Shape Analysis of White Matter Tracts via the Laplace-Beltrami Spectrum

Diffusion-weighted magnetic resonance imaging (dMRI) allows for non-invasive, detailed examination of the white matter structures of the brain. White matter tract specific measures based on either the diffusion tensor model (e.g. FA, ADC, and MD) or tractography (e.g. volume, streamline count or density) are often compared between groups of subjects to localize differences within the white matter. Less commonly examined is the shape of the individual white matter tracts. In this paper, we propose to use the Laplace-Beltrami (LB) spectrum as a descriptor of the shape of white matter tracts. We provide an open, automated pipeline for the computation of the LB spectrum on segmented white matter tracts and demonstrate its efficacy through machine learning classification experiments. We show that the LB spectrum allows for distinguishing subjects diagnosed with bipolar disorder from age and sex matched healthy controls, with classification accuracy reaching 95%. We further demonstrate that the results cannot be explained by traditional measures, such as tract volume, streamline count, or mean and total length. The results indicate that there is valuable information in the anatomical shape of the human white matter tracts.