Robust GRAPPA-Accelerated Diffusion-Weighted Readout-Segmented (RS)-EPI

Abstract

Readout segmentation (RS-EPI) has been suggested as a promising variant to echo-planar imaging (EPI) for high-resolution imaging, particularly when combined with parallel imaging. This work details some of the technical aspects of diffusion-weighted (DW)-RS-EPI, outlining a set of reconstruction methods and imaging parameters that can both minimize the scan time and afford high-resolution diffusion imaging with reduced distortions. These methods include an efficient generalized autocalibrating partially parallel acquisition (GRAPPA) calibration for DW-RS-EPI data without scan time penalty, together with a variant for the phase correction of partial Fourier RS-EPI data. In addition, the role of pulsatile and rigid-body brain motion in DW-RS-EPI was assessed. Corrupt DW-RS-EPI data arising from pulsatile nonlinear brain motion had a prevalence of ~7% and were robustly identified via k-space entropy metrics. For DW-RS-EPI data corrupted by rigid-body motion, we showed that no blind overlap was required. The robustness of RS-EPI toward phase errors and motion, together with its minimized distortions compared with EPI, enables the acquisition of exquisite 3 T DW images with matrix sizes close to 512².

Although multishot echo-planar imaging (EPI) reduces blurring and geometric distortions over single-shot EPI, a shortcoming of this method for diffusion imaging is that even minuscule physiologic motion can cause nonlinear phase errors that usually result in profound ghosting artifacts. Although navigator-based nonlinear phase correction ameliorates the ghosting problem, residual nonequidistant sampling with regionally undersampled k-space still exists and requires excessive oversampling or averaging (1). While parallel imaging can also be used to accelerate k-space traversal and reduce distortions in EPI (2,3), the net acceleration for EPI is currently limited to realistic values of 3 and 4, producing images that still suffer from distortion artifacts, especially at high field strengths or higher spatial resolution.

Instead of interleaving EPI trajectories along the phase-encoding dimension (k_PE) to increase k-space velocity, another variant of multishot EPI for diffusion-weighted (DW) imaging is readout-segmented EPI (RS-EPI) (4–11). In RS-EPI, adjacent ‘blinds’ are acquired (each accompanied with a navigator) to produce the combined k-space data that support the desired resolution along the readout dimension (k_RO). RS-EPI increases the k-space velocity compared with EPI by shortening the trajectory along k_RO, thus diminishing distortions. Further distortion reduction can be achieved in RS-EPI via parallel imaging methods (7,9,10). Here, the net gain in acceleration of k-space traversal compared with standard single-shot EPI is governed by the blind width, the GRAPPA-acceleration factor, and slew rate constraints (shown in Table 1). Ignoring slew rate limitations, an RS-EPI scan theoretically offers an N/#blinds-fold distortion reduction over a conventional single-shot EPI scan.

Table 1.

Effective Acceleration Through k-Space for RS-EPI Blinds (Thus Reduction in Geometric Distortion), With Reference to o Single-Shot EPI With a Target Resolution of 288 × 288, an FOV = 24 cm, and Various Blind Widths (G = 40 mT/m; SLR = 150 mT/ m per sec)^*

Blind width	Effective and (theoretical, assuming infinite slew rate) k-space acceleration
	R = 1	R = 2	R = 3	R = 4
32	3.5 (9)	7 (18)	10.5 (27)	14 (36)
64	2.4 (4.5)	4.7 (9)	7.1 (18)	9.4 (32)
128	1.6 (2.3)	3.2 (4.5)	4.9 (9)	6.5 (18)
192	1.3 (1.5)	2.6 (2.3)	3.9 (4.5)	5.2 (9)
256	1.1 (1.1)	2.2 (1.5)	3.2 (2.3)	4.3 (4.5)
288	1 (1)	2 (1.1)	3 (1.5)	4 (2.3)

^*The theoretical acceleration (without slew rate limitations) is shown in parentheses.

Due to its greater data consistency within the blind, in practice, DW-RS-EPI is much more manageable for motion and phase correction than interleaved DW-EPI (9). However, despite the consistency of each blind, a potential problem can arise between blinds; that is, image domain phase errors that arise from motion during the presence of diffusion encoding can lead to shifts of k-space along both readout dimensions, which can lead to gaps between adjacent RS-EPI blinds in the final assembled k-space. Gaps in k-space can also occur following the correction of rotational motion of individual blinds. To include a safety margin, scan time can be traded for increased robustness against motion by partially overlapping adjacent blinds.

The objective of this study was to expand upon our recent work (9) (which was inspired by related work by Robson et al. (4) and Porter and Mueller (5)) and outline in detail the implementation procedure for GRAPPA-accelerated DW-RS-EPI, as well as to explore options for overcoming artifacts arising from brain pulsatile and rigid-body motion. To optimize parallel imaging calibration in RS-EPI, we introduce a self-calibrated RS-EPI regime that uses neither additional interleaves for the GRAPPA-weights estimation nor external reference scans. Moreover, we outline a phase-correction approach to handle partial-Fourier DW-RS-EPI data, investigate the extent to which blind overlap is required for RS-EPI in the presence of rigid-body motion, and introduce and explore the use of a k-space entropy metric to identify blinds corrupted by pulsatile brain motion. Using the reconstruction methods and corresponding imaging parameters that we are using for human brain DW-RS-EPI imaging, we show that, together with the entropy-based data selection criteria, one can obtain high-quality DW-RS-EPI images without the need for cardiac gating.

