  There is increasing evidence on the importance of brain morphology in
predicting and classifying mental disorders. However, the vast majority of
current shape approaches rely heavily on vertex-wise analysis that may not
successfully capture complexities of subcortical structures. Additionally, the
past works do not include interactions between these structures and exposure
factors. Predictive modeling with such interactions is of paramount interest in
heterogeneous mental disorders such as PTSD, where trauma exposure interacts
with brain shape changes to influence behavior. We propose a comprehensive
framework that overcomes these limitations by representing brain substructures
as continuous parameterized surfaces and quantifying their shape differences
using elastic shape metrics. Using the elastic shape metric, we compute shape
summaries of subcortical data and represent individual shapes by their
principal scores. These representations allow visualization tools that help
localize changes when these PCs are varied. Subsequently, these PCs, the
auxiliary exposure variables, and their interactions are used for regression
modeling. We apply our method to data from the Grady Trauma Project, where the
goal is to predict clinical measures of PTSD using shapes of brain
substructures. Our analysis revealed considerably greater predictive power
under the elastic shape analysis than widely used approaches such as
vertex-wise shape analysis and even volumetric analysis. It helped identify
local deformations in brain shapes related to change in PTSD severity. To our
knowledge, this is one of the first brain shape analysis approaches that can
seamlessly integrate the pre-processing steps under one umbrella for improved
accuracy and are naturally able to account for interactions between brain shape
and additional covariates to yield superior predictive performance when
modeling clinical outcomes.
