is necessary since the inverse FFTs assume all the submatrices are centered ink-space.4. The phase ramp corresponding to each set’s estimated delay is applied to its subma-trix in the frequency-encoded spatial dimension.5. For each submatrix entry, the inverse DFT across submatrices is computed to obtain N shot subimages of size M × ( N/ (2 × N shot )) , which are concatenated in the columndimension to form the final M × N image.For efficiency, the phase shifts of steps 2 through 4 are combined into a single precomputedmatrix that is applied to each submatrix by elementwise multiplication. To perform theforward segmented FFT (image space to k-space), the steps are reversed, with the phaseramps and shifts negated. Steps 1 and 5 dominate the computational cost, and respectivelyrequire O ( M N N shot ) and O ( M N log ( N/ (2 N shot ))) operations. Methods
Algorithm Implementation
The EPI-TrACR algorithm was implemented in MATLAB 2016a (The Mathworks, Natick,MA, USA) on a workstation with dual 6-core 2.8 GHz X5660 Intel Xeon CPUs (IntelCorporation, Santa Clara, CA) and 96 GB of RAM. For each iteration of the algorithm’souter loop, image updates were initialized with zeros to prevent noise amplification, andwere performed using MATLAB’s lsqr function and a fixed tolerance of − , capped at25 iterations. CG delay and phase updates were each fixed to a maximum of 5 iterations per uter loop iteration, and terminated early if all steps were less than − cm − (for delays)or − radians (for phase shifts). The maximum permitted delay in a single iteration waslimited to /F OV , and the maximum permitted phase step in a single iteration was limitedto π/ radians. Outer loop iterations stopped when the change in squared error was lessthan the previous iteration’s error times − . Code and example data for EPI-TrACR canbe downloaded at https://bitbucket.org/wgrissom/tracr . Experiments
A healthy volunteer was scanned on a 7T Philips Achieva scanner (Philips Healthcare,Best, Netherlands) with the approval of the Institutional Review Board at Vanderbilt Uni-versity. A birdcage coil was used for excitation and a 32-channel head coil for reception(Nova Medical Inc., Wilmington, MA, USA). EPI scans were acquired with 24 ×
24 cmFOV, 1.5 × × voxels, TR 3000 ms, TE 56 ms, flip angle 60°. They wererepeated for 1 to 4 shots, acceleration factors of 1x to 4x, and a single scan (2-shot, 1x)was performed with 20 repetitions. The TE of 56 ms was chosen to maintain the samecontrast between images, and was the shortest possible for the single-shot, 1x acquisition,which had a readout duration of 102 ms. A calibration scan with phase encodes turned offwas acquired in each configuration, and delays and phase shifts were estimated from it us-ing cross-correlation followed by an optimization transfer-based refinement [29]. SENSEmaps were also collected using the vendor’s mapping scan. Images were reconstructedto 160 ×
160 matrices using lsqr with no corrections, conventional calibration (usingthe phase and delay estimates from the calibration scan), EPI-TrACR initialized with thedelays and phase shifts from the conventional calibration, and EPI-TrACR initialized withzeros. For comparison of EPI-TrACR corrections on the time series data with anotherdynamic method, PAGE [17] was also implemented. To characterize the amount of datanecessary for the EPI-TrACR reconstruction, the algorithm was repeated after truncating he 2-shot, 1x in vivo data in both k-space dimensions across a range of truncation factors.The reconstructed image resolution within EPI-TrACR was correspondingly reduced ineach case, so that the image matrix size matched the data matrix size. The final estimateddelays and phase shifts were then applied in a full-resolution reconstruction. Except whereindicated, displayed images shown are windowed down to 20% of their maximum ampli-tude for clear display of ghosting, and ghosted signals were measured in all images as theroot-mean-square (RMS) signal outside an elliptical region-of-interest that excluded thebrain and skull. Results
Figure 2 shows reconstructed images across multishot factors. Ghosting was lowest withEPI-TrACR in all cases, and the differences between zero initialization and calibratedinitialization results are negligible: averaged across multishot factors, the RMS differ-ence between estimated delays and phase shifts with and without calibrated initializationwas 0.014%. Compared to conventional calibration-based correction, EPI-TrACR RMSghosted signals were on average 37% lower. In addition, the conventional 4-shot recon-struction contained a visible aliased edge inside the brain (indicated by the yellow arrow),which did not appear in the EPI-TrACR reconstructions. All of the single-shot recon-structions contain a visible off-resonance artifact at the back of the brain (indicated in theconventional reconstruction by the green arrow). Figure 3 shows reconstructed 2-shot EPIimages with 1-4 × acceleration. Compared to conventional calibration, EPI-TrACR withcalibrated initialization again reduced ghosting up to 4 × acceleration, and RMS ghostedsignals were 18% lower on average. Furthermore, EPI-TrACR estimates matched with andwithout calibrated initialization up to 3 × acceleration: averaged across factors of 1-3 × ,the RMS difference between estimated delays and phase shifts with and without