Statistical Computation and Inference on the Subcortical Surface
Lei Wang
Washington University/School of Medicine
Large-deformation high-dimensional brain mapping (HDBM-LD) technology enables the computation of diffeomorphisms that map a population of target anatomies to a provisional template MR scan. The velocity field in the space of diffeomorphisms is modeled as a Gaussian random field, allowing computation of average anatomies by applying the mean diffeomorphic mapping to the template anatomy.
Within these mappings, specific subcortical structures such as the hippocampus and thalamus are represented by their external boundary surfaces, modeled as two-dimensional smooth manifolds. Template-to-target diffeomorphic mappings can be expressed as Gaussian random vector fields over these smooth manifolds. This representation enables extraction of eigenfunction expansions of the deformation vector fields and characterization of subcortical structural shape variation through these eigenfunctions.
We describe the numerical algorithm used to compute the eigenfunctions via singular value decomposition and explain how the eigenfunctions and their associated coefficients are employed in statistical hypothesis testing for clinical applications and in characterizing shape differences between clinical populations. Extensions of the framework to assess surface shape asymmetry and time-dependent surface shape change are also discussed.
Illustrative results include comparisons of hippocampal and thalamic surface patterns between schizophrenia and control groups, analyses of asymmetry patterns, comparisons between very mild Alzheimer’s disease (DAT) and elderly control groups, and longitudinal hippocampal surface changes over a two-year period in the very mild DAT group.
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