To introduce an efficient Multi-Shot Diffusion-Weighted (DW) 3D-GRASE acquisition that replaces the need for time-consuming navigator echoes with a single reference shot for the whole acquisition.

Compared to 2D DW acquisitions, 3D DW methods allow perfectly isotropic voxels without slice profile issues and increased SNR efficiency, which could potentially reduce scan time for a given image resolution and b-value. In practice however, the rapid signal decay requires segmentation of k-space encoding into multiple shots. Consequently, navigator echoes are needed for each shot to capture its motion-induced phase information and produce artefact-free images. Even then, these navigator echoes cannot correct for through-slice dephasing and corresponding signal loss unless they are acquired in 3D. Moreover, they noticeably lengthen the acquisition time and contribute to making 3D-DW sequences impractical for clinical use.

Here we propose a reconstruction scheme that exploits virtual coil GRAPPA reconstruction^1,2 to allow Multi-Shot 3D-DW GRASE with a single reference shot and no navigator echoes.

As with a standard GRASE acquisition, a plane of k-space (called here “partition”) is sampled with an EPI readout after each refocusing pulse (Figure 1, left). The signal is undersampled by a factor R_z along k_z and N_s along k_y, where N_s is the number of shots. Each subsequent shot is shifted by one Δk_y, leading to fully-sampled partitions (middle). Additionally a reference shot samples the same partitions around their centre with a fully-sampled $$$ \frac{N\scriptsize{x}}{N\scriptsize{s}}\times{N\scriptsize{y}}$$$ readout, preserving the bandwidth. Alternatively a $$${N\scriptsize{x}}\times\frac{N\scriptsize{y}}{N\scriptsize{s}}$$$reference shot can be acquired (right) by increasing the readout bandwidth by a factor Ns, neglecting image distortion along the readout direction.

Image reconstruction is similar to other virtual coil Parallel Imaging methods³, with the motion-generated phase information treated as part of the coil sensitivities: the signal is viewed as if acquired with N_c×N_s virtual coils, where N_c is the number of receive channels. The reconstruction is performed in two steps:

Step 1: Using the reference shot as an auto-calibration set⁴, a GRAPPA weightset can be computed that linearly combines acquired source points into missing target points with the same motion-induced phase information as the reference shot (figure 2). Each shot has its own set of virtual coil sensitivities due to differences in motion. Since each shot acquires different lines of k-space, the order in which the shots appear within the kernel changes as it shifts along k_y (in the figure the order of the red, green and blue changes with such shifts), requiring different GRAPPA weightsets. Therefore a total of Ns different GRAPPA weightsets are computed and used. Applying these weightsets on a multi-shot partition yields a partition with uniform motion-induced phase information.

Step 2: The missing partitions are reconstructed using GRAPPA with weightsets computed from the b=0 volume.

To test this method, a multi-shot DW 3D-GRASE acquisition was simulated from conventional 2D diffusion-weighted data from a healthy volunteer (3T Siemens Skyra, 32-channel head coil, 110×92×80, 2mm3 resolution, b=1000, 45 directions). For each volume, 4 shots were simulated with N_e=12 spin echoes and Partial Fourier (PF) = 6/8 along k_z with R_z=5. An additional 110×23×12 calibration shot was simulated as described above. For each shot a 3D-polynomial phase pattern was randomly generated with several phase wraps across the field of view. T2 decay along kz was simulated assuming T2=70ms and inter-echo spacing of 21ms. Complex random noise was added to the signal for an average SNR of 18 at the central k-space line. The reconstruction used 5×5×1 and 3×4×3 GRAPPA kernels for the first and second step respectively. The reference scan was injected in the reconstructed signal after the 1st step. The equivalent acquisition time for real data would be ~5min, compared to 10min with a 2D sequence.

Examples of the randomly generated phase maps are shown in figure 3. Example reconstructed volumes are displayed in figure 4. Without applying the first reconstruction step, the image volumes are heavily ghosted (top left). These artefacts are no longer apparent when applying the proposed method (top right). The difference image (lower right) with the ground truth (lower left) appears as random noise. The average normalized root-mean-square error for all reconstructed volumes was 10.9±2.7%.The proposed multi-shot DW 3D-GRASE acquisition and reconstruction produced DWI volumes free of motion-induced phase artefacts without the need for per-shot navigator echoes, through the introduction of virtual coil image reconstruction in conjunction with a single reference scan. This approach would be particularly useful for high-resolution 3D-DWI, where many shots would be required.