Joong Ho Won MS, Presenter: Nothing to Disclose

Geoffrey David Rubin MD, Abstract Co-Author: Nothing to Disclose

Bhargav Raman, Abstract Co-Author: Nothing to Disclose

Sandy Napel PhD, Abstract Co-Author: Nothing to Disclose

Visualization of a 3D vascular structure is difficult because its complex tree-like geometry often causes misleading intersections of vessels when the tree is projected onto a 2D display. The conventional method for resolving this is to change viewpoints prior to projection or to view only small portions at a time. The goal of this research is to provide a single, 2D overview of the vascular tree without intersections with minimal user input.

A vascular tree is modeled as a collection of 3D curves representing vessel centerlines. The tree is projected to a plane with a specified view angle. This projected tree is simplified by replacing each centerline by a straight line segment (edge). An untangling step is then performed: Edges are drawn in breadth-first order and their intersections are removed by shrinking crossing edges. This results in a tree with no intersections. Next, a force-directed graph drawing algorithm that preserves edge crossings is applied so as to relax the structure towards its original shape while avoiding new intersections. Finally, each edge is recursively subdivided, gradually refining the approximation to recover the original curved shapes.

We tested the algorithm with abdominal aortic trees obtained using custom software from multidetector CT scans of 6 patients with abdominal vascular disease. For each patient, we chose anterior-posterior and left-to-right views for projection so as to introduce severe false intersections in the renal artery region. The algorithm resolved all false intersections for all cases. For shape conservation, 10 of 12 cases showed less than 0.25 of length distortion, defined as a weighted average of branch length change ratios, and less than 0.05 shape distortion, defined as relative change of sample point locations. 2 cases showed moderate (less than 0.40) length distortion primarily due to the aggressive untangling step.

Our algorithm flattens tree-like vascular structures using graph drawing algorithms, conserving overall shape while eliminating misleading intersections, and can be combined with curved planar reformation methods to visualize large portions of the human aortic vascular tree in a single image.

Won, J, Rubin, G, Raman, B, Napel, S, Flattening of the Abdominal Aortic Vascular Tree for Effective Visualization.  Radiological Society of North America 2005 Scientific Assembly and Annual Meeting, November 27 - December 2, 2005 ,Chicago IL. http://archive.rsna.org/2005/4415208.html