calibratedinitialization was 0.024%. Figure 4a plots RMS ghosted signal across repetitions of the shot 2 shot 4 shot3 shot N o C o rr e c t i on R M S g h o s t e d s i g n a l ( % ) C on v en t i ona l EP I T r A CR + c a li b r a t ed i n i t. EP I T r A CR + i n i t. Figure 2: Multishot echo-planar images (no acceleration) reconstructed with no correction, conven-tional calibrated correction, EPI-TrACR with calibrated initialization, and EPI-TrACR with zeroinitialization. The length and color of the horizontal bars beneath each image represent the residualRMS ghosted signal as a percentage of maximum image intensity, as defined by the color scale onthe right. The green arrow in the conventional single-shot reconstruction indicates an off-resonanceartifact which appears in all of the single-shot reconstructions. The yellow arrow in the conven-tional 4-shot reconstruction indicates an edge that aliased into the brain, which is not visible in theEPI-TrACR reconstructions. 10 x 2x 4x3x EP I T r A CR + i n i t. N o C o rr e c t i on R M S g h o s t e d s i g n a l ( % ) C on v en t i ona l EP I T r A CR + c a li b r a t ed i n i t. Figure 3: 1x, 2x, 3x and 4x 2-shot echo-planar images reconstructed with no correction, conven-tional calibrated correction, EPI-TrACR with calibrated initialization, and EPI-TrACR with zeroinitialization. The length and color of the horizontal bars beneath each image represent the residualRMS ghosted signal as a percentage of maximum image intensity, as defined by the color scale onthe right. 11 I n c r e a s e i n R M S G h o s t e d S i g n a l a Repetition Number c Conventional EPI-TrACR
ROI width [pixels] N o r m a li z e d C o e (cid:1) c i e n t o f V a r i a t i o n -1 b ConventionalEPI-TrACRPAGE EPI-TrACRConventionalTheoretical RDC = 1.08PAGE RDC = 12.94RDC = 1.46
PAGE
Figure 4: 2-shot echo-planar images over 20 repetitions reconstructed using conventional calibra-tion, PAGE, and EPI-TrACR with zero initialization. (a) Percentage increase in RMS ghostedsignal versus repetition number, normalized to that of the EPI-TrACR reconstruction of the firstrepetition. (b) Weisskoff plot showing the normalized coefficient of variation over repetitions foran ROI of increasing size, for conventional calibration, PAGE, and EPI-TrACR compared to thetheoretical ideal. (c) Windowed-down conventional calibration, PAGE, and EPI-TrACR recon-structions, at the 14th repetition (indicated by the arrow in (a)). × scan for conventional calibrated reconstruction, PAGE, and EPI-TrACR. Thesignal levels are normalized to that of the first repetition’s EPI-TrACR reconstruction.Figure 4b shows a Weisskoff plot [30] for all three reconstructions compared to the theo-retical ideal; the coefficient of variation over repetitions is plotted for an ROI of increasingsize. Figure 4c shows conventional calibration, PAGE, and EPI-TrACR (with zero initial-ization) images at the 14th repetition. The conventional, PAGE, and EPI-TrACR images t the 14th repetition respectively have 190%, 35%, and 16% higher RMS ghosted signalcompared to the first repetition EPI-TrACR reconstruction. EPI-TrACR maintained con-sistently low ghosting across repetitions, and a much higher radius of decorrelation thanthe conventional calibrated and PAGE reconstructions. A video of the full time series isprovided as Supporting Information.The truncated 2-shot EPI-TrACR results are shown in Figure 5. Figure 5a shows thatdelay and phase shift estimation errors relative to full-data EPI-TrACR estimates are lowup to very high truncation factors, and Figure 5b shows that compute time can be reducedup to 90% by truncating the data by 90%. Figures 5c and d show that images reconstructedwith full data and 90%-truncated data delay and phase estimates are indistinguishable:RMS ghosted signal was 8% higher in the truncated EPI-TrACR image versus the full-datareconstruction, but still 40% lower than the conventional calibrated reconstruction (whichappears in Figure 2). For greater than 90% truncation though, the compute time startsto increase again due to increasing iterations. For full data, reconstruction times rangedfrom one minute (for 1 shot, 1 × acceleration, and calibrated initialization) to 88 minutes(for 2 shots, 4 × acceleration, and zero initialization). Reconstructions using NUFFTs[28] in place of the piecewise FFTs in EPI-TrACR ranged from 8 minutes (for 1 shot, 1 × acceleration, and calibrated initialization) to 269 minutes (for 2 shots, 4 × acceleration,and zero initialization). Discussion
EPI-TrACR is an iterative algorithm that jointly estimates EPI echo delays and phaseshifts, along with images that are compensated for them. Compared to conventional cali-brated corrections, EPI-TrACR consistently reduced image ghosting across multishot fac-tors, acceleration factors, and a dynamic time series. In most cases it was able to do sowithout being initialized with calibrated delays and phase shifts. A further characterization o m p u t e t i m e ( % o f f u ll r e c o n s t r u c t i o n ) e s t i m a t e R M S E ( % ) Truncated 90%Full data reduction (% of phase encode lines) a bc d data reduction (% of phase encode lines)
