Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes

In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The Electrostatic Energy Minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI, was recently generalized to multi-shell schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the Human Connectome Project (HCP). However, EEM does not directly address the goal of optimal sampling, i.e., achieving large angular separation between sampling points. In this paper, we propose a more natural formulation, called Spherical Code (SC), to directly maximize the minimal angle between different samples in single or multiple shells. We consider not only continuous problems to design single or multiple shell sampling schemes, but also discrete problems to uniformly extract sub-sampled schemes from an existing single or multiple shell scheme, and to order samples in an existing scheme. We propose five algorithms to solve the above problems, including an incremental SC (ISC), a sophisticated greedy algorithm called Iterative Maximum Overlap Construction (IMOC), an 1-Opt greedy method, a Mixed Integer Linear Programming (MILP) method, and a Constrained Non-Linear Optimization (CNLO) method. To our knowledge, this is the first work to use the SC formulation for single or multiple shell sampling schemes in dMRI. Experimental results indicate that SC methods obtain larger angular separation and better rotational invariance than the state-of-the-art EEM and GEEM. The related codes and a tutorial have been released in DMRITool.Comment: Accepted by IEEE transactions on Medical Imaging. Codes have been released in dmritool https://diffusionmritool.github.io/tutorial_qspacesampling.htm

Diffusion sampling schemes: A generalized methodology with nongeometric criteria

Producción CientíficaPurpose:The aim of this paper is to show that geometrical criteria for designingmultishellq-space sampling procedures do not necessarily translate into recon-struction matrices with high figures of merit commonly used in the compressedsensing theory. In addition, we show that a well-known method for visitingk-space in radial three-dimensional acquisitions, namely, the Spiral Phyllotaxis,is a competitive initialization for the optimization of our nonconvex objectivefunction.Theory and Methods:We propose the gradient design method WISH (WeIght-ing SHells) which uses an objective function that accounts for weighted dis-tances between gradients withinM-tuples of consecutive shells, withMrangingbetween 1 and the maximum number of shellsS. All theM-tuples share thesame weight�M. The objective function is optimized for a sample of theseweights, using Spiral Phyllotaxis as initialization. State-of-the-art General Elec-trostatic Energy Minimization (GEEM) and Spherical Codes (SC) were used forcomparison. For the three methods, reconstruction matrices of the attenuationsignal using MAP-MRI were tested using figures of merit borrowed from theCompressed Sensing theory (namely, Restricted Isometry Property —RIP— andCoherence); we also tested the gradient design using a geometric criterion basedon Voronoi cells.Results:For RIP and Coherence, WISH got better results in at least one com-bination of weights, whilst the criterion based on Voronoi cells showed anunrelated pattern.Conclusion:The versatility provided by WISH is supported by better results.Optimization in the weight parameter space is likely to provide additionalimprovements. For a practical design with an intermediate number of gradients,our results recommend to carry out the methodology here used to determine theappropriate gradient table.Agencia Estatal de Investigación,(under Grants RTI2018-094569-B-I00,PID2020-115339RB-I00 and TED2021-130090B-I00)ESAOTE, Ltd (Grant/Award Number: 18IQBM

Deterministic diffusion fiber tracking improved by quantitative anisotropy

Diffusion MRI tractography has emerged as a useful and popular tool for mapping connections between brain regions. In this study, we examined the performance of quantitative anisotropy (QA) in facilitating deterministic fiber tracking. Two phantom studies were conducted. The first phantom study examined the susceptibility of fractional anisotropy (FA), generalized factional anisotropy (GFA), and QA to various partial volume effects. The second phantom study examined the spatial resolution of the FA-aided, GFA-aided, and QA-aided tractographies. An in vivo study was conducted to track the arcuate fasciculus, and two neurosurgeons blind to the acquisition and analysis settings were invited to identify false tracks. The performance of QA in assisting fiber tracking was compared with FA, GFA, and anatomical information from T 1-weighted images. Our first phantom study showed that QA is less sensitive to the partial volume effects of crossing fibers and free water, suggesting that it is a robust index. The second phantom study showed that the QA-aided tractography has better resolution than the FA-aided and GFA-aided tractography. Our in vivo study further showed that the QA-aided tractography outperforms the FA-aided, GFA-aided, and anatomy-aided tractographies. In the shell scheme (HARDI), the FA-aided, GFA-aided, and anatomy-aided tractographies have 30.7%, 32.6%, and 24.45% of the false tracks, respectively, while the QA-aided tractography has 16.2%. In the grid scheme (DSI), the FA-aided, GFA-aided, and anatomy-aided tractographies have 12.3%, 9.0%, and 10.93% of the false tracks, respectively, while the QA-aided tractography has 4.43%. The QA-aided deterministic fiber tracking may assist fiber tracking studies and facilitate the advancement of human connectomics. © 2013 Yeh et al

