title: Topological Analysis for Arteriovenous Malformations via Computed Tomography Angiography: Part 1: Mathematical Concepts.
abstract: BACKGROUND
  Evaluating the progression of soft-tissue arteriovenous malformation (AVMs) is still problematic. To establish a quantitative method, we took a morphological approach.
  
  
  METHODS
  Normal blood vessels in early-phase 3D-computed tomography angiography images are theoretically expected to be tree-like structures without loops, whereas AVM blood vessels are expected to be mesh-like structures with loops. Simplified to the utmost limit, these vascular structures can be symbolized with wire-frame models composed of nodes and connecting edges, in which making an extra loop always needs one more of edges than of nodes.
  
  
  RESULTS
  TOTAL AMOUNT OF ABNORMAL VASCULAR STRUCTURES IS ESTIMATED FROM A SIMPLE EQUATION: Number of vascular loops = 1 - ([Number of nodes] - [Number of edges]).
  
  
  CONCLUSIONS
  Abnormalities of AVM vascular structures can be mathematically quantified using computed tomography angiography images.
authors.affiliation: Department of Plastic Surgery, Osaka University Graduate School of Medicine, Osaka, Japan; and Department of Diagnostic and Interventional Radiology, Osaka University Graduate School of Medicine, Osaka, Japan.
authors.forename: Yuki
authors.initials: Y
authors.lastname: Hata
authors.affiliation: Department of Plastic Surgery, Osaka University Graduate School of Medicine, Osaka, Japan; and Department of Diagnostic and Interventional Radiology, Osaka University Graduate School of Medicine, Osaka, Japan.
authors.forename: Keigo
authors.initials: K
authors.lastname: Osuga
authors.affiliation: Department of Plastic Surgery, Osaka University Graduate School of Medicine, Osaka, Japan; and Department of Diagnostic and Interventional Radiology, Osaka University Graduate School of Medicine, Osaka, Japan.
authors.forename: Tateki
authors.initials: T
authors.lastname: Kubo
authors.affiliation: Department of Plastic Surgery, Osaka University Graduate School of Medicine, Osaka, Japan; and Department of Diagnostic and Interventional Radiology, Osaka University Graduate School of Medicine, Osaka, Japan.
authors.forename: Ken
authors.initials: K
authors.lastname: Matsuda
authors.affiliation: Department of Plastic Surgery, Osaka University Graduate School of Medicine, Osaka, Japan; and Department of Diagnostic and Interventional Radiology, Osaka University Graduate School of Medicine, Osaka, Japan.
authors.forename: Koichi
authors.initials: K
authors.lastname: Tomita
authors.affiliation: Department of Plastic Surgery, Osaka University Graduate School of Medicine, Osaka, Japan; and Department of Diagnostic and Interventional Radiology, Osaka University Graduate School of Medicine, Osaka, Japan.
authors.forename: Mamoru
authors.initials: M
authors.lastname: Kikuchi
authors.affiliation: Department of Plastic Surgery, Osaka University Graduate School of Medicine, Osaka, Japan; and Department of Diagnostic and Interventional Radiology, Osaka University Graduate School of Medicine, Osaka, Japan.
authors.forename: Takashi
authors.initials: T
authors.lastname: Fujiwara
authors.affiliation: Department of Plastic Surgery, Osaka University Graduate School of Medicine, Osaka, Japan; and Department of Diagnostic and Interventional Radiology, Osaka University Graduate School of Medicine, Osaka, Japan.
authors.forename: Kenji
authors.initials: K
authors.lastname: Yano
authors.affiliation: Department of Plastic Surgery, Osaka University Graduate School of Medicine, Osaka, Japan; and Department of Diagnostic and Interventional Radiology, Osaka University Graduate School of Medicine, Osaka, Japan.
authors.forename: Ko
authors.initials: K
authors.lastname: Hosokawa