MATERIALS AND METHODS

MR Pulse Sequence

The timing diagram for the spin-echo RS-EPI pulse sequence with twice-refocused diffusion-encoding preparation (12) is shown in Fig. 1a (5,9). For each repetition (pulse repetition time [TR]), an imaging echo and its accompanying navigator echo (second spin echo) are formed. During each echo formation, RS-EPI sampling trajectories are played out to acquire specific segments or blinds of k-space (Fig. 1b). Here, the navigator blind always samples the central blind of k-space and is equivalent in size (and extent of image distortion) to the imaging blind. Along the readout dimension, each imaging blind is offset from the origin of k-space by a fixed factor (using balanced dephaser and rephaser gradients straddling the corresponding RS-EPI gradient train, shown in Fig. 1a). Depending upon the number of blinds chosen, B; the blind width, W; and the target resolution, N, the blinds may overlap by dW, which is characterized by the overlap factor (OF) given by (9):

$$\mathit{OF}=100\%\frac{\mathit{dW}}{W}=100\%\left(1-\frac{N}{W\times B}\right)$$ [1]

FIG. 1.

a: Pulse sequence timing diagram for the RS-EPI, twice-refocused spin echo–based diffusion sequence (9). The RF pulses (spectral-spatial 90° and refocusing 180°) and the diffusion gradients (shaded regions) are shown. TE₁ and TE₂ are the echo times of the imaging and navigator echo, respectively, T_over the time for collecting the number of overscans (N_o). The strength of G_dp varies, depending upon the position of the blind along the x-direction. Note that the phase-encoding gradient size for the imaging and navigator echo is equivalent. b: k-Space imaging and navigator blind trajectories for the RS-EPI sequence (9). k-Space is filled with an odd number of separate blinds, B, of a given blind width, W, and OF = dW/W. c: Two options for estimating the ghost calibration parameters and GRAPPA weights. The first is to estimate the ghost parameters and GRAPPA weights on a fully sampled central b = 0 s/mm² blind, and the second is to estimate these parameters on a fully sampled central strip formed by R b = 0 s/mm² navigators.

In an effort to reduce both the echo time of the imaging blind and the echo time difference between navigator and imaging blind, all blinds were acquired with partial Fourier encoding along the phase-encoding direction using an overscan factor (100% × N₀/N_PE/2) of approximately 12%, where N₀ is the number of overscans, and N_PE is the number of phase encoding steps (9). Typically, a larger overscan factor will yield a more robust estimation of the image phase (13).

For optimal field of view (FOV)/2-ghost correction and GRAPPA-weights estimation discussed in detail below, a fully sampled b = 0 s/mm² imaging blind (made up of R interleaves) can be acquired, preferably at the center of k-space (option 1 in Fig. 1c) (9). Here, (R – 1) additional interleaves at the center blind location need to be acquired at the expense of extra scan time. Since the navigator blinds that accompany the b = 0 s/mm² imaging blinds are not required for navigator-based phase correction, another option is to vary the phase-encode dephaser area of R navigator blinds to yield R offset interleaves (option 2 in Fig. 1c). In this case, the combination of the R navigator blinds yields a fully sampled central strip that can be used for the GRAPPA calibration and FOV/2 ghost parameter estimation. Since the RS-EPI imaging blind and navigator blind are designed for the same FOV and R and differing only by the offset along k_RO, the ghost correction and GRAPPA parameters are interchangeable between both blinds. Thus, option 2 allows one to scan DW-RS-EPI without any overhead time to obtain extra calibration data. Two points must be noted when using the R-interleaved navigator for the calibration: (1) in order to acquire a fully sampled central strip, the number of blinds B must be greater than the acceleration factor R; and (2), one must perform echo time shifting (14) between the navigator interleaves to avoid stepwise phase accrual along the ky-direction.

k-Space Entropy Metric

Pulsatile brain motion can be particularly problematic in ungated DW experiments, as it can leave a blind completely corrupted by nonlinear motion. To identify the effects of nonlinear motion, it is helpful to recognize that nonlinear phase errors on the navigator image cause a substantial dispersion of k-space data, which will affect the entropy of k-space. The DC peak amplitude (1,15) and the width of the signal distribution in k-space (6) have been shown as methods to identify corrupt data. Here we explore the utility of using k-space entropy (16) as an alternative metric to identify navigator blinds corrupted by nonlinear, nonrigid brain motion. The equation for total k-space entropy, E, is given by:

$$E=-\mathrm{\Sigma }\frac{B_{\text{ij}}}{\text{log}(B_{\text{ij}})};B_{\text{ij}}=K_{\text{ij}}/\mathrm{\Sigma }{K}_{\text{ij}}^2$$ [2]

where K_ij is the magnitude of the k-space data.

Image Reconstruction

The following steps include a detailed description of the methods used for reconstructing DW-RS-EPI parallel imaging data outlined in Holdsworth et al. (9), combined with an additional description on how to reduce scan time and correct for motion.

