Topological Analysis for Arteriovenous Malformations via Computed Tomography Angiography: Part 1: Mathematical Concepts

• Main Authors: Yuki Hata, MD, Keigo Osuga, MD, PhD, Tateki Kubo, MD, PhD, Ken Matsuda, MD, PhD, Koichi Tomita, MD, PhD, Mamoru Kikuchi, MD, PhD, Takashi Fujiwara, MD, Kenji Yano, MD, PhD, Ko Hosokawa, MD, PhD
• Format: Article
• Language: English
• Published: Wolters Kluwer 2014-08-01
• Series: Plastic and Reconstructive Surgery, Global Open
• Online Access: http://journals.lww.com/prsgo/Fulltext/2014/08000/Article.9.aspx

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]). Conclusion: Abnormalities of AVM vascular structures can be mathematically quantified using computed tomography angiography images.