  Vessel tracing by modeling vascular structures in 3D medical images with
centerlines and radii can provide useful information for vascular health.
Existing algorithms have been developed but there are certain persistent
problems such as incomplete or inaccurate vessel tracing, especially in
complicated vascular beds like the intracranial arteries. We propose here a
deep learning based open curve active contour model (DOST) to trace vessels in
3D images. Initial curves were proposed from a centerline segmentation neural
network. Then data-driven machine knowledge was used to predict the stretching
direction and vessel radius of the initial curve, while the active contour
model (as human knowledge) maintained smoothness and intensity fitness of
curves. Finally, considering the nonloop topology of most vasculatures,
individually traced vessels were connected into a tree topology by applying a
minimum spanning tree algorithm on a global connection graph. We evaluated DOST
on a Time-of-Flight (TOF) MRA intracranial artery dataset and demonstrated its
superior performance over existing segmentation-based and tracking-based vessel
tracing methods. In addition, DOST showed strong adaptability on different
imaging modalities (CTA, MR T1 SPACE) and vascular beds (coronary arteries).
