Assumption-Free Assessment of Corpus Callosum Shape: Benchmarking and Application

Shape analysis provides a unique insight into biological processes. This paper evaluates the properties, performance, and utility of elliptical Fourier (eFourier) analysis to operationalise global shape, focussing on the human corpus callosum. 8000 simulated corpus callosum contours were generated, systematically varying in terms of global shape (midbody arch, splenium size), local complexity (surface smoothness), and nonshape characteristics (e.g., rotation). 2088 real corpus callosum contours were manually traced from the PATH study. Performance of eFourier was benchmarked in terms of its capacity to capture and then reconstruct shape and systematically operationalise that shape via principal components analysis. We also compared the predictive performance of corpus callosum volume, position in Procrustes-aligned Landmark tangent space, and position in eFourier n-dimensional shape space in relation to the Symbol Digit Modalities Test. Jaccard index for original vs. reconstructed from eFourier shapes was excellent (M=0.98). The combination of eFourier and PCA performed particularly well in reconstructing known n-dimensional shape space but was disrupted by the inclusion of local shape manipulations. For the case study, volume, eFourier, and landmark measures were all correlated. Mixed effect model results indicated all methods detected similar features, but eFourier estimates were most predictive, and of the two shape operationalization techniques had the least error and better model fit. Elliptical Fourier analysis, particularly in combination with principal component analysis, is a powerful, assumption-free and intuitive method of quantifying global shape of the corpus callosum and shows great promise for shape analysis in neuroimaging more broadly.