New Algorithms for Local and Global Fiber Tractography in Diffusion-Weighted Magnetic Resonance Imaging

by Helen Schomburg
Doctoral thesis
Date of Examination:2017-09-29
Date of issue:2017-11-28
Advisor:Prof. Dr. Thorsten Hohage
Referee:Prof. Dr. Thorsten Hohage
Referee:Prof. Dr. Jens Frahm
Persistent Address: http://dx.doi.org/10.53846/goediss-6602

 

 

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Abstract

English

Fiber tractography based on diffusion-weighted magnetic resonance imaging is to date the only method for the three-dimensional visualization of nerve fiber bundles in the living human brain noninvasively. However, various existing methods suffer from reconstructing anatomically implausible fiber tracks due to exclusively local treatment of the input data. In this thesis, we develop improved tractography strategies which yield an increased proportion of anatomically correct tracks. We present a novel fiber orientation distribution function (ODF) based semi-local streamline approach which includes information of neighboring regions derived from a Bayesian model. From this setting, we derive both a deterministic and a probabilistic tracking algorithm. Compared to fiber tracking methods that rely only on the local ODF, the proposed algorithms prove more robust in the presence of noise and partial volume effects. Tests and comparisons to state-of-the-art methods on data obtained from computer simulations and on MR scans of diffusion phantoms and of a human brain in vivo demonstrate the effectiveness of our new methods. A global tractography approach which seeks to filter out invalid tracks in a post-processing step by solving a convex optimization problem with l1-norm regularization is introduced in the article by Daducci et al. (2015). In this thesis, we derive an improved version of this method by adding Sobolev-norm regularization terms. We solve the resulting optimization problem using the alternating direction method of multipliers (ADMM) and develop strategies for efficient computation based on dimension reduction using truncated singular value decomposition. Qualitative results show the applicability of the algorithm to large in vivo data sets. Furthermore, quantitative results for diffusion phantom data with known ground truth clearly show the benefits of the proposed method.
Keywords: tractography; fiber tracking; diffusion MRI; DTI; Bayesian statistics; white matter microstructure; convex optimization; l1-norm regularization; Sobolev-norm regularization; low-rank approximation; medical image processing; medical imaging; high angular resolution diffusion imaging; orientation distribution function; alternating direction method of multipliers
 
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