Isosurfaces as deformable models for magnetic resonance angiography

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 toward edges in the image. However, smoothing is produced by a moment that aligns the normals of adjacent surface triangles. Notably, the moment produces no translational motion of surface triangles. The deformable isosurface was applied to a digital phantom of a stenotic artery, to MRA of three renal arteries with atherosclerotic disease and MRA of one carotid artery with atherosclerotic disease. Results of the surface reconstruction from the deformable model were compared with conventional X-ray angiography for the renal arteries. Measurement of the degree of stenosis of the renal arteries was within 12% ± 6%. The deformable model provided improvements over the isosurface in all cases in terms of measurement of the degree of stenosis or improving the surface smoothness.