Statistical Computation and Inference on the Subcortical Surface

Lei Wang
Washington University/School of Medicine

Large-deformation high dimensional brain mapping (HDBM-LD) technology has allowed
us to compute diffeomorphisms for a population of target anatomies mapped from a
provisory template MR scan. The velocity field of the space of diffeomorphisms is
modeled as a Gaussian random field, which allowed us to compute average anatomies
as the provisory template anatomy under the average diffeomorphic mappings. Within
the mappings of the MR anatomies, specific subcortical structures such as the
hippocampus and the thalamus are represented by their external boundary surface,
modeled as 2D smooth manifolds. Template-target diffeomorphic mappings can be
represented as Gaussian random vector fields over the smooth manifold. This allowed
us to extract eigenfunction representation of the deformation vector fields, and
characterize subcoritcal structural shape variation using eigenfunctions. We describe the
numeric algorithm for computing these eigenfunctions via singular value decomposition.
We describe how we use these eigenfunctions and their associated coefficients for
statistical hypothesis testing in clinical applications and for characterizing shape
differences between clinical populations. We also describe the extension of shape
analysis to assessing surface shape asymmetry and time-dependent surface shape

A) Differences in hippocampal surface patterns between schizophrenia and
control groups. B) Differences in thalamic surface patterns between the
same groups in (A). C) Patterns of hippocampal asymmetry for the
schizophrenia group. D) Patterns of thalamic asymmetry for the
schizophrenia group. E) Differences in hippocampal surface patterns
between very mild DAT and elderly control groups. F) Patterns of
hippocampal change over a two-year period in very mild DAT group

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