Step 1: EPI Ghost Correction

To correct for EPI FOV/2 ghost correction (Nyquist) ghosts in EPI, zero- and first-order phase-correction terms need to be applied to the echoes in the frequency domain. With the use of a fully sampled central strip (formed either by option 1 or 2 described in Fig. 1c), the phase-correction terms that minimize the ghosts (as measured by image entropy) were determined iteratively (17,18) and applied to all blinds (the b = 0, the DW blinds, and their respective navigators).

Step 2: Ramp Sampling Correction

To minimize distortions and shorten echo time, EPI typically also acquires data during the rising and falling portions of the EPI readout gradients, which leads to nonuniform k-space sampling. The nonuniformly sampled k-space sample points of each blind were therefore interpolated (via truncated sinc) to an equidistant blind grid (17) to form an individual Cartesian k-space of size W × N_PE for each blind.

Step 3: Parallel Imaging Reconstruction

The fully sampled central strip was used to determine the GRAPPA (19,20) weights, and each R-fold undersampled blind then underwent parallel imaging reconstruction to synthesize missing k-space lines.

Step 4: Phase Error Correction

Each DW imaging blind must be phase corrected to remove unwanted phase due to motion occurring during the diffusion-encoding gradients. In our experience, performing phase correction before partial Fourier reconstruction can also help to reduce the signal dropout in data corrupted by severe nonlinear pulsatile motion. As shown in Fig. 2b, each navigator blind was windowed in k-space by a triangular function (21,22) in both the readout- and phase-encoding directions prior to FFT. The windowed navigator blind image provides a low spatially varying estimate of the motion-induced linear and nonlinear phase, ϕ_{DWI_est}. Since the time between the imaging and navigator blinds is ~60 ms, one can safely assume that no motion occurs between them. Thus, the undesired phase, ϕ_{DWI_est}, can then be subtracted from the complex blind image, leaving just the imaging phase of the blind (ϕ_im). Note that the imaging blind will have a nominal phase (in the image domain) due to its position along the x and y direction; however, this phase (which we want to keep) will be unaffected by the subtraction described above.

FIG. 2.

a: Summary of the reconstruction steps applied to the partial Fourier RS-EPI b = 0 and DW data. b: Triangular phase correction process applied to each partial Fourier DW blind in RS-EPI. Since the navigator blind is partial Fourier-encoded in the k_y direction, the k-space peak is centered so that a low-resolution phase map can be extracted without the y-encoding phase present. To achieve this, the bottommost pixels of the navigator are discarded, and this truncated k-space was zero-padded back to its full size to center the k-space peak. This ensures that resolution (or size) of the navigator and imaging blind remains equivalent. Since the phase is inverted due to the 180° refocusing pulse between the imaging and navigator blinds, the phase correction step is a multiplication. Note that the blinds are zero-padded prior to the inverse FFT to avoid wrapping of the signal due to the phase correction process. c: Rigid-body motion correction method applied to the RS-EPI data.

Step 5: Rigid-Body Motion Correction

Rigid-body motion parameters (translation and rotation in x and y) were obtained by means of an image-based registration using the navigators (Fig. 2c). The first navigator blind for each b = 0 and b > 0 plane was used as reference for the motion correction. Phase ramps that correspond to the relative amount of translation to the reference navigator were applied to each blind separately to correct for translational motion along both the x and y dimension. The corresponding rotation parameters were applied to the k-space coordinates to be used as part of the final gridding process, thus avoiding additional resampling errors (see next step). DW and non-DW volumes can be aligned later via mutual information-based registration.

Step 6: Gridding

Phase- and motion-corrected blinds can now be combined to form a single k-space that supports the desired resolution along the readout dimension. A gridding reconstruction using a Kaiser-Bessel window-based gridding kernel (23) placed the blinds at positions that correspond to the individual offset along the readout axis, modifying the trajectory for individual blind’s rotational corrections.

Step 7: Partial Fourier Reconstruction

Projection onto convex sets (POCS) reconstruction (24,25) was performed for each coil to fill in the remaining extent of k-space. Here, POCS is preferred over homodyne reconstruction to preserve image phase. Complex averaging is performed for each diffusion-encoding direction on a per-coil basis to minimize the Rice-Nakagami–distributed noise bias from magnitude-only reconstructions (26,27). The final image was produced by means of sum-of-squares reconstruction. Note that the sum-of-squares operation used here is a complex-preserving reconstruction that estimates and removes the differential coil phase offsets, allowing the complex sum-of-squares combination of coil images.

MR Experiments

All scans were performed on a 3-T whole-body GE EXCITE system (Milwaukee, WI), using an eight-channel head coil and a high-performance gradient system (40 mT/m; SLR = 150 mT/m/sec). Datasets were acquired on healthy volunteers. All human studies were performed under Institutional Review Board approval from our institution, and written informed consent was obtained from each subject participating in these experiments.

Unless stated otherwise, the imaging parameters that remained fixed throughout the experiments were FOV = 24 cm, slice thickness of 5 mm, the minimum echo time (68 ms), partial Fourier encoding with N_O = 12%, number of averages (NEX) = 3, and TR = 3 sec.

The following themes were explored:

1. Determine whether the use of a fully sampled blind formed by R b = 0 s/mm² navigator blinds as proposed in Fig. 1c (as a means to reduce scan time) is a suitable method for estimating the FOV/2 ghost correction parameters and GRAPPA weights.

