title: Skeleton-based cerebrovascular quantitative analysis.
abstract: Cerebrovascular disease is the most common cause of death worldwide, with millions of deaths annually. Interest is increasing toward understanding the geometric factors that influence cerebrovascular diseases, such as stroke. Cerebrovascular shape analyses are essential for the diagnosis and pathological identification of these conditions. The current study aimed to provide a stable and consistent methodology for quantitative Circle of Willis (CoW) analysis and to identify geometric changes in this structure.
  
  
  
  An entire pipeline was designed with emphasis on automating each step. The stochastic segmentation was improved and volumetric data were obtained. The L1 medial axis method was applied to vessel volumetric data, which yielded a discrete skeleton dataset. A B-spline curve was used to fit the skeleton, and geometric values were proposed for a one-dimensional skeleton and radius. The calculations used to derive these values were illustrated in detail.
  
  
  
  In one example(No. 47 in the open dataset) all values for different branches of CoW were calculated. The anterior communicating artery(ACo) was the shortest vessel, with a length of 2.6mm. The range of the curvature of all vessels was (0.3, 0.9) ± (0.1, 1.4). The range of the torsion was (-12.4,0.8) ± (0, 48.7). The mean radius value range was (3.1, 1.5) ± (0.1, 0.7) mm, and the mean angle value range was (2.2, 2.9) ± (0, 0.2) mm. In addition to the torsion variance values in a few vessels, the variance values of all vessel characteristics remained near 1. The distribution of the radii of symmetrical posterior cerebral artery(PCA) and angle values of the symmetrical posterior communicating arteries(PCo) demonstrated a certain correlation between the corresponding values of symmetrical vessels on the CoW.
  
  
  
  The data verified the stability of our methodology. Our method was appropriate for the analysis of large medical image datasets derived from the automated pipeline for populations. This method was applicable to other tubular organs, such as the large intestine and bile duct.
authors.affiliation: College of Information Science and Technology, Beijing Normal University, Beijing, China.
authors.forename: Xingce
authors.initials: X
authors.lastname: Wang
authors.affiliation: College of Information Science and Technology, Beijing Normal University, Beijing, China.
authors.forename: Enhui
authors.initials: E
authors.lastname: Liu
authors.affiliation: College of Information Science and Technology, Beijing Normal University, Beijing, China. zwu@bnu.edu.cn.
authors.forename: Zhongke
authors.identifier: 0000-0002-3177-8902
authors.initials: Z
authors.lastname: Wu
authors.affiliation: Department of Neurology, Peking Union Medical College Hospital, Beijing, China.
authors.forename: Feifei
authors.initials: F
authors.lastname: Zhai
authors.affiliation: Department of Neurology, Peking Union Medical College Hospital, Beijing, China.
authors.forename: Yi-Cheng
authors.initials: YC
authors.lastname: Zhu
authors.affiliation: College of Information Science and Technology, Beijing Normal University, Beijing, China.
authors.forename: Wuyang
authors.initials: W
authors.lastname: Shui
authors.affiliation: College of Information Science and Technology, Beijing Normal University, Beijing, China.
authors.forename: Mingquan
authors.initials: M
authors.lastname: Zhou
mesh_terms: D002561:Cerebrovascular Disorders / Q000473:pathology*; D002941:Circle of Willis / Q000473:pathology*; D006801:Humans; D008953:Models, Anatomic; D013269:Stochastic Processes
keywords: B-spline curve; Circle of Willis; Geometric factors; Quantitative analysis; Skeleton; Stochastic analysis