Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space

High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures are proposed to summarize such data, and to locally characterize spatial features of the diffusion probability density function (PDF), relying on the geometry of the characteristic function. Summary statistics are defined so that their distributions are, to first-order, both independent of nuisance parameters and also analytically tractable. The dominant direction of the diffusion at a spatial location (voxel) is determined, and a new set of axes are introduced in Fourier space. Variation quantified in these axes determines the local spatial properties of the diffusion density. Nonparametric hypothesis tests for determining whether the diffusion is unimodal, isotropic or multi-modal are proposed. More subtle characteristics of white-matter microstructure, such as the degree of anisotropy of the PDF and symmetry compared with a variety of asymmetric PDF alternatives, may be ascertained directly in the Fourier domain without parametric assumptions on the form of the diffusion PDF. We simulate a set of diffusion processes and characterize their local properties using the newly introduced summaries. We show how complex white-matter structures across multiple voxels exhibit clear ellipsoidal and asymmetric structure in simulation, and assess the performance of the statistics in clinically-acquired magnetic resonance imaging data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS441 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

7T multi-shell hybrid diffusion imaging (HYDI) for mapping brain connectivity in mice

Diffusion weighted imaging (DWI) is widely used to study microstructural characteristics of the brain. High angular resolution diffusion imaging (HARDI) samples diffusivity at a large number of spherical angles, to better resolve neural fibers that mix or cross. Here, we implemented a framework for advanced mathematical analysis of mouse 5-shell HARDI (b=1000, 3000, 4000, 8000, 12000 s/mm^2), also known as hybrid diffusion imaging (HYDI). Using q-ball imaging (QBI) at ultra-high field strength (7 Tesla), we computed diffusion and fiber orientation distribution functions (dODF, fODF) to better detect crossing fibers. We also computed a quantitative anisotropy (QA) index, and deterministic tractography, from the peak orientation of the fODFs. We found that the signal to noise ratio (SNR) of the QA was significantly higher in single and multi-shell reconstructed data at the lower b-values (b=1000, 3000, 4000 s/mm^2) than at higher b-values (b=8000, 12000 s/mm2); the b=1000 s/mm^2 shell increased the SNR of the QA in all multi-shell reconstructions, but when used alone or in <5-shell reconstruction, it led to higher angular error for the major fibers, compared to 5-shell HYDI. Multi-shell data reconstructed major fibers with less error than single-shell data, and was most successful at reducing the angular error when the lowest shell was excluded (b=1000 s/mm2). Overall, high-resolution connectivity mapping with 7T HYDI offers great potential for understanding unresolved changes in mouse models of brain disease

Mapping Topographic Structure in White Matter Pathways with Level Set Trees

Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees---which provide a concise representation of the hierarchical mode structure of probability density functions---offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N=30), we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber tracks and an efficient segmentation of the tracks that has empirical accuracy comparable to standard nonparametric clustering methods. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output

Beyond the Gaussian Model in Diffusion-Weighted Imaging: The Package dti

Diffusion weighted imaging (DWI) is a magnetic resonance (MR) based method to investigate water diffusion in tissue like the human brain. Inference focuses on integral properties of the tissue microstructure. The acquired data are usually modeled using the diffusion tensor model, a three-dimensional Gaussian model for the diffusion process. Since the homogeneity assumption behind this model is not valid in large portion of the brain voxel more sophisticated approaches have been developed. This paper describes the R package dti. The package offers capabilities for the analysis of diffusion weighted MR experiments. Here, we focus on recent extensions of the package, for example models for high angular resolution diffusion weighted imaging (HARDI) data, including Q-ball imaging and tensor mixture models, and fiber tracking. We provide a detailed description of the package structure and functionality. Examples are used to guide the reader through a typical analysis using the package. Data sets and R scripts used are available as electronic supplements

Information-Theoretic Registration with Explicit Reorientation of Diffusion-Weighted Images

We present an information-theoretic approach to the registration of images with directional information, and especially for diffusion-Weighted Images (DWI), with explicit optimization over the directional scale. We call it Locally Orderless Registration with Directions (LORD). We focus on normalized mutual information as a robust information-theoretic similarity measure for DWI. The framework is an extension of the LOR-DWI density-based hierarchical scale-space model that varies and optimizes the integration, spatial, directional, and intensity scales. As affine transformations are insufficient for inter-subject registration, we extend the model to non-rigid deformations. We illustrate that the proposed model deforms orientation distribution functions (ODFs) correctly and is capable of handling the classic complex challenges in DWI-registrations, such as the registration of fiber-crossings along with kissing, fanning, and interleaving fibers. Our experimental results clearly illustrate a novel promising regularizing effect, that comes from the nonlinear orientation-based cost function. We show the properties of the different image scales and, we show that including orientational information in our model makes the model better at retrieving deformations in contrast to standard scalar-based registration.Comment: 16 pages, 19 figure

Probing white-matter microstructure with higher-order diffusion tensors and susceptibility tensor MRI.

Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains

Generalized Richardson-Lucy (GRL) for analyzing multi-shell diffusion MRI data

Spherical deconvolution is a widely used approach to quantify fiber orientation distribution from diffusion MRI data. The damped Richardson-Lucy (dRL) is developed to perform robust spherical deconvolution on single shell diffusion MRI data. While the dRL algorithm could in theory be directly applied to multi-shell data, it is not optimised to model the signal from multiple tissue types. In this work, we introduce a new framework based on dRL - dubbed Generalized Richardson Lucy (GRL) - that uses multi-shell data in combination with user-chosen tissue models to disentangle partial volume effects and increase the accuracy in FOD estimation. The optimal weighting of multi-shell data in the fit and the robustness to noise and partial volume effects of GRL was studied with synthetic data. Subsequently, we investigated the performances of GRL in comparison to dRL on a high-resolution diffusion MRI dataset from the Human Connectome Project and on an MRI dataset acquired at 3T on a clinical scanner. The feasibility of including intra-voxel incoherent motion (IVIM) effects in the modelling was studied on a third dataset. Results of simulations show that GRL can robustly disentangle different tissue types at SNR above 20 and improves the angular accuracy of the FOD estimation. On real data, GRL provides signal fraction maps that are physiologically plausible and consistent between datasets. When considering IVIM effects, high blood pseudo-diffusion fraction is observed in the medial temporal lobe and in the sagittal sinus. In comparison to dRL, GRL provides sharper FODs and less spurious peaks in presence of partial volume effects and results in a better tract termination at the grey/white matter interface or at the outer cortical surface. In conclusion, GRL offers a new modular and flexible framework to perform spherical deconvolution of multi-shell data