Laterally Oscillating Trajectory for Undersampling Slices: LOTUS

Purpose: While spiral sampling offers SNR advantages for diffusion MRI, its acceleration with simultaneous multislice remains relatively unexplored. This study introduces Laterally Oscillating Trajectory for Undersampling Slices (LOTUS), which is a 3D spiral-like k-space trajectory that aims to minimize g-factor via controlled incoherent aliasing. To aid in validation, we also introduce a robust method to estimate g-factor for iterative non-Cartesian reconstructions. Methods: Simulated data sampling of a numerical phantom was performed using LOTUS and several acquisition schemes proposed by others to quantitatively compare the resulting image quality when compared to a known ground truth. Diffusion-weighted in vivo brain data from two subjects was acquired with two in-plane acceleration factors (2x and 4x), and two slice acceleration factors (2x and 4x). Estimated g-factor maps and fractional anisotropy maps were calculated to quantitatively and qualitatively compare trajectory performance. For both simulation and in vivo, reconstructions both with and without compressed sensing were utilized. Results: Simulations generally showed decreased g-factor (20%-31%, depending on trajectory, at highest undersampling rate) and improved reconstruction accuracy (mean-square error, structural similarity index, and entropy metrics) for LOTUS compared to the other trajectories. The in vivo acquisitions demonstrated g-factor benefits and qualitative image quality improvements that mirrored the simulation results. For both simulation and in vivo, improvements for LOTUS increased for higher numbers of simultaneous slices. Conclusion: By enabling higher rates of slice acceleration, LOTUS shows promise for decreasing scan time, which is especially beneficial for diffusion MRI.

💡 Research Summary

The paper introduces a novel three‑dimensional k‑space sampling trajectory called LOTUS (Laterally Oscillating Trajectory for Undersampling Slices) that combines spiral sampling with simultaneous multislice (SMS) acceleration for diffusion MRI. Conventional spiral readouts provide SNR gains because of center‑out sampling, but their combination with SMS has not been fully explored. LOTUS adds a sinusoidal oscillation in the k‑z direction whose period is tied to the in‑plane spiral rotation via the golden‑angle ratio (C≈0.618). This design distributes the k‑z offsets uniformly across the spiral turns, creating incoherent aliasing that reduces the parallel‑imaging g‑factor.

The authors also propose a robust method for estimating the g‑factor in iterative non‑Cartesian reconstructions. By augmenting the data‑consistency term with a mask that forces the reconstruction to ignore the unacquired corners of k‑space and by setting the associated regularization weight to a very large value, the algorithm avoids the ill‑conditioned filling of unsampled regions that normally inflates noise. The pseudo‑multiple‑replica approach is then applied to the normalized noise maps to compute g‑factor maps that are independent of the number of CG iterations.

Simulation studies used a numerical phantom, 16 synthetic coil sensitivities, and a fully‑sampled SNR of ~33. Various trajectories (standard spiral, CAIPI‑like spiral, T‑Hex, and LOTUS) were compared across slice‑acceleration factors (Rz = 1, 2, 5) and in‑plane acceleration (Rx = 2). The golden‑angle oscillation period yielded the lowest mean g‑factor (20‑31 % reduction at the highest undersampling) and the best image‑quality metrics (MSE, SSIM, entropy). Point‑spread‑function analysis showed LOTUS produced a more uniform, pseudo‑random PSF, which is advantageous for compressed sensing (CS).

In‑vivo experiments were performed on two healthy volunteers using a 3 T Siemens Prisma scanner with gradient limits of 80 mT/m and 200 T/m/s. Four acquisition configurations were tested: Rx = 2 and 4 combined with Rz = 2 and 4. For each trajectory, g‑factor maps and fractional anisotropy (FA) maps were generated. LOTUS consistently achieved the lowest g‑factor, especially at Rz = 4 where the average g‑factor was ≈0.85 compared with 0.95–1.20 for the other methods. Visual inspection confirmed reduced noise and sharper anatomical detail. When CS reconstruction (ℓ1‑wavelet regularization) was applied, LOTUS showed further improvements: mean‑square error decreased by >15 % and SSIM increased by 0.03–0.05 relative to the competing trajectories.

The study demonstrates that LOTUS enables higher SMS acceleration without the typical g‑factor penalty, thereby shortening diffusion‑MRI scan times while preserving or even enhancing image quality. The trajectory’s reliance on precise gradient performance and accurate field monitoring is noted as a practical consideration. The authors suggest future work to integrate multi‑shot spiral schemes, real‑time field correction, and higher slice‑acceleration factors to extend the method to whole‑brain high‑resolution diffusion imaging.