Circle of Willis Centerline Graphs: A Dataset and Baseline Algorithm

Abstract

The Circle of Willis (CoW) is a critical network of arteries in the brain, often implicated in cerebrovascular pathologies. Voxel-level segmentation is an important first step toward an automated CoW assessment, but a full quantitative analysis requires centerline representations. However, conventional skeletonization techniques often struggle to extract reliable centerlines due to the CoW's complex geometry, and publicly available centerline datasets remain scarce. To address these challenges, we used a thinning-based skeletonization algorithm to extract and curate centerline graphs and morphometric features from the TopCoW dataset, which includes 200 stroke patients, each imaged with MRA and CTA. The curated graphs were used to develop a baseline algorithm for centerline and feature extraction, combining U-Net-based skeletonization with A* graph connection. Performance was evaluated on a held-out test set, focusing on anatomical accuracy and feature robustness. Further, we used the extracted features to predict the frequency of fetal PCA variants, confirm theoretical bifurcation optimality relations, and detect subtle modality differences. The baseline algorithm consistently reconstructed graph topology with high accuracy (F1 = 1), and the average Euclidean node distance between reference and predicted graphs was below one voxel. Features such as segment radius, length, and bifurcation ratios showed strong robustness, with median relative errors below 5% and Pearson correlations above 0.95. Our results demonstrate the utility of learning-based skeletonization combined with graph connection for anatomically plausible centerline extraction. We emphasize the importance of going beyond simple voxel-based measures by evaluating anatomical accuracy and feature robustness. The dataset and baseline algorithm have been released to support further method development and clinical research.