Non-parametric graphnet-regularized representation of dMRI in space and time

Effective representation of the four-dimensional diffusion MRI signal - varying over three-dimensional q-space and diffusion time tau - is a sought-after and still unsolved challenge in diffusion MRI (dMRI). We propose a functional basis approach that is specifically designed to represent the dMRI signal in this q tau-space. Following recent terminology, we refer to our q tau-functional basis as "q tau-dMRI". q tau-dMRI can be seen as a time-dependent realization of q-space imaging by Paul Callaghan and colleagues. We use GraphNet regularization - imposing both signal smoothness and sparsity - to drastically reduce the number of diffusion-weighted images (DWIs) that is needed to represent the dMRI signal in the q tau-space. As the main contribution, q tau-dMRI provides the framework to - without making biophysical assumptions - represent the q tau-space signal and estimate time-dependent q-space indices (q tau-indices), providing a new means for studying diffusion in nervous tissue. We validate our method on both in-silico generated data using Monte-Carlo simulations and an in-vivo test-retest study of two C57Bl6 wild-type mice, where we found good reproducibility of estimated q tau-index values and trends. In the hopes of opening up new tau-dependent venues of studying nervous tissues, q tau-dMRI is the first of its kind in being specifically designed to provide open interpretation of the q tau-diffusion signal. (C) 2017 Elsevier B.V. All rights reserved.