Differentiable centerline-aware framework for aneurysm neck delineation in volumetric angiography

Accurate morphological characterization of the intracranial aneurysm (IA) neck is fundamental to clinical decision-making and interventional planning. While Three-Dimensional Rotational Angiography serves as the reference standard, automated analysis across volumetric modalities (CTA/MRA) is hindered by topological discontinuities near bifurcations. Existing voxel-wise methods often produce jagged boundaries, compromising metric reliability. To address this, we propose NeckSpline, a differentiable framework treating the neck as a continuous, periodic cubic B-spline. Unlike discrete approaches, it optimizes a closed curve anchored by the parent-vessel centerline, integrating a tightness regularizer and Euler Characteristic (EC) topological loss. Extensive evaluations on MCA-CTA and ADAM-TOF benchmarks demonstrate that NeckSpline achieves superior localization accuracy and clinical non-inferiority, with a neck width Mean Absolute Error (MAE) of 0.44 mm and an angle MAE of 4.6°, significantly outperforming state-of-the-art baselines while maintaining sub-second inference. By guaranteeing topological integrity and sub-voxel precision, the framework offers a robust solution for automated pre-procedural assessment.