Hybrid Diffusion Imaging (HYDI) was one of the first attempts to use multi-shell samplings of the q-space to infer diffusion properties beyond Diffusion Tensor Imaging (DTI) or High Angular ResolutionDiffusion Imaging (HARDI). HYDI was intended as a flexible protocol embedding both DTI (for lower b-values) and HARDI (for higher b-values) processing, as well as Diffusion Spectrum Imaging (DSI) when the entire data set was exploited. In the latter case, the spherical sampling of the q-space is re-gridded by interpolation to a Cartesian lattice whose extent covers the range of acquired b-values, hence being acquisition-dependent. The Discrete Fourier Transform (DFT) is afterwards used to compute the corresponding Cartesian sampling of the Ensemble Average Propagator (EAP) in an entirely non-parametric way. From this lattice, diffusion markers such as the Return To Origin Probability (RTOP) or the Mean Squared Displacement (MSD) can be numerically estimated.

We aim at re-formulating this scheme by means of a Fourier Transform encoding matrix that eliminates the need for q-space re-gridding at the same time it preserves the non-parametric nature of HYDI-DSI. The encoding matrix is adaptively designed at each voxel according to the underlying DTI approximation, so that an optimal sampling of the EAP can be pursued without being conditioned by the particular acquisition protocol. The estimation of the EAP is afterwards carried out as a regularized Quadratic Programming (QP) problem, which allows to impose positivity constraints that cannot be trivially embedded within the conventional HYDI-DSI. We demonstrate that the definition of the encoding matrix in the adaptive space allows to analytically (as opposed to numerically) compute several popular descriptors of diffusion with the unique source of error being the cropping of high frequency harmonics in the Fourier analysis of the attenuation signal. They include not only RTOP and MSD, but also Return to Axis/Plane Probabilities (RTAP/RTPP), which are defined in terms of specific spatial directions and are not available with the former HYDI-DSI. We report extensive experiments that suggest the benefits of our proposal in terms of accuracy, robustness and computational efficiency, especially when only standard, non-dedicated q-space samplings are available.

Purpose To accurately estimate the partial volume fraction of free water in the white matter from diffusion MRI acquisitions not demanding strong sensitizing gradients and/or large collections of different b-values. Data sets considered comprise 32-64 gradients near plus 6 gradients near . Theory and Methods The spherical means of each diffusion MRI set with the same b-value are computed. These means are related to the inherent diffusion parameters within the voxel (free- and cellular-water fractions; cellular-water diffusivity), which are solved by constrained nonlinear least squares regression. Results The proposed method outperforms those based on mixtures of two Gaussians for the kind of data sets considered. W.r.t. the accuracy, the former does not introduce significant biases in the scenarios of interest, while the latter can reach a bias of 5\%{\textendash}7\% if fiber crossings are present. W.r.t. the precision, a variance near , compared to 15\%, can be attained for usual configurations. Conclusion It is possible to compute reliable estimates of the free-water fraction inside the white matter by complementing typical DTI acquisitions with few gradients at a lowb-value. It can be done voxel-by-voxel, without imposing spatial regularity constraints.

}, keywords = {diffusion MRI, free water, spherical means, white matter}, doi = {https://doi.org/10.1002/mrm.28997}, author = {Antonio Trist{\'a}n-Vega and Guillem Par{\'\i}s and Rodrigo de Luis-Garc{\'\i}a and Santiago Aja-Fern{\'a}ndez} }