Space-Varying Coefficient Models for Brain Imaging

The methodological development and the application in this paper
originate from diffusion tensor imaging (DTI), a powerful nuclear
magnetic resonance technique enabling diagnosis and monitoring of
several diseases as well as reconstruction of neural pathways. We
reformulate the current analysis framework of separate voxelwise
regressions as a 3d space-varying coefficient model (VCM) for the
entire set of DTI images recorded on a 3d grid of voxels. Hence by
allowing to borrow strength from spatially adjacent voxels, to
smooth noisy observations, and to estimate diffusion tensors at any
location within the brain, the three-step cascade of standard data
processing is overcome simultaneously. We conceptualize two VCM
variants based on B-spline basis functions: a full tensor product
approach and a sequential approximation, rendering the VCM
numerically and computationally feasible even for the huge
dimension of the joint model in a realistic setup. A simulation
study shows that both approaches outperform the standard method of
voxelwise regressions with subsequent regularization. Due to major
efficacy, we apply the sequential method to a clinical DTI data set
and demonstrate the inherent ability of increasing the rigid grid
resolution by evaluating the incorporated basis functions at
intermediate points. In conclusion, the suggested fitting methods
clearly improve the current state-of-the-art, but ameloriation of
local adaptivity remains desirable.