2. Investigate the use of the k-space entropy metric (using the DW navigator data) for identifying DW data corrupted by nonlinear motion to eliminate the need for gating procedures.

3. Get an indication of the minimum blind overlap required to produce high-quality DW-RS-EPI images.

Comparison Between GRAPPA Calibration on Fully Sampled Central Imaging Blind and R Navigator Blinds

The purpose of this experiment was to explore the two options given in Fig. 1c for the FOV/2 Nyquist ghost and GRAPPA calibration. Both the ‘slow’ option (option 1, whereby a fully sampled imaging blind is used for the calibration) and the ‘faster’ option (option 2, whereby a fully sampled center strip formed by R-interleaved navigators) were tested using an R-shot and R-interleaved DW-RS-EPI dataset (that is, R = NEX = 3). One b = 0 s/mm² and one b = 1000 s/mm² (S/I direction) were acquired on a healthy volunteer using the following parameters: an in-plane target resolution of 288 × 288; B = 33 blinds (the large number used to get a SNR high enough to enhance the differences between the two options); W = 64, and R = 3 (where R also equaled the number of interleaves per blind). The dataset was acquired with peripheral cardiac gating (TR = 3 RR intervals and trigger delay ~100 msec) to avoid the complication of pulsatile brain motion that may occur between interleaves.

The multishot b = 0 and b = 1000 s/mm² data then underwent three different reconstructions. First, the ghost calibration was performed on the middle blind – but GRAPPA was not used (in the absence of motion, this is considered the gold standard). Second, option 1 was tested by using the fully sampled middle b = 0 blind for both the FOV/2 Nyquist ghost and GRAPPA calibration (these calibration parameters were then applied to all other b = 0 and b = 1000 s/mm² blinds). Third, option 2 was tested by randomly choosing three offset navigator blinds to be used as the fully sampled central strip for the calibration. For all options, the NEX = 3 data were then phase corrected and complex averaged before the gridding procedure.

Explore the Use of k-Space Entropy for Corrupt Blind Elimination

For this experiment, data were acquired on three healthy volunteers. On each volunteer, the RS-EPI diffusion scheme was repeated four times for all three principal diffusion encoding directions (i.e., along x, y, and z) and performed both with and without peripheral cardiac gating. Seven blinds and NEX = 3 were used. To account for potential dispersion of k-space arising from geometric distortion, this scheme was also repeated with four different R factors (ranging from 1–4). This yielded a total of 84 × R navigator blinds per diffusion-encoding direction for the analysis. A target resolution of 288 × 288 was used; a TR = 3 s (or 3 RR intervals and minimum trigger delay for the gated acquisition); a blind width W = 64, b = 1000 s/mm²; and 21 slices for full brain coverage. The navigator blinds from each of the 84 (diffusion repetitions) × 3 (diffusion directions) × 4 (acceleration factor, R) × 3 (volunteers) × 2 (gated/ungated) datasets were analyzed for brain motion. Since entropy is a relative metric that depends upon the acquisition parameters and the structure of the object, a threshold to identify corrupted blinds was for each scan set to the <E> + 2σ taken over all available navigator blinds. The correlation of bad blind selection using this entropy threshold and visual inspection was investigated. Note that the entropy metric may not be effective at detecting small linear brain rotation occurring during the DW gradients, which causes just a simple shift of the k-space peak (without dispersion). However, this type of motion can largely be corrected via phase correction followed by rigid-body rotation correction.

The minimum and maximum intensity projection taken across the entire stack of available navigator blinds was used as a measure for determining the efficacy of the k-space entropy threshold. As the resulting minimum intensity projection image for each pixel will show the lowest signal intensity over all navigator blinds, this map shows in a compact form the ‘worst case’ signal dropout. Only after successful rejection of the blinds containing signal dropouts will the minimum and maximum intensity projection image be close to identical (save for white noise).

Rigid-Body Motion and Blind Overlap

DW-RS-EPI images were acquired at an in-plane target resolution of 288 × 288, using B = 7, W = 64, R = 3, and NEX = 3. The acquisitions consisted of one b = 0 s/mm² and three b = 1000 s/mm² applied in the x, y, and z direction. Two datasets were acquired on a healthy volunteer, the first without motion and the second with continuous in-plane rotation throughout the scan and over the maximum range possible within the head coil. Using the procedure outlined in Fig. 2c, the second dataset was corrected for motion. Since the use of seven 64 × 288 blinds yielded an OF = 36% for a target acquisition matrix of 288 × 288, the significance of the amount of blind overlap in the presence of motion on the final image quality was tested by reducing the individual blind widths to yield various blind OFs.

RESULTS

Comparison Between GRAPPA Calibration on Fully Sampled Central Imaging Blind and R Navigator Blinds

Fig. 3 shows side-by-side comparisons between RS-EPI b = 0 and DW images reconstructed without GRAPPA (Fig. 3a), as well as with the FOV/2 Nyquist ghost and GRAPPA calibration options outlined in Fig. 1c. In Fig. 3b, the dataset is reconstructed with the FOV/2 ‘deghosting’ parameters and GRAPPA weights estimated from the central imaging b = 0 blind, and in Fig. 3c this calibration procedure is performed using a fully sampled central strip formed by R b = 0 s/mm² navigators. The right side of Fig. 3b–c show the images subtracted from the image reconstructed without GRAPPA, with the resulting difference image magnified by a factor of 10. Although slightly more structure is visible in the b = 0 difference image derived from the navigator-based calibration, this difference is negligible in the reconstructed images.

