Abstract
The circle of Willis (CoW) is a circular arrangement of arteries in the human brain, exhibiting significant anatomical variability. The CoW is extensively studied in relation to neurovascular pathologies, with certain anatomical variants previously linked to ischemic stroke and intracranial aneurysms. In an individual CoW, arteries might be absent (aplasia) or underdeveloped (hypoplasia, diameter < 1 mm). As the assessment of such variations is time-consuming and susceptible to subjectivity, robust automatic extraction of personalized CoW topology from time-of-flight magnetic resonance angiography (TOF-MRA) images would highly benefit large-scale clinical investigations. Previous work has sought to extract CoW topology from voxel-based semantic segmentation masks. However, hypoplastic arteries are challenging to recover in voxel-based segmentation. Instead, we propose using a complete CoW as an anatomical prior for extracting all possible CoW arteries as shortest paths between automatically identified anatomical landmarks, guided by automatically determined artery orientation vector fields. These fields are obtained using a scale-invariant and rotation-equivariant mesh-CNN-based model (SIRE). For a 3D TOF-MRA volume, a potentially overcomplete graph of the CoW is thus extracted in which each edge represents an artery. Subsequently, a binary Random Forest classifier labels each artery as normal or hypo-/aplastic. The model was optimized and validated using a data set of 351 3D TOF-MRA scans in a cross-validation setup. We showed that using a shortest path algorithm with a cost function based on local artery orientations results in continuous artery paths, even in hypoplastic cases. We tracked the correct path in the posterior communicating arteries in 70-74% of the cases, an artery that is known to pose challenges in voxel-based segmentation models. Our downstream artery path classifier obtained an average F1 score of 0.91, demonstrating the potential of our proposed framework to extract personalized CoW topology automatically.