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Updated: Apr 20, 2026
Comprehensive Endovascular and Open Surgical Management of Cerebral Arteriovenous Malformations
Published on: October 20, 2017
Topological Analysis for Arteriovenous Malformations via Computed Tomography Angiography: Part 1: Mathematical
Yuki Hata1, Keigo Osuga1, Tateki Kubo1
1Department 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.
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.
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