A Multi-Scale Geometric Flow for Seg- menting Vasculature in MRI: Theory and Validation

Often in neurosurgical planning a dual echo acquisition is performed that yields proton density (PD) and T2-weighted images to evaluate edema near a tumor or lesion. The development of vessel segmentation algorithms for PD images is of general interest since this type of acquisition is widespread and is entirely noninvasive. Whereas vessels are signaled by black blood contrast in such images, extracting them is a challenge because other anatomical structures also yield similar contrasts at their boundaries. In this thesis we present a novel multi-scale geometric flow for segmenting vasculature from PD images which can also be applied to the easier cases of MR angiography data or Gadolinium enhanced MRI. The key idea is to first apply Frangi’s vesselness measure [Frangi et al. (1998)] to find putative centerlines of tubular structures along with their estimated radii. This multi-scale measure is then distributed to create a vector field which is orthogonal to vessel boundaries so that the flux maximizing flow algorithm of Vasilevskiy and Siddiqi (2002) can be applied to recover them. We carry out a qualitative validation of the approach on PD, MR angiography and Gadolinium enhanced MRI volumes and suggest a new way to visualize the segmentations in 2D with masked projections. We also validate the approach quantitatively on a data set consisting of PD, phase contrast (PC) angiography and time of flight (TOF) angiography volumes, all obtained for the same subject. A significant finding is that over 80% of the vasculature recovered in the angiographic data sets is also recovered from the PD volume. Furthermore, over 25% of the vasculature recovered from the PD volume is not detectable in the TOF angiographic data. Thus, the technique can be used not only to improve upon results obtained from angiographic data but also as an alternative when such data is not available.