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Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. (English) Zbl 1121.76076
Summary: 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, luminal 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 luminal 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.

76Z05 Physiological flows
76M25 Other numerical methods (fluid mechanics) (MSC2010)
92C35 Physiological flow
Full Text: DOI
[1] Cubit mesh generation toolkit, web site: <http://sass1693.sandia.gov/cubit>.
[2] C.W. Anderson, S. Crawford-Hines, Fast generation of nurbs surfaces from polygonal mesh models of human anatomy, in: Technical Report CS-99-101, Colorado State University, 2000.
[3] C. Armstrong, D. Robinson, R. McKeag, T. Li, S. Bridgett, R. Donaghy, C. McGleenan, Medials for meshing and more, in: 4th Int. Meshing Roundtable, 1995, pp. 277-288.
[4] Bajaj, C.; Chen, J.; Xu, G., Modeling with cubic A-patches, ACM transactions on graphics, 14, 103-133, (1995)
[5] C. Bajaj, Q. Wu, G. Xu, Level Set Based Volumetric Anisotropic Diffusion, in: ICES Technical Report 301, the University of Texas at Austin, 2003.
[6] Bazilevs, Y.; Calo, V.M.; Zhang, Y.; Hughes, T.J.R., Isogeometric fluid – structure interaction analysis with applications to arterial blood flow, Comput. mech., 38, 310-322, (2006) · Zbl 1161.74020
[7] Bazilevs, Y.; Beirao da Veiga, L.; Cottrell, J.A.; Hughes, T.J.R.; Sangalli, G., Isogeometric analysis: approximation, stability and error estimates for h-refined meshes, Math. models methods appl. sci., 16, 1031-1090, (2006) · Zbl 1103.65113
[8] Bitter, I.; Kaufman, A.; Sato, M., Penalized distance volumetric skeleton algorithm, Ieee tvcg, 7, 3, (2001)
[9] Blacker, T., A new approach to automated quadrilateral mesh generation, Int. J. numer. meth. engrg., 32, 811-847, (1991) · Zbl 0755.65111
[10] T. Blacker, The Cooper Tool, in: 5th Int. Meshing Roundtable, 1996, pp. 13-29.
[11] G. Borgefors, I. Nystrom, G.D. Baja, Computing skeletons in three dimensions, Pattern Recognit. 32 (7) (1999).
[12] Bouix, S.; Siddiqi, K.; Tannenbaum, A., Flux driven fly throughs, IEEE conf. comput. vision pattern recognit., 449-454, (2003)
[13] CGAL Consortium, CGAL: Computational Geometry Algorithms Library, <http://www.cgal.org>.
[14] Cirak, F.; Scott, M.J.; Antonsson, E.K.; Ortiz, M.; Schröder, P., Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision, Comput.-aided design, 34, 137-148, (2002)
[15] Cocone, Tight Cocone Software for surface reconstruction and medial axis approximation, <http://www.cse.ohio-state.edu/ tamaldey/cocone.html>.
[16] Cook, W.A.; Oakes, W.R., Mapping methods for generating three-dimensional meshes, Comput. mech. engrg., 67-72, (1982)
[17] Cornea, N.; Silver, D.; Min, P., Curve skeleton applications, IEEE visualiz., 95-102, (2005)
[18] Cornea, N.; Silver, D.; Yuan, X.; Balasubramaniam, R., Computing hierarchical curve skeletons of 3D objects, Visual comput., 21, 11, 945-955, (2005)
[19] L. Costa, Multidimensional scale space shape analysis, in: IWSNHC3DI, 1999, pp. 214-217.
[20] Cottrell, J.A.; Reali, A.; Bazilevs, Y.; Hughes, T.J.R., Isogeometric analysis of structural vibrations, Comput. methods appl. mech. engrg., 195, 5257-5296, (2006) · Zbl 1119.74024
[21] de Berg, M.; van Kreveld, M.; Overmars, M.; Schwarzkopf, O., Comput. geometry: algorithms appl., (1997), Springer-Verlag Berlin
[22] T.K. Dey, J. Giesen, S. Goswami, Shape segmentation and matching with flow discretization, in: F. Dehne, J.-R. Sack, M. Smid, (Eds.), Proc. Workshop Algorithms Data Structures (WADS 03), LNCS 2748, Berlin, Germany, 2003, pp. 25-36. · Zbl 1278.68331
[23] T.K. Dey, S. Goswami, Tight cocone: a water-tight surface reconstructor, in: Proc. 8th ACM Sympos. Solid Modeling Appl., 2003, pp. 127-134.
