Classification of mathematics deficiency using shape and scale analysis of 3D brain structures

We investigate the use of a recent technique for shape analysis of brain substructures in identifying learning disabilities in third-grade children. This Riemannian technique provides a quantification of differences in shapes of parameterized surfaces, using a distance that is invariant to rigid motions and re-parameterizations. Additionally, it provides an optimal registration across surfaces for improved matching and comparisons. We utilize an efficient gradient based method to obtain the optimal re-parameterizations of surfaces. In this study we consider 20 different substructures in the human brain and correlate the differences in their shapes with abnormalities manifested in deficiency of mathematical skills in 106 subjects. The selection of these structures is motivated in part by the past links between their shapes and cognitive skills, albeit in broader contexts. We have studied the use of both individual substructures and multiple structures jointly for disease classification. Using a leave-one-out nearest neighbor classifier, we obtained a 62.3% classification rate based on the shape of the left hippocampus. The use of multiple structures resulted in an improved classification rate of 71.4%.