Circle of Willis Centerline Graphs: A Dataset and Baseline Algorithm

TL;DR

This work addresses the need for anatomically faithful centerline representations of the Circle of Willis (CoW) to enable quantitative vascular morphometry. It introduces TopCoW, a public dataset of CoW centerline graphs derived from 200 stroke patients with CTA and MRA, and proposes an end-to-end baseline pipeline that converts segmentation masks into anatomically plausible centerlines via a U-Net skeletonization followed by A* reconnection and Voreen graph extraction. The approach achieves high topological fidelity (F$1=1$) and sub-voxel node localization, with robust segment and bifurcation features across modalities; modality-related differences and fetal PCA variants are also characterized. By releasing the dataset and baseline implementation, the work provides a benchmark for learning-based centerline extraction and enables broader quantitative analyses in hemodynamics and cerebrovascular research. The centerline representation supports downstream tasks such as variant detection, bifurcation analysis, and comparison across imaging modalities, with open data facilitating reproducibility and methodological development.

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.

Figures (8)

• Figure 1: Topological errors of the centerline graphs as introduced by the Voreen skeletonization algorithm: a) Invalid connection between R-ICA and R-ACA, b) invalid connection between Acom and L-ACA, c) invalid connection between L-ICA and L-Pcom, d) self-loop of L-ICA.
• Figure 2: Overview of CoW components used for feature computation: (a) List of artery segments and subsegments with labels as defined by the TopCoW challenge: basilar artery (BA), left and right posterior cerebral artery (PCA), left and right internal carotid artery (ICA), left and right middle cerebral artery (MCA), left and right posterior communicating artery (Pcom), anterior communicating artery (Acom), and left and right anterior cerebral artery (ACA). (b) Schematic representation of the CoW and its components. (c) Anatomical locations of CoW bifurcations.
• Figure 3: Overview of the baseline centerline extraction pipeline. Starting from a multi-class segmentation mask of the CoW, a U-Net model predicts a binary skeleton. The skeleton is then refined by assigning anatomical labels from the original mask and by reconnecting broken segments using the A$^*$ algorithm. Finally, a labeled centerline graph is extracted using the Voreen tool.
• Figure 4: CoW Centerline Dataset: The dataset includes centerline graphs and surface meshes enriched with spatial, topological, and semantic node and cell attributes. Three derived data files provide complementary information: the variant file encodes anterior (AV) and posterior (PV) CoW variants based on the presence or absence of four artery segments each, along with fetal-type PCA variants; the node file lists key anatomical nodes with ID, degree, label, and coordinates; and the feature file contains morphometric features for CoW segments and bifurcations.
• Figure 5: Comparison of morphometric features extracted from the Voreen-based and U-Net–predicted centerline graphs, evaluated by median relative error (MedRE) and Pearson correlation coefficient. (a) comparison of segment features, aggregated across the P1, C7, Pcom, and A1 segments. The Acom segment is excluded due to its significantly higher error rates. (b) comparison of the bifurcation features, aggregated across the BA and both ICA bifurcations.