[24] T.K. Dey, J. Sun, Defining and computing curve-skeletons with medial geodesic functions, in: Sympos. Geom. Proces., 2006, pp. 143-152.
[25] Dey, T.K.; Zhao, W., Approximating the medial axis from the Voronoi diagram with convergence guarantee, Algorithmica, 38, 179-200, (2004) · Zbl 1072.68107
[26] Figueroa, A.; Vignon-Clementel, I.E.; Jansen, K.E.; Hughes, T.J.R.; Taylor, C.A., A coupled momentum method for modeling blood flow in three-dimensional deformable arteries, Comput. methods appl. mech. engrg., 195, 41-43, 5685-5706, (2006) · Zbl 1126.76029
[27] S. Goswami, T.K. Dey, C.L. Bajaj, Identifying flat and tubular regions of a shape by unstable manifolds, in: Proc. 11th Sympos. Solid Phys. Modeling, 2006, pp. 27-37.
[28] Gursoy, H.N., Tetrahedral finite element mesh generation from nurbs solid models, Engineering with computers, 12, 19, 211-223, (1996)
[29] Hassouna, M.S.; Farag, A.A., Robust centerline extraction framework using level sets, IEEE conf. comput. vision pattern recognit., 458-465, (2005)
[30] Holzapfel, G.A., Computational biomechanics of soft biological tissue, (), (Chapter 18)
[31] Hughes, T.J.R., The finite element method: linear static and dynamic finite element analysis, (2000), Dover Publications Mineola, NY
[32] Hughes, T.J.R.; Cottrell, J.A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement, Comput. methods appl. mech. engrg., 194, 4135-4195, (2005) · Zbl 1151.74419
[33] Ito, Y.; Shum, P.C.; Shih, A.; Soni, B.K.; Nakahashi, K., Robust generation of high-quality unstructured meshes on realistic biomedical geometry, Int. J. numer. meth. engrg., 65, 943-973, (2006) · Zbl 1110.92022
[34] T. Ju, F. Losasso, S. Schaefer, J. Warren, Dual contouring of hermite data, in: SIGGRAPH, 2002, pp. 339-346.
[35] P. Knupp, Next-generation sweep tool: a method for generating all-hex meshes on two-and-one-half dimensional geometries, in: 7th Int. Meshing Roundtable, 1998, pp. 505-513.
[36] W. Lorensen, H. Cline, Marching cubes: a high resolution 3D surface construction algorithm, in: SIGGRAPH, 1987, pp. 163-169.
[37] Ogniewicz, R.L.; Kubler, O., Hierachic Voronoi skeletons, Pattern recognit., 28, 3, 343-359, (1995)
[38] Piegl, L.; Tiller, W., The NURBS book (monographs in visual communication), (1997), Springer-Verlag New York
[39] Price, M.A.; Armstrong, C.G.; Sabin, M.A., Hexahedral mesh generation by medial surface subdivision: I. solids with convex edges, Int. J. numer. meth. engrg., 38, 3335-3359, (1995) · Zbl 0835.73080
[40] W.R. Quadros, S.J. Owen, M. Brewer, K. Shimada, Finite element mesh sizing for surfaces using skeleton, in: 13th International Meshing Roundtable, 2004, pp. 389-400.
[41] Rogers, D.F., An introduction to NURBS with historical perspective, (2001), Academic Press San Diego, CA
[42] Sahni, O.; Muller, J.; Jansen, K.E.; Shephard, M.S.; Taylor, C.A., Efficient anisotropic adaptive discretization of the cardiovascular system, Comput. methods appl. mech. engrg., 195, 5634-5655, (2006) · Zbl 1125.76046
[43] M. Scott, M. Earp, S. Benzley, Adaptive sweeping techniques, in: 14th Int. Meshing Roundtable, 2005, pp. 417-432.
