A novel approach to multiple anatomical shape analysis: Application to fetal ventriculomegaly

Fetal ventriculomegaly (VM) is a condition in which one or both lateral ventricles are enlarged, and is diagnosed as an atrial diameter larger than 10 mm. Evidence of altered cortical folding associated with VM has been shown in the literature. However, existing works use a single scalar value such as diagnosis or lateral ventricular volume to characterize VM and study its relationship with alterations in cortical folding, thus failing to reveal the spatially-heterogeneous associations. In this work, we propose a novel approach to identify fine-grained associations between cortical folding and ventricular enlargement by leveraging the vertex-wise correlations between their growth patterns in terms of area expansion and curvature. Our approach comprises three steps. In the first step, we define a joint graph Laplacian matrix using cortex-to-ventricle correlations. The joint Laplacian is built based on multiple cortical features. Next, we propose a spectral embedding of the cortex-to-ventricle graph into a common underlying space where its nodes are projected according to the joint ventricle-cortex growth patterns. In this low-dimensional joint ventricle-cortex space, associated growth patterns lie close to each other. In the final step, we perform hierarchical clustering in the joint embedded space to identify associated sub-regions between cortex and ventricle. Using a dataset of 25 healthy fetuses and 23 fetuses with isolated non-severe VM within the age range of 26-29 gestational weeks, our approach reveals clinically relevant and heterogeneous regional associations. Cortical regions forming these associations are further validated using statistical analysis, revealing regions with altered folding that are significantly associated with ventricular dilation.