Shape Analysis on Subcortical Structures with its Application in Children with Autism

Introduction Template-based shape analysis has been widely used to assess structural shape abnormalities (volume loss and its location) in a variety of neurodegenerative and neuropsychiatric diseases. Thus far, most existing morphometric shape analysis has largely focused on a single structure, such as the hippocampus, or thalamus. Nevertheless, there is considerable morphological variation in multiple structures in neural circuits across disease population. The assessment of the degree and pattern of multiple structural shapes is necessary to optimally distinguish subjects with early forms of various neuropsychiatric diseases. We introduce an automatic shape analysis procedure through large deformation diffeomorphic metric mapping (LDDMM) that generates subcortical template, segments the structures from raw MR images, quantifies the shape variation of each individual subject relative to the template, as well as makes statistical inference on covariance of the shape variations of multiple subcortical structures [1]. Methods A Bayesian framework under the LDDMM setting was used to estimate average diffeomorphic deformation of subcortical structures among a population and thus generate subcortical template shapes representing the population (bottom panel in Fig 1). For each individual subject, volume-based probabilistic segmentation was first used to label subcortical structures in the raw MRI scan. The subcortical template shape was then injected into the subcortical parcellations generated from the volume-based segmentation to smooth the structural boundary and correct topology via LDDMM (second and third panels in Fig 1). The statistical analysis was performed on random field representation of the template surface momentum maps that encode the shape variation of subcortical structure targets of each individual subject relative to the template. The momentum maps have the optimum property that they are supported only on the boundary of the subcortical structures with the direction normal to the subcortical nuclei boundary thereby reducing the dimension of shape variation significantly. A two-level statistical model was built on these momentum maps to assess their covariance among the subcortical structures via Laplace-Beltrami (LB) basis functions [1, 2].