Multi-Spherical Diffusion MRI: Exploring Diffusion Time Using Signal Sparsity

Effective representation of the diffusion signal’s dependence on diffusion time is a sought-after, yet still unsolved, challenge in diffusion MRI (dMRI). We propose a functional basis approach that is specifically designed to represent the dMRI signal in this four-dimensional space – varying over gradient strength, direction and diffusion time. In particular, we provide regularization tools imposing signal sparsity and signal smoothness to drastically reduce the number of measurements we need to probe the properties of this multi-spherical space. We illustrate a novel application of our approach, which is the estimation of time-dependent q-space indices, on both synthetic data generated using Monte-Carlo simulations and in vivo data acquired from a C57Bl6 wild-type mouse. In both cases, we find that our regularization approach stabilizes the signal fit and index estimation as we remove samples, which may bring multi-spherical diffusion MRI within the reach of clinical application.