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

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

Multimodality and Nonrigid Image Registration with Application to Diffusion Tensor Imaging

The great challenge in image registration is to devise computationally efficient algorithms for aligning images so that their details overlap accurately. The first problem addressed in this thesis is multimodality medical image registration, which we formulate as an optimization problem in the information-theoretic setting. We introduce a viable and practical image registration method by maximizing a generalized entropic dissimilarity measure using a modified simultaneous perturbation stochastic approximation algorithm. The feasibility of the proposed image registration approach is demonstrated through extensive experiments. The rest of the thesis is devoted to nonrigid medical image registration. We propose an informationtheoretic framework by optimizing a non-extensive entropic similarity measure using the quasi-Newton method as an optimization scheme and cubic B-splines for modeling the nonrigid deformation field between the fixed and moving 3D image pairs. To achieve a compromise between the nonrigid registration accuracy and the associated computational cost, we implement a three-level hierarchical multi-resolution approach in such a way that the image resolution is increased in a coarse to fine fashion. The feasibility and registration accuracy of the proposed method are demonstrated through experimental results on a 3D magnetic resonance data volume and also on clinically acquired 4D computed tomography image data sets. In the same vein, we extend our nonrigid registration approach to align diffusion tensor images for multiple components by enabling explicit optimization of tensor reorientation. Incorporating tensor reorientation in the registration algorithm is pivotal in wrapping diffusion tensor images. Experimental results on diffusion-tensor image registration indicate the feasibility of the proposed approach and a much better performance compared to the affine registration method based on mutual information, not only in terms of registration accuracy in the presence of geometric distortions but also in terms of robustness in the presence of Rician noise

Characterising population variability in brain structure through models of whole-brain structural connectivity

Models of whole-brain connectivity are valuable for understanding neurological function. This thesis seeks to develop an optimal framework for extracting models of whole-brain connectivity from clinically acquired diffusion data. We propose new approaches for studying these models. The aim is to develop techniques which can take models of brain connectivity and use them to identify biomarkers or phenotypes of disease. The models of connectivity are extracted using a standard probabilistic tractography algorithm, modified to assess the structural integrity of tracts, through estimates of white matter anisotropy. Connections are traced between 77 regions of interest, automatically extracted by label propagation from multiple brain atlases followed by classifier fusion. The estimates of tissue integrity for each tract are input as indices in 77x77 ”connectivity” matrices, extracted for large populations of clinical data. These are compared in subsequent studies. To date, most whole-brain connectivity studies have characterised population differences using graph theory techniques. However these can be limited in their ability to pinpoint the locations of differences in the underlying neural anatomy. Therefore, this thesis proposes new techniques. These include a spectral clustering approach for comparing population differences in the clustering properties of weighted brain networks. In addition, machine learning approaches are suggested for the first time. These are particularly advantageous as they allow classification of subjects and extraction of features which best represent the differences between groups. One limitation of the proposed approach is that errors propagate from segmentation and registration steps prior to tractography. This can cumulate in the assignment of false positive connections, where the contribution of these factors may vary across populations, causing the appearance of population differences where there are none. The final contribution of this thesis is therefore to develop a common co-ordinate space approach. This combines probabilistic models of voxel-wise diffusion for each subject into a single probabilistic model of diffusion for the population. This allows tractography to be performed only once, ensuring that there is one model of connectivity. Cross-subject differences can then be identified by mapping individual subjects’ anisotropy data to this model. The approach is used to compare populations separated by age and gender

Methods for improved mapping of brain lesion connectivity

Recent advances over the past two decades in neuroimaging methods have enabled us to map the connectivity of the brain. In parallel, pathophysiological models of brain disease have shifted from an emphasis on understanding pathology in specific brain regions to characterizing disruptions to interconnected neural networks. Nevertheless, these recent methods for mapping brain connectivity are still under development. Every step of the mapping process becomes a potential source for additional error due to noise or artifacts that could impact final analyses. Segmentation, parcellation, registration, and tractography are some of the steps where this occurs. Moreover, mapping the connectivity in a brain lesion is even more susceptible to errors in these steps. In this body of work, I describe multiple new methods for improving the accuracy of mapping lesion connectivity by reducing errors at the tractography stage which is the most error prone stage. First, we develop an approach for directly normalizing streamlines into a template space that avoids performing tractography in the normalized template space, reducing the error of connectomes constructed in the template space with respect to the ground truth native space connectome. Second, we develop a rapid approach for performing shortest path tractography and constructing shortest path probability weighted connectomes which increases the connection specificity relative to local streamline tracking approaches. We then demonstrate how our shortest path tractography approach can be used construct a disconnectome, a connectivity map of the proportion of connections lost due to intersecting a lesion. We then develop a fast, greedy graph-theoretic algorithm that extracts the maximally disconnected subgraph containing brain regions with the greatest shared loss of connectivity. Finally, we demonstrate how combining methods from diffusion based image inpainting and optimal estimation can be used to restore or inpaint corrupted fiber diffusion models in lesioned white matter tissue, enabling tractography and the study of lesion connectivity and modeling of microstructural measures in the patient’s native space

Near-tubular fiber bundle segmentation for diffusion weighted imaging: Segmentation through frame reorientation

This paper proposes a methodology to segment near-tubular fiber bundles from diffusion weighted magnetic resonance images (DW-MRI). Segmentation is simplified by locally reorienting diffusion information based on large-scale fiber bundle geometry. Segmentation is achieved through simple global statistical modeling of diffusion orientation. Utilizing a modification of a recent segmentation approach by Bresson et al. allows for a convex optimization formulation of the segmentation problem, combining orientation statistics and spatial regularization. The approach compares favorably with segmentation by full-brain streamline tractography