We describe an approach to construct hexahedral solid NURBS (Non-Uniform Rational B-Splines) meshes for patient-specific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segmentation, are used to improve the quality of the input imaging data. Then, lumenal surfaces are extracted by isocontouring the preprocessed data, followed by the extraction of vascular skeleton via Voronoi and Delaunay diagrams. Next, the skeleton-based sweeping method is used to construct hexahedral control meshes. Templates are designed for various branching configurations to decompose the geometry into mapped meshable patches. Each patch is then meshed using one-to-one sweeping techniques, and boundary vertices are projected to the lumenal surface. Finally, hexahedral solid NURBS are constructed and used in isogeometric analysis of blood flow. Piecewise linear hexahedral meshes can also be obtained using this approach. Examples of patient-specific arterial models are presented.
Figure 1: The abdominal aorta model is divided into 26 patches, and each color represents one different patch. (a) - volume rendering result; (b) - isocontouring result; (c) - surface model and its path after removing unnecessary components; (d) - control mesh; (e) - solid NURBS mesh after refinement (73,314 elements); (f) - fluid-structure interaction simulation results: contours of the arterial wall velocity (cm/s) during late cystole plotted on the current configuration. Only major branches are kept in (d-f).
Figure 2: Thoracic aorta. (a) - surface model and the path, a LVAD is inserted; (b) - control mesh; (c) - solid NURBS (41,526 elements); (d) - fluid-structure interaction simulation results: contours of the arterial wall velocity (cm/s) during late diastole plotted on the current configuration.
Figure 3: Coronary artery. (a) - isocontouring results (two different view angles); (b) - path; (c) - control mesh; (d) - solid NURBS model (20,824 elements); (e) - rigid wall simulation results: isosurface of the drug concentration at 50% colored by the blood velocity magnitude (cm/s).