Vascular decomposition using weighted approximate convex decomposition

Objective

Stroke treatment often requires analysis of vascular pathology evaluated using computed tomography (CT) angiography. Due to vascular variability and complexity, finding precise relationships between vessel geometries and arterial pathology is difficult. A new convex shape decomposition strategy was developed to understand complex vascular structures and synthesize a weighted approximate convex decomposition (WACD) method for vascular decomposition in computer-aided diagnosis.

Materials and methods

The vascular tree is decomposed into optimal number of components (determined by an expert). The decomposition is based on two primary features of vascular structures: (i) the branching factor that allows structural decomposition and (ii) the concavity over the vessel surface seen primarily at the site of an aneurysm. Such surfaces are decomposed into subcomponents. Vascular sections are reconstructed using CT angiograms. Next the dual graph is constructed, and edge weights for the graph are computed from shape indices. Graph vertices are iteratively clustered by a mesh decimation operator, while minimizing a cost function related to concavity.

Results

The method was validated by first comparing results with an approximate convex decomposition (ACD) method and next on vessel sections (n = 177) whose number of clusters (ground truth) was predetermined by an expert. In both cases, WACD produced promising results with 84.7 % of the vessel sections correctly clustered and when compared with ACD produced a more effective decomposition. Next, the algorithm was validated in a longitudinal study data of 4 subjects where volumetric and surface area comparisons were made between expert segmented sections and WACD decomposed sections that contained aneurysms. The results showed a mean error rate of 7.8 % for volumetric comparisons and 10.4 % for surface area comparisons.

Conclusion

Decomposition of the cerebral vasculature from CT angiograms into a geometrically optimal set of convex regions may be useful for computer-assisted diagnosis. A new WACD method capable of decomposing complex vessel structures, including bifurcations and aneurysms, was developed and tested with promising results.