FIG. 3.

Multishot (NEX = R = 3) RS-EPI b = 0 and b = 1000 s/mm² (S/I direction) images. In (a), the image is reconstructed without performing GRAPPA. In (b) the GRAPPA weights are estimated from a fully sampled central b = 0 s/mm² imaging blind, and in (c) the GRAPPA weights are estimated from a fully sampled central strip formed by R b = 0 s/mm² navigator blinds. The right-hand sides of (b) and (c) depict the difference image using the dataset reconstructed without GRAPPA and are windowed by one order of magnitude. The DW-RS-EPI dataset is acquired with peripheral cardiac gating at a target resolution of 288 × 288, using 33 blinds of W = 64.

Corrupt Blind Elimination via the k-Space Entropy Metric

A plot of the k-space entropy for 84 DW-RS-EPI navigator blinds (b = 1000 s/mm², W = 64, N = 288, R = 3) acquired at the base of the brain (where pulsatile motion is usually most dominant) from a healthy volunteer is shown in Fig. 4a–c, for the x, y, and z diffusion encoding directions, respectively. The analysis of linear components of the image phase in all navigators revealed that, in the absence of rigid-body motion, coherent k-space shifts emanating from pulsatile motion are negligible, regardless of the diffusion-encoding direction. As shown in Fig. 4, corrupted data instead manifested as significant dispersion of k-space and signal voids and/or shading occurring predominantly in the center of the image. As shown, this effect is paralleled by a significant increase of k-space entropy. Consistent with Wirestam et al. (15), the S/I (through-plane) diffusion-encoding direction is the most sensitive direction for signal loss (Fig. 4c). Using the data acquired on the three healthy volunteers with slice locations below the corpus callosum, the percentage of the DW navigators acquired in S/I direction that exceeded the entropy threshold was 7% (compared with 1% and 2% for the L/R and A/P directions, respectively). Do note, however, that these values are pessimistic, given that brain motion becomes less of an issue for superior slices. Also note that, according to the threshold (given by the mean plus two standard deviations), and consistent with visual inspection, the use of peripheral cardiac-gated sequences (black lines) produces blinds that are all usable.

FIG. 4.

Plot showing the entropy of k-space calculated for 84 DW-RS-EPI navigator blinds for (a) L/R, (b) A/P, and (c) S/I diffusion-encoding directions (b = 1000 s/mm²). The diffusion images were acquired on a healthy volunteer, both without (red lines) and with (black lines) peripheral cardiac gating. Imaging parameters were N = 288 × 288, W = 64, with a TR = 3 s for ungated acquisitions and three RR intervals and minimum trigger delay for gated acquisitions. As shown in (c), nonlinear pulsatile brain motion causes significant dispersion of k-space, which correlates with high k-space entropy and signal voids in image space. Note that the 84 repetitions arise from four repetitions of a typical RS-EPI dataset with B = 7 blinds and NEX = 3. The black dotted line corresponds to the threshold (given by the mean of the entropy over the 84 navigator blinds + 2 standard deviations) above which data are discarded. The large peaks in the graphs refer to single incidents where the k-space entropy and signal dropout in the image domain are significant.

Further analysis of the efficacy of k-space entropy as a metric for corrupt blind elimination is shown in Fig. 5. Here, all blinds from a dataset that exceeded the proposed threshold (that is, those deemed as corrupted blinds) are shown in Fig. 5a, and all contain significant signal dropouts in the reconstructed navigator images at the level of the cerebellar peduncles and the vermis (white arrows). In Fig. 5b–c the minimum intensity projection and maximum intensity projection are taken over the remaining 77 blinds where entropy values were found below the threshold. These data show that the k-space entropy metric is quite deterministic, and the similarity between the minimum intensity projection and maximum intensity projection images shows that data with signal voids have successfully been excluded.

FIG. 5.

Two slices from a DW-RS-EPI ungated dataset where (a) shows all the blinds that exceed the k-space entropy threshold (given by the mean plus 2 standard deviations). In (b), the minimum intensity projection (minIP) is performed over the remaining 77 ‘uncorrupted’ blinds, and (c) shows the corresponding maximum intensity projection (MIP) for reference. This dataset was acquired on a healthy volunteer using 84 repetitions of the diffusion scheme with R = 3, W = 64, and N = 288 × 288. Both the minIP and MIP are sensitive to residual outliers and demonstrate how well the entropy threshold is able to single out corrupted blinds. The blinds were zero-filled to achieve the same aspect ratio in the y and x direction.

