Statistical Diffusion Tensor Imaging

Magnetic resonance diffusion tensor imaging (DTI) allows to infere
the ultrastructure of living tissue. In brain mapping, neural fiber
trajectories can be identified by exploiting the anisotropy of
diffusion processes. Manifold statistical methods may be linked
into the comprehensive processing chain that is spanned between DTI
raw images and the reliable visualization of fibers. In this work,
a space varying coefficients model (SVCM) using penalized B-splines
was developed to integrate diffusion tensor estimation,
regularization and interpolation into a unified framework. The
implementation challenges originating in multiple 3d space varying
coefficient surfaces and the large dimensions of realistic datasets
were met by incorporating matrix sparsity and efficient model
approximation. Superiority of B-spline based SVCM to the standard
approach was demonstrable from simulation studies in terms of the
precision and accuracy of the individual tensor elements. The
integration with a probabilistic fiber tractography algorithm and
application on real brain data revealed that the unified approach
is at least equivalent to the serial application of voxelwise
estimation, smoothing and interpolation. From the error analysis
using boxplots and visual inspection the conclusion was drawn that
both the standard approach and the B-spline based SVCM may suffer
from low local adaptivity. Therefore, wavelet basis functions were
employed for filtering diffusion tensor fields. While excellent
local smoothing was indeed achieved by combining voxelwise tensor
estimation with wavelet filtering, no immediate improvement was
gained for fiber tracking. However, the thresholding strategy needs
to be refined and the proposed model of an incorporation of
wavelets into an SVCM needs to be implemented to finally assess
their utility for DTI data processing. In summary, an SVCM with
specific consideration of the demands of human brain DTI data was
developed and implemented, eventually representing a unified
postprocessing framework. This represents an experimental and
statistical platform to further improve the reliability of
tractography.