Figure 5: 2-shot, 1x-accelerated EPI-TrACR reconstructions from truncated data. The plots show(a) combined root mean square error (RMSE) in the estimates of DC and linear phase shifts com-pared to full-data EPI-TrACR estimates and (b) compute time as a percentage of a full-data EPI-TrACR compute time; both are shown as a function of percentage of degree of data reduction ineach dimension. (c-d) Images reconstructed using the full data EPI-TrACR estimates using 90%-truncated EPI-TrACR estimates (16 PE lines) (d) (the red data point in a-b). of the convergence of EPI-TrACR with varying initialization is included as Figure S1 inthe Supporting Information. An additional validation experiment comparing EPI-TrACRestimates (1 shot, 1 × acceleration) to a full k-space trajectory measurement [31] in a phan- om at 3 Tesla is shown in Supporting information Figure S2. The EPI-TrACR bulk linedelay estimate was similar to the median measured delay (13% RMS difference), and theEPI-TrACR image contained 19% lower RMS ghosted signal. Because EPI-TRACR re-lies on data redundancy between nearby lines of k-space, its performance is expected todegrade with increasing acceleration factor, which was observed here. Nevertheless, wheninitialized with calibrated delays and phase shifts, the method always reduced ghostingcompared to conventional calibrated reconstruction.The main tradeoff for EPI-TrACR’s improved delay and phase shift estimates is in-creased computation, but this can be mitigated in several ways. First, we showed thatcompute time can be reduced by truncating the data matrix down to the low frequencies,without compromising the delay and phase shift estimates. Compute times are also shorterwhen the algorithm is initialized with calibrated estimates, since fewer iterations are re-quired to reach a solution. The algorithm could be applied in parallel across repetitions orslices, or within the algorithm the FFTs could be parallelized across receive coils.There are a number of ways the method could be extended. First, in the present workit was assumed that all the echoes within a set of even or odd echoes of a shot had thesame delay and phase shift. However, it is also possible to estimate different delays andphase shifts for different echoes within a set by expressing them as a weighted sum ofbasis functions. We have previously tested this extension using triangular basis functions,but found little improvement with our data. Nevertheless, as others may find it useful thisfunctionality is included in the provided code. Second, the method could be extended tojointly estimate a single set of delays and phase shifts over a whole stack of slices simul-taneously, which would increase the effective signal-to-noise ratio for estimation. Thiscould in particular help for highly accelerated acquisitions where the method is currentlymore sensitive to poor initialization. onclusions The EPI-TrACR method alleviates ghosting artifacts by exploiting data redundancy be-tween adjacent k-space lines in multicoil EPI data. It benefits from initialization withcalibration data but does not require it at moderate acceleration and multishot factors. EPI-TrACR reduced dynamic ghosting without sacrificing temporal resolution, is compatiblewith multishot and accelerated acquisitions, and unlike previous data-based approaches,it does not rely on a ghost-free image region. It was validated in vivo at 7T, at multipleacceleration and multishot factors and in a dynamic time series.
Acknowledgments
This work was supported by NIH grants R25 CA136440, R01 EB016695, and R01 DA019912.The authors would like to thank Dr. Manus Donahue for help with experiments. upporting Information Figures and Captions initial k-space delay (cycles/cm from best) Phase Error p h a s e e rr o r ( m u l t i p l e s o f (cid:0) f r o m b e s t s o l u t i o n ) i n i t i a l p h a s e ( m u l t i p l e s o f (cid:2) f r o m b e s t ) k-space Delay Error k - s p a c e d e l a y e rr o r ( c y c l e s / c m f r o m b e s t s o l u t i o n ) initial k-space delay (cycles/cm from best) RMS Ghosted Signal -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 R M S g h o s t e d s i g n a l ( % i n c r e a s e f r o m b e s t s o l u t i o n ) initial k-space delay (cycles/cm from best) -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 a cb Figure S1: The performance of EPI-TrACR on the single-shot, 1x data is characterized for varyingcombinations of initialization parameters (i.e. a single phase offset and a single k-space delayfor each). Shown are the resulting final (a) phase error (multiples of π ), (b) k-space delay error(cycles/cm), and (c) RMS ghosted signal, for each initialization. All parameters and errors areexpressed relative to the solution with the lowest ghosting (”best” solution), which corresponds toa phase offset of -2.96 radians and a k-space delay of 0.075 cycles/cm. Uncorrected EPI-TrACR Measured 01 imppr range: [0.00658 1] imppr range: [0.00658 1] b x10-3 ConventionalTrACR a e v e n / o dd li n e d e l a y ( n o r m a li z e d t r a j e c t o r y un i t s ) -0.04-0.0200.020.040.060.080.1 D C p h a s e s h i f t ( r a d i a n s ) c Figure S2: A separate experiment was performed in a phantom at 3T (Philips Achieva),using a volume coil for excitation and a 32-channel coil for reception (Nova Medical Inc.,Wilmington, MA, USA). Data were collected for a single off-axis slice (5°/20°/30°) usinga single-shot EPI scan with 60 dynamics; scan parameters were: 23 ×
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