Using the ungated RS-EPI dataset (b = 1000 s/mm², S/I direction, R = 3, W = 64, N = 288), the worst out of the three blinds for each of the seven blind locations (as determined by the k-space entropy metric) were gridded together. Using all 84 repetitions, a center blind and two offset blinds that exceeded the entropy tolerance level were chosen. As shown in Fig. 6b, the result is significant shading across the center of the image at the level of the cerebellar peduncles (white arrows). By replacing the corrupted center blind with an uncorrupted blind, the image quality is shown to be greatly improved (Fig. 6c), despite the presence of the two corrupted off-center blinds in this dataset. It appears that, while offset-center blinds corrupted by nonlinear motion do not result in much SNR loss, the acquisition of an uncorrupted center blind is crucial. For this particular experimental setup, there was a 7% risk of obtaining a corrupted blind in the S/I direction for an ungated RS-EPI scheme. In a full-brain-coverage scan (using in this example 21 slices), the total risk that one or more of the slices will be acquired during the brain motion period becomes (1 − (1 − 0.07)^21) = 78% per volume. If one is willing to accept the use of corrupt off-center blinds, the acquisition of three additional center blinds reduces the risk of obtaining signal loss anywhere in the brain to (1 − (1 − 0.07^3)^21) = 0.7% per image volume at the expense of ~20% extra scan time.

FIG. 6.

Reconstruction of one repetition of the DW-RS-EPI selected from the (a) gated and (b,c) ungated dataset from Fig. 4 (b = 1000 s/mm², S/I direction). Imaging parameters were N = 288 × 288, R = 3, B = 7, and W = 64. In (b), a repetition with a corrupted center blind is shown. Despite the selection of two corrupted offcenter blinds in this particular dataset, replacing the central imaging blind with an uncorrupted central blind reveals good image quality, as shown in (c).

Rigid-Body Motion and Blind Overlap

Fig. 7 shows RS-EPI isotropic diffusion (isoDWI) images acquired without and with continuous rigid-body motion. The extent of rotation for the motion-corrupted case ranged from −6 to 6° throughout the scan, while the translation ranged from −4 to 4 mm. Both rotation and translation were determined by the image-based registration/motion correction procedure illustrated in Fig. 2c. With an OF = 0%, the motion-corrupted data have been corrected with little observable degradation in image quality compared with the motionless case, despite the resulting gaps in k-space following rotation correction. Interestingly, even with a negative OF of 5% (that is, a gap between blinds), the motion correction yielded good image quality. As the OF is pushed to −10%, aliasing artifacts become evident as marked by ghosting artifacts around the periphery of the image.

FIG. 7.

RS-EPI isoDW images acquired (a) without and (b) with continuous rigid-body motion (b = 1000 s/mm² in the x,y,z direction, N = 288 × 288, R = 3, B = 7, and W = 64). In this case, the OF = 0%. After motion correction, one can see good image quality in (c), despite the gaps in k-space produced by the rotation of the coordinates. Even a negative OF in (d) shows similar high image quality. e: Aliasing artifacts become prominent as the OF drops further below the Nyquist limit, as indicated by the black arrows. f,g: The corrected k-space coordinates from one diffusion encoding direction.

Finally, Fig. 8 shows a high-resolution RS-EPI DTI of the brain stem and cerebellum (480 × 480 with b = 1000 s/mm² along 15 noncollinear directions). Such high spatial resolution data underscore the ability of RS-EPI to handle phase correction and to minimize geometric distortions, even for acquisition matrices close to 512². They also demonstrate the utility of improved spatial resolution to better resolve directional information in regions of intermingling fiber tracts, which would be hard to separate with larger voxel sizes.

FIG. 8.

High-resolution DTI of (a) the brain stem and cerebellum and (b) the cerebrum. From left to right, the b = 0 s/mm², b = 1000 s/mm² isoDWI, FA, and FA with 1st eigenvector color encoding. The scan parameters were as follows: B = 15, W = 64, N = 480 × 480, R = 3, NEX = 3, 4 mm slice thickness, FOV = 24 cm, 2 b = 0 and 1 b = 1000 s/mm² scan along 15 noncollinear directions, TR/echo time = 3 sec/60 ms, and a 35-min total scan time. Retrospective motion correction was applied on each DW image before final tensor processing to minimize blurring. Note that the reddish hue in the color map arises from the slightly larger b-value given by the crushers that accompany the slice-select pulse.

DISCUSSION

A substantial amount of research on DW imaging sequences has focused on diminishing the profound artifacts that arise from the nonlinear phase errors induced by motion occurring during the strong diffusion-encoding gradients. However, this remains a considerable challenge. The correction of these phase-error terms allows one to move beyond ssEPI, and take advantage of the reduced geometric distortion achievable with multishot techniques. However, the price to be paid with multishot techniques is typically a longer overall scan time and an increased chance of patient motion, especially when many diffusion encoding directions are desired. Therefore, one objective of this work was to use the reduced geometric distortion capability of RS-EPI, as well as to explore solutions for correcting motion that can occur between blinds. The reconstruction techniques discussed here lead to images with high resolution and image quality while offering reduced partial volume effects and better capabilities to potentially separate white matter tracts of different origin.

GRAPPA Calibration Option for Reducing Scan Time

While the scan time for RS-EPI is still shorter than that of other high-resolution techniques proposed in the literature (22,28,29), a particular concern for RS-EPI is that it is still longer than ssEPI. This is certainly an issue for the acquisition of a large number of diffusion directions, such as is required for HARDI (30,31) or Q-ball imaging (32,33), but is a consequence if one desires images with higher resolution. For less complex encoding schemes, one procedure that helped to reduce the scan time was to use the b = 0 s/mm² navigators for the Nyquist ghost and GRAPPA-weights calibration (Fig. 3). This scan time reduction came without any change in reconstruction quality and scan time penalty from acquiring extra calibration data, despite the lower SNR of the navigator blind.

