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THEORY AND SIMULATION OF DIFFUSION MAGNETIC RESONANCE
IMAGING ON BRAIN'S WHITE MATTER
by
Shahryar Karimi-Ashtiani
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2010
Copyright 2010 Shahryar Karimi-Ashtiani
Object Description
| Title | Theory and simulation of diffusion magnetic resonance imaging on brain's white matter |
| Author | Karimi-Ashtiani, Shahryar |
| Author email | karimias@usc.edu; shahryar.karimi@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Electrical Engineering |
| School | Viterbi School of Engineering |
| Date submitted | 2010 |
| Date published | 2012-08-09 |
| Advisor (committee chair) | Kuo, C.-C. Jay |
| Advisor (committee member) |
Leahy, Richard Singh, Manbir |
| Abstract | Diffusion MRI (D-MRI) has opened a new front for uncovering the convoluted structure of the central nervous system by providing capability for the non-invasive identification of white matter tract geometries in the brain. One of the major open issues in fully extending this technology to the clinical domain is the lack of in vivo validation of the results, which makes it diffcult to have objective comparisons of different D-MRI techniques. To this end, the application of simulated data from known ground truths appears to be the second best choice. It is well understood that, this imaging modality is characterized by the shape of the self-diffusion (SD) profile within the brain fibers. The previous methods for the quantification of the SD process in the white matter environments suffer from the lack of enough generality or solution precision, and often impose excessive computational complexity, which limits their full extent of applicability. The contributions of this research are two folds: 1) the development of a new numerical method to compute the self-diffusion SD profile and 2) the provision of a generic framework for reconstruction of diffusion MR images under imperfect imaging conditions.; In the first part of this thesis, a numerical paradigm based on the finite element methods (FEM) for finding the solution of SD partial differential equation (PDE) in the white matter environment is proposed. The standard FEM is incapable of accommodating the boundary conditions of the PDE on the interfaces of different white matter materials. Theoretical constraints to modify the FEM are investigated such that it becomes applicable to the problem of interest. Our method is not confined to any special geometry and virtually can handle any microscopic models of white matters. One of the highlights of the developed method is addressing the effect of partial permeability of the cell membrane. Also, a self-validation technique is proposed to guarantee the accuracy of the solution. In the meantime, the aggregate SD profile of the MRI voxel is analytically derived to show the dependency of the macroscopic behavior of the diffusion at the macroscopic level, as a function of the contained tissue microscopic parameters. Several simulation results are provided to showcase the effectiveness of our method.; In the second part of this thesis, a generic theoretical framework for reconstruction of MR images, which factors most of the imaging artifacts due to true values of imaging conditions, is developed. It is worthwhile to point out that, on the simulation front, the previous D-MRI reconstruction formulations were derived under ideal imaging conditions. However, in reality, the actual values of imaging parameters leave the available reconstruction techniques inapplicable. The severe impacts of those parameters on the quality of the white matter mapping from the D-MRI data necessitate the extension of existing methods to include them. For example, the existing methods cannot accommodate spatially varying T1 and T2 parameters, a condition very common in the white matter tissues. We provide an analytical derivation for such conditions, and show that, under these situations, the k-space signal and the effective spin magnet density will no longer form a Fourier transform pair. Hence, the arising question is the interpretation of the image under spatially varying relaxation parameters, which is the time average of the spin density during the sampling period. Besides, under long data acquisition periods, the spin magnets experience different material by having diffusion motion, which urges to finding effective values for those parameters. We provide a formulation for those quantities as functions of the parameters of the composing materials. In reality, the D-MRI data acquisitions are performed with a long diffusion gradient, where spin phase encodings also occur during the wide pulses. This requires the quantification of the spin magnet motions in the white matter environment. This problem is addressed analytically, and it is shown that the change in the reconstruction formulation appears in the form of modification in the q-space vector. |
| Keyword | brain imaging; white matter; MRI |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3353 |
| Rights | Karimi-Ashtiani, Shahryar |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-KarimiAshtiani-3752 |
| Archival file | uscthesesreloadpub_Volume51/etd-KarimiAshtiani-3752.pdf |
Description
| Title | Page 1 |
| Full text | THEORY AND SIMULATION OF DIFFUSION MAGNETIC RESONANCE IMAGING ON BRAIN'S WHITE MATTER by Shahryar Karimi-Ashtiani A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) August 2010 Copyright 2010 Shahryar Karimi-Ashtiani |
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