Anatomical Labeling of the Circle of Willis Using Maximum A Posteriori Probability Estimation

Abstract

Anatomical labeling of the cerebral arteries forming the Circle of Willis (CoW) enables inter-subject comparison, which is required for geometric characterization and discovering risk factors associated with cerebrovascular pathologies. We present a method for automated anatomical labeling of the CoW by detecting its main bifurcations. The CoW is modeled as rooted attributed relational graph, with bifurcations as its vertices, whose attributes are characterized as points on a Riemannian manifold. The method is first trained on a set of pre-labeled examples, where it learns the variability of local bifurcation features as well as the variability in the topology. Then, the labeling of the target vasculature is obtained as maximum a posteriori probability (MAP) estimate where the likelihood of labeling individual bifurcations is regularized by the prior structural knowledge of the graph they span. The method was evaluated by cross-validation on 50 subjects, imaged with magnetic resonance angiography, and showed a mean detection accuracy of 95%. In addition, besides providing the MAP, the method can rank the labelings. The proposed method naturally handles anatomical structural variability and is demonstrated to be suitable for labeling arterial segments of the CoW.

Simultaneous segmentation and anatomical labeling of the cerebral vasculature

“…This is done implicitly by our edge labeling algorithm. Finally, it should be noted that the method of Bogunović et al [1] requires topologically correct segmentations, and uses reference graphs explicitly stating PoI connectivity and order for the entire vasculature. Extending it to a larger number of bifurcations requires a steep increase in the number of reference graphs.…”

“…The MR brain images from healthy volunteers used in this paper were collected and made available by the CASILab at The University of North Carolina at Chapel Hill and were distributed by the MIDAS Data Server at Kitware Inc. We thank the authors of [1] for sharing their centerline delineations.…”

“…For example, Robben et al [6] label the CoW by matching bifurcations in this graph to a probabilistic atlas, taking into account both unary potentials of the bifurcations and also pairwise potentials between them. Bogunović et al [1] also label the CoW by matching bifurcations to an atlas. They use the bifurcation properties and have several reference graphs to model the topology of the bifurcations.…”

Simultaneous Segmentation and Anatomical Labeling of the Cerebral Vasculature

“…All experiments are done with a leave-one-image-out cross-validation, using 50 MRA images of the cerebral vasculature from a public dataset [2] together with their ground truth segmentations (as used in and provided by [1]) and anatomical labels manually annotated by an expert. The images are rigidly aligned and cropped to the region that covers the segmentations [1].…”

“…If the Euclidean distance is smaller than 2mm, it is considered a true positive. Since we use the same dataset as [1], we can directly compare the performance. Results are given in table 1.…”