Pulsatile Brain Motion and k-Space Entropy

During the design of DW-RS-EPI pulse sequence, there was some concern that brain motion occurring throughout the acquisition of the DW blinds may result in gaps in k-space, implying the need for a large blind OF. Cardiac gating can help to rule out this problem; however, in addition to signal fluctuations that can affect gated data with TR ~< 4 sec (because of incomplete T₁-relaxation), in our experience cardiac gating can result in a scan time increase of 20–100%, depending upon the heart rate. In this work, a large number of navigator phase maps were analyzed, revealing that brain motion is predominantly nonlinear (consistent with Butts et al. (34) and Miller and Pauly (35)) and the significant dispersion of k-space was paralleled by large signal voids in the image domain (Fig. 4). Thus, gaps between the blinds will not generally be introduced in k-space due to pulsatile brain motion itself, implying that it is not necessary to overlap the blinds, and that blind reacquisition techniques (36) are not needed for this purpose.

The use of a k-space entropy-based metric was found to be a robust measure for the quality of blinds in ungated acquisitions but should be applicable to other diffusion acquisition trajectories, including DW-ssEPI. As seen from our ungated DW-RS-EPI experiments, only corrupted center blinds seem to considerably compromise the final image quality (Fig. 6), which we attribute to the smaller contribution to the overall image contrast of off-center blinds. While a corrupt off-center blind may affect the resolution to some extent, the most dramatic effect of motion on the final image can be attributed to the center blind.

The threshold calculated from the mean of the k-space entropy plus two standard deviations used in this work was effective at eliminating corrupt blinds. With a 7% chance (calculated from the entropy metric) of acquiring a corrupted blind in an ungated RS-EPI scheme, the risk that any slice in the image volume is corrupt is much higher (78%). However, if one is willing to accept the use of corrupt off-center blinds, the acquisition of three additional center blinds reduce the risk of corrupted data to 0.7% at the expense of ~20% extra scan time. Alternatively, one could use a real-time feedback system such as used in Porter and Heidemann (7,36), whereby near the end of the diffusion experiment all blinds are used to find an entropy threshold above which both new and old corrupted blinds are reacquired at an expense of ~7% increase in scan time. Compared to the use of cardiac gating to avoid acquiring data during brain motion, this method of eliminating bad data overcomes the brain motion artifacts, with a much smaller scan time penalty.

One important point to note is that, while the entropy method appears to be a reliable method for determining k-space corrupted by nonlinear motion, our recent work on ssEPI data has shown that the use of more than eight overscans can considerably reduce the extent of the signal dropout in the image domain. This would imply that fewer blinds need to be rejected.

Rigid-Body Motion and Blind Overlap

Our experiments indicate that DW-RS-EPI is relatively benign to blind OF in the presence of motion and that it remained robust even in the presence of large rigid-body motion (Fig. 6). While gaps between blinds introduced in phantom data give rise to ringing artifacts (data not shown), this effect seems to ‘drown’ in vivo. For the range of head motion one would normally expect inside a head coil (in our experience, head motion has typically been confined to <10°), the resulting gaps in k-space that arise have shown little practical effect; thus, to avoid a heavily prolonged scan time, we suggest that one does not need to use a large blind overlap. Indeed, extreme motion occurring throughout the acquisition could render large and harmful gaps in k-space. However, large in-plane head motion is likely to be coupled with through-plane motion and/or the disappearance of the k-space peak outside the sampling window (in the case of extreme head rotation), and even a large blind OF would not be sufficient to correct for this.

One potential cause for concern is patient motion occurring throughout the calibration scan, which leads to ghosting in the final image. Previous work has demonstrated that GRAPPA reconstruction has been shown to be quite robust in the presence of motion (3); however, extreme motion occurring during the acquisition of the b = 0 center blind could lead to a failed ghost correction and poor GRAPPA weights. The ‘fast’ GRAPPA calibration option 2 (in Fig. 1c) can be beneficial here. By interleaving all b = 0 navigators and using various combinations of the navigators, this option can reveal the most optimal set of GRAPPA weights, guided by the GRAPPA least-squares estimation fit having the lowest residual error.

Although beyond the scope of this work, another issue is the effect of different diffusion encoding directions for each blind when rotational motion is present. A non-linear optimization procedure applied to spiral and SAP-EPI data has been used to correct for this effect (37,38), and it can easily be extended to correct for incorrect diffusion-encoding directions in RS-EPI data.

Practical Issues

As there is little difference in distortion property of RS-EPI between blind widths of 32 to 64 for our gradient system due to slew rate limitations, a wider blind (W = 64) has been our choice in subsequent experiments, resulting in a smaller sacrifice in total scan time than originally expected. Wider blinds also benefit DW acquisitions, since, in the presence of motion and without the application of the k-space entropy metric, it is easier to recover signal lost in dispersed k-space blinds, and there is a slightly smaller chance that the k-space peak will be displaced outside the sampling range. As determined from simulated data (not shown), the only apparent constraint for a robust coregistration and motion correction is that the width of the navigator blind must be >16 to avoid Gibbs ringing. Overall, we found that, at 3 T and with our gradient system, it is not worth the scan time increase and negligible distortion reduction to use blind widths less than approximately 32. Certainly, this choice depends on the individual hardware. With flexible gradient insert coils on the horizon, which achieve higher maximum gradient strengths/slew rates and reduced peripheral nerve stimulation potential, RS-EPI would be even more efficient.

