Browsing by Subject "Diffusion MRI"

Now showing 1 - 3 of 3
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    Approaches to Anatomical and Functional Brain Connectivity Analysis with Applications to Adolescent Major Depressive Disorder
    (2018-09) Chu, Shu-Hsien
    Magnetic Resonance Imaging (MRI) has been extensively utilized in brain studies. Diffusion MRI (dMRI) measures brain microstructure and functional MRI (fMRI) reveals neural activity in vivo. Neuroimaging studies can be performed from various spatial perspectives such as voxel, region, connectivity between a pair of regions, and connectome which is a network consisting of brain regions as nodes and connectivity as edges. In a brain, information is processed by the combined interactions of neurons, ensembles of neurons, and collaborating brain regions, which form a special (small-world) topological structure. Network analysis offers tools for characterizing and studying the topological structure of brain networks. In addition to the network analysis established using fMRI or dMRI separately, joint analysis has shown favorable benefits in leveraging the advantages from dMRI and fMRI. However, it is difficult to combine information from dMRI and fMRI and create a joint network. This thesis presents solutions for three problems based on an interdisciplinary framework combining domain knowledge, neuroimaging techniques, signal processing, graph theory, machine learning and statistical analysis. First, a joint model is proposed to create function-specific structural networks, i.e., joint networks, from both dMRI and fMRI simultaneously. Function-specific structural networks inherit the detailed neuron connectome from dMRI and the functional specificity from fMRI, which potentially can improve the statistical power and the limitation of small sample size in clinical applications. Secondly, anatomical features including connectivity and network topological measures established from dMRI data are analyzed using statistical tools, along-track analysis and machine learning techniques to reveal alterations in brain network for adolescents with major depressive disorder (MDD). Last, wavelet-filtered functional connectivity and network topology features are extracted from fMRI data to characterize the correlation of neural activity between brain regions. The functional features are analyzed using statistical tools and false discovery rate control to discover neurological responders to selective serotonin reuptake inhibitors (SSRIs) and neurological correlations with clinical improvement in treating depression. The identified features add new knowledge to the current understanding of the underlying mechanisms of adolescent MDD and the responses to SSRIs and may be further developed and utilized in monitoring disease progression and effectiveness of therapy. Applications in MDD show how network analysis, signal processing and machine learning are utilized to reveal spatial, temporal and frequency information in brain activity, connectivity and network topology.
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    A generalized CSA-ODF model for fiber orientation mapping.
    (2012-10) Kamath, Amith J.
    This work involves advances in modeling and estimating white matter fiber orientations for use in tractography studies and axonal microstructure analysis in the human brain. We make use of preferential movement of water along axon fibers rather than across it's membrane as an indirect measure using MRI data acquisition sensitized to diffusion. Over the past decade, several mathematically elegant models have been proposed, with varying acceptance levels from the clinical fraternity. With practical feasibility in mind, the trade-offs between resolution, acquisition time and SNR make the optimization of data capture protocols ever more crucial. We focus on generalizing the current state-of-art models to allow for any acquisition scheme, and go on to understand how the acquisition parameters affect the results. The Constant Solid Angle -Orientation Distribution Function (CSA-ODF) model provides a vital correction in the Q-ball method for High Angular Resolution Diffusion Imaging (HARDI) data. The HARDI data is decomposed on a modified Spherical Harmonic (SH) basis, due to which the otherwise necessary 3-D inverse Fourier Transform can be easily estimated using a linear approximation of the Funk Radon Transform (FRT) on a single shell. This results in a simple linear-least-squares approximation, prone to over-fitting errors and low SNR. We explore an adaptive regularization scheme to generalize well for the inverse problem of interpolating the q-space data. We use a bi-exponential radial signal decay model, which uses more information about the axonal microstructure than the single-shell approximation. The 'staggered' acquisition scheme increases the angular spread of samples and allows for higher angular resolution of the fiber orientations. A comprehensive analysis of the reconstruction is shown on synthetic data, and the best parameters for acquisition is demonstrated. The optimal level of b-value, number of gradient directions, order of SH decomposition and interpolation is derived from experiments, and results on a brain data set is shown to validate the method. We hope that this generalization of the CSA-ODF algorithm is going to provide better models of the diffusion process in MR images, and prove to be a guide for setting up the acquisition protocols for the Human Connectome Project and other future studies.
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    Geometric and Optimization Methods for Diffusion Magnetic Resonance Imaging
    (2017-08) Farooq, Hamza
    This thesis presents novel mathematical and computational methods aimed at enhancing and improving brain tissue structural imaging techniques that are based on diffusion Magnetic Resonance Imaging (dMRI). The most commonly used dMRI technique is Diffusion Tensor Imaging (DTI), which models water diffusion via a Gaussian pattern and estimates the corresponding covariance, also known as diffusion tensor. DTI forms the basis of brain structural connectivity methods like tractography and sub-cortical region parcellation, and thus provides useful markers for brain white matter integrity. Other, recently proposed dMRI techniques rely on modeling water diffusion in intra-axonal and extra-axonal spaces separately. Thereby, these so-called multi-compartment models hold the promise to provide detailed tissue microstructure information and to identify markers that may be specific to particular tissue development/diseases. In this thesis we address key mathematical challenges encountered by DTI, as well as by these newly proposed dMRI techniques, that pertain to recovering more detailed microstructure information. We begin by focusing on DTI and present novel geometrical methods to improve DTI analysis (Chapters 3, 4, and 5). In particular, (i) we utilize the mathematical theory of Optimal Mass Transport to improve brain parcellation by comparing sub-cortical regions connectivity profiles and compute their corresponding geometric ``average'' connectivity profiles, (ii) we introduce Ricci flow applied to diffusion tensor fields to enhance feature extraction, and finally (iii) we introduce a notion of discrete Ricci curvature in brain connectivity networks as a novel nodal measure to detect critical regions (nodes) of the structural brain networks. This notion of node curvature can be used to identify changes in brain network structure due to disease/development as it supplements information that can be obtained by other conventional network nodal measures. We then study multi-compartment dMRI models, and present a novel model fitting method to such tissue models (Chapter 6). Our proposed method is generic to all multicompartment models and enables for the first time dMRI-imaging in multiple fiber orientations and fiber-crossings situations. In addition to potential improvements in imaging technology, we hope that the advances presented in this work will contribute to the diagnosis and treatment of neurological disorders.