A deformable isosurface and vascular applications

Vascular disease produces changes in lumenal shape evident in magnetic resonance angiography (MRA). However, quantification of vascular shape from MRA is problematic due to image artifacts. Prior deformable models for vascular surface reconstruction primarily resolve problems of initialization of the surface mesh. However, initialization can be obtained in a trivial manner for MRA using isosurfaces. We propose a methodology for deforming the isosurface to conform to the boundaries of objects in the image with minimal a priori assumptions of object shape. As in conventional methods, external forces attract the surface towards edges in the image. However, smoothing is produced by torsional forces that align the normals of adjacent surface triangles. The torsional forces are unbiased with regard to determination of object size. The deformable isosurface was applied to MRA of carotid and renal arteries with moderate stenosis and to a digital phantom of an artery with high-grade stenosis (6-voxel normal diameter). The reconstruction of the carotid and renal arteries from MRA was entirely consistent with expert interpretation of the MRA. The deformable isosurface determined the degree of stenosis of the digital phantom to within 10.0% accuracy. The deformable isosurface is an excellent method for analysis of vascular shape.