While the RS-EPI trajectory has the upper hand over the ssEPI trajectory for several parameters relating to image distortions, this comes at the expense of an increased scan time, as shown in Table 2 and lower SNR. However, normalizing for whole brain coverage (21 slices) using a TR = 3 sec, a target resolution of 288 × 288 implies only a 3-fold increase in scan time for RS-EPI (W = 64, OF = 10%) at a 7-fold reduction of geometric distortion. For most of the volunteer and patient data we have acquired thus far, our parameter settings have been largely the same, with RS-EPI parameters as follows: B = 7, W = 64, N = 288, R = 3, and NEX = 3. One reconstruction issue to be aware of is the choice of triangular-window width for the phase correction: with a larger window width, more of the image phase is removed causing more Rician distributed noise in the final complex-averaged isotropic DW image. The converse, using a smaller window width, increases the chance of phase-related artifacts caused by the diffusion gradients, in favor of a lower noise floor. Our empiric results have shown that a triangular window filter covering the most central ~25% of k-space along k_x and k_y is the best tradeoff for ungated DW acquisitions (39).

Table 2.

Scan Time for ssEPI (NEX = 1), and GRAPPA-Accelerated EPI and RS-EPI (R = 3, NEX = 3) Isotropic (x,y,z) DW Acquisitions and One b = 0 s/mm^2*

Target Resolution (N)	Scan time (min)
	ssEPI (R = 1)	EPI (R = 3)	RS-EPI (R = 3, W = 64)	RS-EPI (R = 3, W = 32)
128	0:12	0:60	1:80 (B = 3)	3:00 (B = 5)
192	0:22	0:82	1:92 (B = 3)	4:20 (B = 7)
288	0:29	1:40	4:30 (B = 5)	5:94 (B = 9)

^*A NEX = 3 was used for the GRAPPA-accelerated cases in order to increase the SNR from g-factor–related SNR-loss. The scan time is normalized for whole brain coverage (21 slices) and a desired minimum TR of 3 s (for full signal recovery). However, because of the long ssEPI train for R = 1, the minimum TR was breached. This implies that as the EPI trains become shorter with parallel imaging (and even more so with RS-EPI), the normalized scan time also became shorter. Two blind widths (W) and the corresponding number of blinds (B) required to achieve the minimum overlap are shown for RS-EPI, and the scan time is reported for navigator-based ghost and GRAPPA calibration.

Another advantage of RS-EPI over EPI is that geometric distortions do not change with target resolution (29). Certainly, for some extreme combinations of blind width and target resolution, $T_2^{*}$ decay might apodize higher spatial frequency components, although not to the extent seen in standard ssEPI. A resolution of 480 × 480 chosen for Fig. 8 is even beyond what is used currently for most of the conventional scans. With a slice thickness of 4 mm, the voxels were anisotropic but served to demonstrate the potential of such a high in-plane resolution for future developments in DTI and beyond. For example, with this resolution and color FA maps at hand, different layers of the tapetum in the optic radiation can be seen in Fig. 8.

CONCLUSIONS

This work provides a detailed overview of the reconstruction chain of parallel imaging-enhanced RS-EPI. We investigated ways to produce high-quality DWI and DTI RS-EPI images while keeping the scan time as short as possible. It was shown that RS-EPI data can be acquired at full acceleration (that is, without the acquisition of a fully sampled central blind or an external calibration scan), by estimating the ghost parameters and GRAPPA weights on a fully sampled central strip formed by R navigator b = 0 blinds.

It was shown here that, while gated RS-EPI acquisitions reveal no blinds corrupted by pulsatile brain motion, up to ~7% of the DWIs (S/I direction) were corrupted in ungated acquisitions. Here we propose two acquisition schemes to substantially reduce the chances of ending up with signal voids in the DWI data. One method is to acquire two extra center blinds and choose the best blind candidate via the k-space entropy metric, thereby lowering the risk for signal void by about two orders of magnitude, using about 20% extra scan time. Alternatively, a data rejection scheme via the k-space entropy metric can be incorporated into a real-time data feedback mechanism to automatically reacquire a corrupted blind, yielding even less scan time overhead.

It was also shown that RS-EPI data can be corrected with excellent image quality without any overlap (OF = 0%), even in the presence of relatively large continuous rigid-body motion. Our favorite RS-EPI scan parameters for our hardware were a blind width of 64 at a target resolution of 288 × 288 and a GRAPPA-acceleration factor R = NEX = 3, which on visual inspection balanced distortion levels and SNR. Combined with the pseudo-Cartesian nature of RS-EPI, the use of minimally overlapping and relatively wide blinds may make this sampling strategy an attractive option for high-resolution DW imaging. RS-EPI offers an avenue for DTI beyond the 128 × 128 matrix barrier that is most common with ssEPI, and opens new research opportunities since anatomic structures can be explored in much better detail.