[44] Sederberg, T.W.; Cardon, D.L.; Finnigan, G.T.; North, N.S.; Zheng, J.; Lyche, T., T-spline simplification and local refinement, ACM transact. graphics (TOG), SIGGRAPH, 23, 276-283, (2004)
[45] J. Shepherd, S. Mitchell, P. Knupp, D. White, Methods for multisweep automation, in: 9th International Meshing Roundtable, 2000, pp. 77-87.
[46] Siersma, D., Voronoi diagrams and Morse theory of the distance function, Geometry present day sci., 187-208, (1999) · Zbl 0945.68184
[47] M. Staten, S. Canaan, S. Owen, BMSweep: locating interior nodes during sweeping, in: 7th International Meshing Roundtable, 1998, pp. 7-18.
[48] D. Storti, G. Turkiyyah, M. Ganter, C. Lim, D. Stal, Skeleton-based modeling operations on solids, in: ACM Symposium Solid Modeling Applications, 1997, pp. 141-154.
[49] Taylor, C.A.; Hughes, T.J.R.; Zarins, C.K., Finite element modeling of blood flow in arteries, Comput. methods appl. mech. engrg., 158, 155-196, (1998) · Zbl 0953.76058
[50] Thompson, J.F.; Soni, B.K.; Weatherill, N.P., Grid generation, (1999), CRC Press LLC · Zbl 0980.65500
[51] Tomasi, C.; Madcuchi, R., Bilateral filtering for gray and color images, IEEE int. conf. comput. vision, 839, (1998)
[52] C.S. Verma, P.F. Fischer, S.E. Lee, F. Loth, An all-hex meshing strategy for bifurcation geometries in vascular flow simulation, in: 14th International Meshing Roundtable, 2005, pp. 363-375.
[53] Verroust, A.; Lazarus, F., Extracting skeletal curves from 3D scattered data, Visual comput., 16, 15-25, (2000) · Zbl 0955.68115
[54] White, D.; Saigal, S.; Owen, S., Automatic decomposition of multi-sweep volumes, Engrg. comput., 20, 222-236, (2004)
[55] T.-Y. Yu, B.K. Soni, Nurbs evaluation and utilization for grid generation, in: 5th International Conference on Numerical Grid Generation in Computational Field Simulations, 1996, pp. 323-332.
[56] Z. Yu, C. Bajaj, Image segmentation using gradient vector diffusion and region merging, in: 16th International Conference on Pattern Recognition, vol. 2, 2002, pp. 941-944.
[57] Z. Yu, C. Bajaj, A fast and adaptive algorithm for image contrast enhancement, in: IEEE International Conference on Image Processing (ICIP’04), vol. 2, 2004, pp. 1001-1004.
[58] Zachariah, S.G.; Sanders, J.E.; Turkiyyah, G.M., Automated hexahedral mesh generation from biomedical image data: applications in limb prosthetics, IEEE trans. rehabilit. engrg., 4, 2, 91-102, (1996)
[59] Zhang, Y.; Bajaj, C., Adaptive and quality quadrilateral/hexahedral meshing from volumetric data, Comput. methods appl. mech. engrg. (CMAME), 195, 9-12, 942-960, (2006) · Zbl 1119.65013
[60] Y. Zhang, C. Bajaj, B.-S. Sohn, 3d Finite element meshing from imaging data, The special issue of Comput. Methods Appl. Mech. Engrg. (CMAME) on Unstructured Mesh Generation, 194 (48-49) (2005) 5083-5106.
[61] Y. Zhang, Y. Bazilevs, S. Goswami, C.L. Bajaj, T.J.R. Hughes, Patient-specific vascular nurbs modeling for isogeometric analysis of blood flow, in: 15th International Meshing Roundtable, 2006, pp. 73-92. · Zbl 1121.76076
[62] Zhou, Y.; Toga, A., Efficient skeletonization of volumetric objects, IEEE trans. visual. comput. graphics, 5, 3, 196-209, (1999)
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