Denoising and fast diffusion imaging with physically constrained sparse dictionary learning

International audienceDiffusion-weighted imaging (DWI) allows imaging the geometry of water diffusion in biological tissues. However, DW images are noisy at high b-values and acquisitions are slow when using a large number of measurements, such as in Diffusion Spectrum Imaging (DSI). This work aims to denoise DWI and reduce the number of required measurements, while maintaining data quality. To capture the structure of DWI data, we use sparse dictionary learning constrained by the physical properties of the signal: symmetry and positivity. The method learns a dictionary of diffusion profiles on all the DW images at the same time and then scales to full brain data. Its performance is investigated with simulations and two real DSI datasets. We obtain better signal estimates from noisy measurements than by applying mirror symmetry through the q-space origin, Gaussian denoising or state-of- the-art non-local means denoising. Using a high-resolution dictionary learnt on another subject, we show that we can reduce the number of images acquired while still generating high resolution DSI data. Using dictionary learning, one can denoise DW images effectively and perform faster acquisitions. Higher b-value acquisitions and DSI techniques are possible with approximately 40 measurements. This opens important perspectives for the connectomics community using DSI

Deep learning‐based method for reducing residual motion effects in diffusion parameter estimation

PURPOSE: Conventional motion-correction techniques for diffusion MRI can introduce motion-level-dependent bias in derived metrics. To address this challenge, a deep learning-based technique was developed to minimize such residual motion effects. METHODS: The data-rejection approach was adopted in which motion-corrupted data are discarded before model-fitting. A deep learning-based parameter estimation algorithm, using a hierarchical convolutional neural network (H-CNN), was combined with motion assessment and corrupted volume rejection. The method was designed to overcome the limitations of existing methods of this kind that produce parameter estimations whose quality depends strongly on a proportion of the data discarded. Evaluation experiments were conducted for the estimation of diffusion kurtosis and diffusion-tensor-derived measures at both the individual and group levels. The performance was compared with the robust approach of iteratively reweighted linear least squares (IRLLS) after motion correction with and without outlier replacement. RESULTS: Compared with IRLLS, the H-CNN-based technique is minimally sensitive to motion effects. It was tested at severe motion levels when 70% to 90% of the data are rejected and when random motion is present. The technique had a stable performance independent of the numbers and schemes of data rejection. A further test on a data set from children with attention-deficit hyperactivity disorder shows the technique can potentially ameliorate spurious group-level difference caused by head motion. CONCLUSION: This method shows great potential for reducing residual motion effects in motion-corrupted diffusion-weighted-imaging data, bringing benefits that include reduced bias in derived metrics in individual scans and reduced motion-level-dependent bias in population studies employing diffusion MRI

A New Monte Carlo Method for Time-Dependent Neutrino Radiation Transport

Monte Carlo approaches to radiation transport have several attractive properties compared to deterministic methods. These include simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are relatively easy to extend to multiple spatial dimensions, which makes them particularly interesting in modeling complex multi-dimensional astrophysical phenomena such as core-collapse supernovae. The aim of this paper is to explore Monte Carlo methods for modeling neutrino transport in core-collapse supernovae. We generalize the implicit Monte Carlo photon transport scheme of Fleck & Cummings and gray discrete-diffusion scheme of Densmore et al. to energy-, time-, and velocity-dependent neutrino transport. Using our 1D spherically-symmetric implementation, we show that, similar to the photon transport case, the implicit scheme enables significantly larger timesteps compared with explicit time discretization, without sacrificing accuracy, while the discrete-diffusion method leads to significant speed-ups at high optical depth. Our results suggest that a combination of spectral, velocity-dependent, implicit Monte Carlo and discrete-diffusion Monte Carlo methods represents an attractive approach for use in neutrino radiation-hydrodynamics simulations of core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport

A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations

Recent work by McClarren & Hauck [29] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the three-dimensional (3D) case and find that all of the advantages of the filtering approach identified in 2D are present also in the 3D case. We reformulate the filter operation in a way that is independent of the timestep and of the spatial discretization. We also explore different second- and fourth-order filters and find that the second-order ones yield significantly better results. Overall, our findings suggest that the filtered spherical harmonics approach represents a very promising method for 3D radiation transport calculations.Comment: 29 pages, 13 figures. Version matching the one in Journal of Computational Physic