Constrained estimation of rotational invariants of the cumulant expansion (RICE) for rapid tensor-valued diffusion MRI

Abstract

Purpose: To complement 1.5-minute measurements of common tensor-valued diffusion MRI (dMRI) markers with rapid constrained fitting. Methods: Fast dMRI protocols for obtaining rotational invariants of the cumulant expansion (RICE) were paired with constrained weighted linear least squares (CWLLS) to stabilize the more fragile WLLS fit. A compact constraint set was formulated, including a novel mean-dependent upper bound on total diffusional variance. Evaluation used diffusion tensor distribution (DTD) simulations, healthy-volunteer data with a resolution-dependent SNR experiment, and a glioma patient dataset. A 5-minute q-space trajectory imaging (QTI) protocol served as a reference. Results: Across experiments, CWLLS reduced unphysical estimates and fit outliers in parameters such as microscopic FA and isotropic diffusivity variance. In simulations, it narrowed error distributions most clearly in the CSF-dominant case, while some metrics showed a bias-variance trade-off. In vivo, CWLLS removed negative variance estimates, truncated out-of-bounds tails, and reduced artifacts in fluid-contaminated voxels while preserving anatomical contrast. It also retained more stable maps than WLLS at higher resolution, although both estimators degraded in the lowest-SNR setting. Notably, the new mean-dependent variance bound was violated in 15.4% of voxels in the patient dataset, accounting for nearly half of the 32.7% that violated at least one constraint. Healthy-volunteer benchmarking showed that CWLLS completed in under 30 seconds. The constrained QTI fit required 72 minutes, making CWLLS 160 times faster. Conclusion: CWLLS for fast RICE yielded high-quality parameter maps at an online-ready computational cost. This may enhance the reliability of dMRI tissue characterization and strengthen the path toward clinical translation.