Vessel surface reconstruction with a tubular deformable model

Three-dimensional (3-D) angiographic methods are gaining acceptance for evaluation of atherosclerotic disease. However, measurement of vessel stenosis from 3-D angiographic methods can be problematic due to limited image resolution and contrast. We present a method for reconstructing vessel surfaces from 3-D angiographic methods that allows for objective measurement of vessel stenosis. The method is a deformable model that employs a tubular coordinate system. Vertex merging is incorporated into the coordinate system to maintain even vertex spacing and to avoid problems of self-intersection of the surface. The deformable model was evaluated on clinical magnetic resonance (MR) images of the carotid (n = 6) and renal (n = 2) arteries, on an MR image of a physical vascular phantom and on a digital vascular phantom. Only one gross error occurred for all clinical images. All reconstructed surfaces had a realistic, smooth appearance. For all segments of the physical vascular phantom, vessel radii from the surface reconstruction had an error of less than 0.2 of the average voxel dimension. Variability of manual initialization of the deformable model had negligible effect on the measurement of the degree of stenosis of the digital vascular phantom. Index Terms--Atherosclerosis, deformable model, magnetic resonance angiography, surface reconstruction.