Congrats to Yonas for his successful PhD thesis defense
March 22, 2012
Congratulations to Yonas Weldeselassie for his successful thesis defense! Details of his thesis below.
Title: TENSOR BASED ANALYSIS OF DIFFUSION WEIGHTED MAGNETIC RESONANCE IMAGES
Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) is a non-invasive and in vivo medical imaging technique that allows neural tissue architecture to be probed at a microscopic scale. This is possible due to the diffusion of hydrogen atoms within water molecules in the imaging body; thus capturing the microstructure of the underlying tissues. DW-MRI adds to conventional MRI the capability of measuring this diffusion of water molecules by applying strong magnetic field along several gradient directions in order to measure the apparent diffusion coefficient along those directions.
In this thesis, we look at modeling diffusion of water molecules with Cartesian Tensors: a model known as Diffusion Tensor Magnetic Resonance Imaging (DT-MRI). We begin with second order tensor model which results in an image where at each voxel the preferred direction of water diffusion is locally modeled by a second order 3x3 symmetric positive definite matrix whose coefficients are estimated from the DW-MR data. After briefly reviewing anisotropy and similarity measures of second order tensors, we extend these ideas to develop a novel anisotropy measure. Tensor similarity measures are then used to extend scalar image segmentation algorithms in order to segment tensor images. Next, we look at fiber tractography, a mechanism to non-invasively study the three-dimensional architecture of white matter tracts in the central nervous system, and develop an adaptive seeding algorithm using tensor similarity measures. The concept of fiber tractography is then used for clinical application to investigate various features of white matter fiber tracts extracted from DT-MR images in the cortico-striatal region of the brain in control and Parkinson's disease subjects. Finally, we investigate the limitations of second order tensor model and extend the model to higher order tensors in order to correctly depict crossing, fanning, splitting and merging fiber tracts. In particular, we develop a new technique to model fiber orientation distribution functions using higher order tensors. In attempting to extend the rich set of algorithms developed for second order tensors, we also derive a new anisotropy measure derived directly from fiber orientation distribution functions.
Ph.D. Examining Committee:
Dr. M. Stella Atkins, Senior Supervisor
Dr. Mirza Faisal Beg, Supervisor
Dr. Manfred Trummer, Supervisor
Dr. Torsten Moller, Internal Examiner
Dr. Kaleem Siddiqi, External Examiner
Dr. Anoop Sarkar, Chair