Pixel-RRT*: A Novel Skeleton Trajectory Search Algorithm for Hepatic Vessels

Abstract

In the clinical treatment of liver disease such as tumor, the acquisition of vascular skeleton trajectory is of great worth to untangle the basin and venation of hepatic vessels, because tumor and vessels are closely intertwined. In most cases, skeletonization based on the results of vascular segmentation will be prone to fracture due to the discontinuous segmenting results of vessels. As the overall tree-like system of hepatic vessels is a thin tubular tissue, we expect to start the analysis of vessels from vascular skeleton to vascular boundary, not the contrary, which can more effectively implement the image computing of hepatic vessels and interpret the tree-like expansion. To this issue, in this paper, we propose an innovative approach Pixel-RRT* inspired by Marray's Law and the growing rule of biological vasculature. It can be applied to the skeleton trajectory search for the intricate hepatic vessels. In Pixel-RRT*, we introduce the novel pixel-based cost function, the design of pixel-distributed random sampling, and a multi-goal strategy in the shared graph of random tree based on the general algorithmic framework of RRT* and RRT. Without any prior segmentation of the vessels, the proposed Pixel-RRT* can rapidly return the rationally bifurcated vascular trajectories satisfying the principle of minimal energy and topological continuity. In addition, we put forward an adaptively interpolated variational method as the postprocessing technique to make the vascular trajectory smoother by the means of energy minimization. The simulation experiments and examples of hepatic vessels demonstrate our method is efficient and utilisable. The codes will be made available at https://github.com/JeffJFZ/Pixel-RRTStar.