A Hybrid Framework for Blood Vessel Morphology Classification: Discrete Geometry-based Tortuosity Feature Measurement, Information Gain-based Feature Selection, and Random Forest Classification

Subjective visual grading of blood vessel tortuosity relies heavily on clinical experience, while traditional distance-based indices often fail to adequately characterize three-dimensional spatial deformation. Because abnormal internal carotid artery morphology may be clinically relevant to cerebrovascular assessment and stroke-risk evaluation, objective and reproducible quantification of vascular tortuosity is of considerable importance. To address this limitation, we propose a mathematical framework for the morphological classification of the internal carotid artery (ICA-C1) segment. The framework integrates discrete geometric feature measurement, Information Gain-based feature selection, and Random Forest classification. An initial set of 13 tortuosity features is extracted from the corresponding 379 clinical vascular centerlines using discrete geometric methods and subsequently reduced to a six-feature subset consisting of $\mathcal{TI}$, $\mathcal{AC}$, $\mathcal{TC}$, $\mathcal{AC}/\mathcal{AT}$, $\mathcal{AT}$, and $\mathcal{TT}$. The framework is evaluated in two classification tasks. For binary classification of non-severe and severe tortuosity, the RF model achieves a Macro-F1 score of 0.9206. For ternary morphological grading into straight, low-tortuosity, and high-tortuosity groups, it achieves a Macro-F1 score of 0.8626. The results indicate that elongation- and curvature-related features provide strong discriminatory information for basic screening, whereas torsion-related features contribute additional information for more detailed morphological classification. Based on the RF feature-importance values, we further define a Morphological Risk Index (MRI), which provides a direct numerical reference for vascular morphology and may facilitate more objective and consistent clinical assessment.