Anatomically Conditioned Recurrent Refinement for Topology-Aware Circle of Willis Segmentation

Segmenting the Circle of Willis (CoW) from Magnetic Resonance Angiography (MRA) is challenging due to complex topology and thin vascular structures that are prone to fragmentation. Standard Convolutional Neural Networks (CNNs) often fail to capture these topological constraints, resulting in "broken vessel" artifacts. To address this, we propose the Anatomically Conditioned Recurrent Refinement U-Net (AC2RUNet). Our architecture decouples segmentation into two streams: a Static Stream that extracts invariant anatomical features and a lightweight Dynamic Stream that iteratively refines topological errors over time. We further introduce a dynamic curriculum learning strategy that transitions from high-recall geometric supervision to topology-aware constraints. Validated on the TopCoW dataset, AC2RUNet substantially reduces Hausdorff Distance (4.72 mm vs 9.17 mm) and Betti number errors (0.19 vs 0.40), improving topological connectivity over the nnU-Net baseline while maintaining comparable volumetric Dice.

AG-TAL: Anatomically-Guided Topology-Aware Loss for Multiclass Segmentation of the Circle of Willis Using Large-Scale Multi-Center Datasets

Accurate multiclass segmentation of the Circle of Willis (CoW) is essential for neurovascular disease management but remains challenging due to complex vascular topology and variable morphology. Existing deep learning methods often suffer from vascular discontinuities and inter-class misclassification, while current topological loss functions incur prohibitive computational costs in 3D multiclass settings. To address these limitations, we propose an Anatomically-Guided Topology-Aware Loss (AG-TAL) and introduce a large-scale, multi-center CoW dataset with unified annotations to facilitate robust model training. AG-TAL specifically integrates a radius-aware Dice loss to address class imbalance in small vessels, a breakage-aware clDice loss that utilizes group convolutions to efficiently preserve local connectivity, and an adjacency-aware co-occurrence loss that leverages anatomical priors to enforce distinct boundaries between neighboring arteries. Evaluated using 5-fold cross-validation, AG-TAL achieved an average Dice score of 80.85% for all CoW arteries, with small arteries notably higher by 1.05-3.09% compared to state-of-the-art methods. Across six independent datasets, the performance of AG-TAL achieved Dice scores ranging from 74.46% to 81.17% for all CoW arteries, with improvements of 2.20% to 9.98% for small arteries compared to other methods. This study demonstrates the superiority of AG-TAL in identifying multiclass CoW arteries and its ability to generalize well to multiple independent datasets. Furthermore, reliability analyses and clinical applications in an Alzheimer's disease cohort validate the AG-TAL's robustness and its potential for discovering imaging-based morphological biomarkers.