Multi-scale Characterization of White Matter Tract Geometry

The geometry of white matter tracts is of increased interest for a variety of neuroscientific investigations, as it is a feature reflective of normal neurodevelopment and disease factors that may affect it. In this paper, we introduce a novel method for computing multi-scale fibre tract shape and geometry based on the differential geometry of curve sets. By measuring the variation of a curve's tangent vector at a given point in all directions orthogonal to the curve, we obtain a 2D "dispersion distribution function" at that point. That is, we compute a function on the unit circle which describes fibre dispersion, or fanning, along each direction on the circle. Our formulation is then easily incorporated into a continuous scale-space framework. We illustrate our method on different fibre tracts and apply it to a population study on hemispheric lateralization in healthy controls. We conclude with directions for future work.