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

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.