Diffeomorphic Metric Mapping of High Angular Resolution Diffusion Imaging based on Riemannian Structure of Orientation Distribution Functions

In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. To this end, we first review the Riemannian manifold of ODFs. We then define the reorientation of an ODF when an affine transformation is applied and subsequently, define the diffeomorphic group action to be applied on the ODF based on this reorientation. We incorporate the Riemannian metric of ODFs for quantifying the similarity of two HARDI images into a variational problem defined under the large deformation diffeomorphic metric mapping (LDDMM) framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm

Voxel-wise comparisons of cellular microstructure and diffusion-MRI in mouse hippocampus using 3D Bridging of Optically-clear histology with Neuroimaging Data (3D-BOND)

A key challenge in medical imaging is determining a precise correspondence between image properties and tissue microstructure. This comparison is hindered by disparate scales and resolutions between medical imaging and histology. We present a new technique, 3D Bridging of Optically-clear histology with Neuroimaging Data (3D-BOND), for registering medical images with 3D histology to overcome these limitations. Ex vivo 120 × 120 × 200 μm resolution diffusion-MRI (dMRI) data was acquired at 7 T from adult C57Bl/6 mouse hippocampus. Tissue was then optically cleared using CLARITY and stained with cellular markers and confocal microscopy used to produce high-resolution images of the 3D-tissue microstructure. For each sample, a dense array of hippocampal landmarks was used to drive registration between upsampled dMRI data and the corresponding confocal images. The cell population in each MRI voxel was determined within hippocampal subregions and compared to MRI-derived metrics. 3D-BOND provided robust voxel-wise, cellular correlates of dMRI data. CA1 pyramidal and dentate gyrus granular layers had significantly different mean diffusivity (p > 0.001), which was related to microstructural features. Overall, mean and radial diffusivity correlated with cell and axon density and fractional anisotropy with astrocyte density, while apparent fibre density correlated negatively with axon density. Astrocytes, axons and blood vessels correlated to tensor orientation

Bayesian Estimation of White Matter Atlas from High Angular Resolution Diffusion Imaging

We present a Bayesian probabilistic model to estimate the brain white matter atlas from high angular resolution diffusion imaging (HARDI) data. This model incorporates a shape prior of the white matter anatomy and the likelihood of individual observed HARDI datasets. We first assume that the atlas is generated from a known hyperatlas through a flow of diffeomorphisms and its shape prior can be constructed based on the framework of large deformation diffeomorphic metric mapping (LDDMM). LDDMM characterizes a nonlinear diffeomorphic shape space in a linear space of initial momentum uniquely determining diffeomorphic geodesic flows from the hyperatlas. Therefore, the shape prior of the HARDI atlas can be modeled using a centered Gaussian random field (GRF) model of the initial momentum. In order to construct the likelihood of observed HARDI datasets, it is necessary to study the diffeomorphic transformation of individual observations relative to the atlas and the probabilistic distribution of orientation distribution functions (ODFs). To this end, we construct the likelihood related to the transformation using the same construction as discussed for the shape prior of the atlas. The probabilistic distribution of ODFs is then constructed based on the ODF Riemannian manifold. We assume that the observed ODFs are generated by an exponential map of random tangent vectors at the deformed atlas ODF. Hence, the likelihood of the ODFs can be modeled using a GRF of their tangent vectors in the ODF Riemannian manifold. We solve for the maximum a posteriori using the Expectation-Maximization algorithm and derive the corresponding update equations. Finally, we illustrate the HARDI atlas constructed based on a Chinese aging cohort of 94 adults and compare it with that generated by averaging the coefficients of spherical harmonics of the ODF across subjects

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

Neurite imaging reveals microstructural variations in human cerebral cortical gray matter

We present distinct patterns of neurite distribution in the human cerebral cortex using diffusion magnetic resonance imaging (MRI). We analyzed both high-resolution structural (T1w and T2w images) and diffusion MRI data in 505 subjects from the Human Connectome Project. Neurite distributions were evaluated using the neurite orientation dispersion and density imaging (NODDI) model, optimized for gray matter, and mapped onto the cortical surface using a method weighted towards the cortical mid-thickness to reduce partial volume effects. The estimated neurite density was high in both somatosensory and motor areas, early visual and auditory areas, and middle temporal area (MT), showing a strikingly similar distribution to myelin maps estimated from the T1w/T2w ratio. The estimated neurite orientation dispersion was particularly high in early sensory areas, which are known for dense tangential fibers and are classified as granular cortex by classical anatomists. Spatial gradients of these cortical neurite properties revealed transitions that colocalize with some areal boundaries in a recent multi-modal parcellation of the human cerebral cortex, providing mutually supportive evidence. Our findings indicate that analyzing the cortical gray matter neurite morphology using diffusion MRI and NODDI provides valuable information regarding cortical microstructure that is related to but complementary to myeloarchitecture

Microstructural Alterations in Hippocampal Subfields Mediate Age-Related Memory Decline in Humans.

Aging, even in the absence of clear pathology of dementia, is associated with cognitive decline. Neuroimaging, especially diffusion-weighted imaging, has been highly valuable in understanding some of these changes in live humans, non-invasively. Traditional tensor techniques have revealed that the integrity of the fornix and other white matter tracts significantly deteriorates with age, and that this deterioration is highly correlated with worsening cognitive performance. However, traditional tensor techniques are still not specific enough to indict explicit microstructural features that may be responsible for age-related cognitive decline and cannot be used to effectively study gray matter properties. Here, we sought to determine whether recent advances in diffusion-weighted imaging, including Neurite Orientation Dispersion and Density Imaging (NODDI) and Constrained Spherical Deconvolution, would provide more sensitive measures of age-related changes in the microstructure of the medial temporal lobe. We evaluated these measures in a group of young (ages 20-38 years old) and older (ages 59-84 years old) adults and assessed their relationships with performance on tests of cognition. We found that the fiber density (FD) of the fornix and the neurite density index (NDI) of the fornix, hippocampal subfields (DG/CA3, CA1, and subiculum), and parahippocampal cortex, varied as a function of age in a cross-sectional cohort. Moreover, in the fornix, DG/CA3, and CA1, these changes correlated with memory performance on the Rey Auditory Verbal Learning Test (RAVLT), even after regressing out the effect of age, suggesting that they were capturing neurobiological properties directly related to performance in this task. These measures provide more details regarding age-related neurobiological properties. For example, a change in fiber density could mean a reduction in axonal packing density or myelination, and the increase in NDI observed might be explained by changes in dendritic complexity or even sprouting. These results provide a far more comprehensive view than previously determined on the possible system-wide processes that may be occurring because of healthy aging and demonstrate that advanced diffusion-weighted imaging is evolving into a powerful tool to study more than just white matter properties