Geodesic curvature flow on surfaces for automatic sulcal delineation

Sulcal folds (sulci) on the cortical surface are important landmarks of interest for investigating brain development and disease. Accurate and automatic delineation of the sulci is a challenging problem due to substantial variability in their shapes across populations. We present a geodesic curvature flow method for an automatic and accurate delineation of sulcal curves. We assume as input an atlas brain surface mesh on which a set of sulcal curves have been delineated. The sulcal curves are transferred to approximate corresponding locations on the subject brain using a transformation defined by an automatic surface based registration method. The locations of these curves are then refined to follow the true sulcal fundi more closely using geodesic curvature flow on the cortical surface. We present a level set based formulation of this flow on non-flat surfaces which represents the sulcal curves as zero level sets. We also incorporate a curvature based weighting that drives the sulcal curves to the bottoms of the sulcal valleys in the cortical folds. The resulting PDE is discretized on a triangulated mesh using finite elements. Finally, we present a validation by comparing sets of automatically delineated sul-cal curves with sets of manually delineated sulcal curves and show that the proposed method is able to find them accurately.