Spherical means-based free-water volume fraction from diffusion MRI increases non-linearly with age in the white matter of the healthy human brain.

The term free-water volume fraction (FWVF) refers to the signal fraction that could be found as the cerebrospinal fluid of the brain, which has been demonstrated as a sensitive measure that correlates with cognitive performance and various neuropathological processes. It can be quantified by properly fitting the isotropic component of the magnetic resonance (MR) signal in diffusion-sensitized sequences. Using N=287 healthy subjects (178F/109M) aged 25-94, this study examines in detail the evolution of the FWVF obtained with the spherical means technique from multi-shell acquisitions in the human brain white matter across the adult lifespan, which has been previously reported to exhibit a positive trend when estimated from single-shell data using the bi-tensor signal representation. We found evidence of a noticeably non-linear gain after the sixth decade of life, with a region-specific variate and varying change rate of the spherical means-based multi-shell FWVF parameter with age, at the same time, a heteroskedastic pattern across the adult lifespan is suggested. On the other hand, the FW corrected diffusion tensor imaging (DTI) leads to a region-dependent flattened age-related evolution of the mean diffusivity (MD) and fractional anisotropy (FA), along with a considerable reduction in their variability, as compared to the studies conducted over the standard (single-component) DTI. This way, our study provides a new perspective on the trajectory-based assessment of the brain and explains the conceivable reason for the variations observed in FA and MD parameters across the lifespan with previous studies under the standard diffusion tensor imaging.

Diffusion sampling schemes: A generalized methodology with nongeometric criteria.

PURPOSE: The aim of this paper is to show that geometrical criteria for designing multishell q $$ q $$ -space sampling procedures do not necessarily translate into reconstruction matrices with high figures of merit commonly used in the compressed sensing theory. In addition, we show that a well-known method for visiting k-space in radial three-dimensional acquisitions, namely, the Spiral Phyllotaxis, is a competitive initialization for the optimization of our nonconvex objective function. THEORY AND METHODS: We propose the gradient design method WISH (WeIghting SHells) which uses an objective function that accounts for weighted distances between gradients within M-tuples of consecutive shells, with M $$ M $$ ranging between 1 and the maximum number of shells S $$ S $$ . All the M $$ M $$ -tuples share the same weight ω M $$ {\omega}_M $$ . The objective function is optimized for a sample of these weights, using Spiral Phyllotaxis as initialization. State-of-the-art General Electrostatic Energy Minimization (GEEM) and Spherical Codes (SC) were used for comparison. For the three methods, reconstruction matrices of the attenuation signal using MAP-MRI were tested using figures of merit borrowed from the Compressed Sensing theory (namely, Restricted Isometry Property -RIP- and Coherence); we also tested the gradient design using a geometric criterion based on Voronoi cells. RESULTS: For RIP and Coherence, WISH got better results in at least one combination of weights, whilst the criterion based on Voronoi cells showed an unrelated pattern. CONCLUSION: The versatility provided by WISH is supported by better results. Optimization in the weight parameter space is likely to provide additional improvements. For a practical design with an intermediate number of gradients, our results recommend to carry out the methodology here used to determine the appropriate gradient table.

Efficient estimation of propagator anisotropy and non-Gaussianity in multishell diffusion MRI with micro-structure adaptive convolution kernels and dual Fourier integral transforms.

PURPOSE: We seek to reformulate the so-called Propagator Anisotropy (PA) and Non-Gaussianity (NG), originally conceived for the Mean Apparent Propagator diffusion MRI (MAP-MRI), to the Micro-Structure adaptive convolution kernels and dual Fourier Integral Transforms (MiSFIT). These measures describe relevant normalized features of the Ensemble Average Propagator (EAP). THEORY AND METHODS: First, the indices, which are defined as the EAP's dissimilarity from an isotropic (PA) or a Gaussian (NG) one, are analytically reformulated within the MiSFIT framework. Then a comparison between the resulting maps is drawn by means of a visual analysis, a quantitative assessment via numerical simulations, a test-retest study across the MICRA dataset (6 subjects scanned five times) and, finally, a computational time evaluation. RESULTS: Findings illustrate the visual similarity between the indices computed with either technique. Evaluation against synthetic ground truth data, however, demonstrates MiSFIT's improved accuracy. In addition, the test-retest study reveals MiSFIT's higher degree of reliability in most of white matter regions. Finally, the computational time evaluation shows MiSFIT's time reduction up to two orders of magnitude. CONCLUSIONS: Despite being a direct development on the MAP-MRI representation, the PA and the NG can be reliably and efficiently computed within MiSFIT's framework. This, together with the previous findings in the original MiSFIT's article, could mean the difference that definitely qualifies diffusion MRI to be incorporated into regular clinical settings.

Accurate free-water estimation in white matter from fast diffusion MRI acquisitions using the spherical means technique.

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 b=1000s/mm2 plus ∼ 6 gradients near b=500s/mm2 . 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%-7% if fiber crossings are present. W.r.t. the precision, a variance near 10% , 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.

HYDI-DSI revisited: Constrained non-parametric EAP imaging without q-space re-gridding.

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 Resolution Diffusion 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.

Anisotropy measure from three diffusion-encoding gradient directions.

We propose a method that can provide information about the anisotropy and orientation of diffusion in the brain from only 3 orthogonal gradient directions without imposing additional assumptions. The method is based on the Diffusion Anisotropy (DiA) that measures the distance from a diffusion signal to its isotropic equivalent. The original formulation based on a Spherical Harmonics basis allows to go down to only 3 orthogonal directions in order to estimate the measure. In addition, an alternative simplification and a color-coding representation are also proposed. Acquisitions from a publicly available database are used to test the viability of the proposal. The DiA succeeded in providing anisotropy information from the white matter using only 3 diffusion-encoding directions. The price to pay for such reduced acquisition is an increment in the variability of the data and a subestimation of the metric on those tracts not aligned with the acquired directions. Nevertheless, the calculation of anisotropy information from DMRI is feasible using fewer than 6 gradient directions by using DiA. The method is totally compatible with existing acquisition protocols, and it may provide complementary information about orientation in fast diffusion acquisitions.