Abstract
Efficient and accurate reconstruction of imaging-derived geometries and subsequent quality mesh generation are enabling technologies for both clinical and research simulations. A challenging part of this process is the introduction of computable, orthogonal boundary patches, namely, the outlets, into treed structures, such as vasculature, arterial or airway trees. We present efficient and robust algorithms for automatically identifying and truncating the outlets for complex geometries. Our approach is based on a conceptual decomposition of objects into tips, segments, and branches, where the tips determine the outlets. We define the tips by introducing a novel concept called the average interior center of curvature and identify the tips that are stable and noise resistant. We compute well-defined orthogonal planes, which truncate the tips into outlets. The rims of the outlets are connected into curves, and the outlets are then closed using Delaunay triangulation. We illustrate the effectiveness and robustness of our approach with a variety of complex lung and coronary artery geometries.
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References
Altman DG, Bland JM (1994) Diagnostic tests. 1: sensitivity and specificity. BMJ 308:6943
Alumbaugh T, Jiao X (2005) Compact array-based mesh data structures. In: Proc. 14th Int. meshing roundtable, pp 485–504
Cornea N, Silver D, Yuan X, Balasubramanian R (2005) Computing hierarchical curve-skeletons of 3D objects. Vis Comput (Germany) 21(11):945–55
Cornea ND, Silver D, Min P (2007) Curve-skeleton properties, applications, and algorithms. IEEE Trans Vis Comput Graph 13:530–548
de Berg M, Cheong O, van Kreveld M, Overmars M (2008) Computational geometry: algorithms and applications, Chap 5, Section 2.2, 3rd edn. Springer, Berlin
Dey T, Sun J (2006) Defining and computing curve-skeletons with medial geodesic function. In: Proc. Eurographics Symp. Geometry Proc., pp 143–152
Dyedov V, Einstein DR, Jiao X, Kuprat AP, Carson JP, del Pin F (2009) Variational generation of prismatic boundary-layer meshes for biomedical computing. Int J Numer Meth Eng. doi:10.1002/nme.2583 (in press)
Einstein DR, Neradilak B, Pollisar N, Minard KR, Wallis C, Fanucchi M, Carson JP, Kuprat, Kabilan S, Jacob RE, Corley RA (2008) An automated self-similarity analysis of the pulmonary tree of the Sprague-Dawley rat. Anat Rec 291:1628–1648
Grinberg L, Karniadakis GE (2008) Outflow boundary conditions for arterial networks with multiple outlets. Ann Biomed Eng 36:1496–1514
Huo Y, Kassab GS (2007) A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree. Am J Physiol Heart Circ Physiol 292(6):H2623–33
Jiao X, Zha H (2008) Consistent computation of first- and second-order differential quantities for surface meshes. In: Prof. ACM solid and physical modeling symposium, pp 159–170
Kuprat A, Khamayseh A, George D, Larkey L (2001) Volume conserving smoothing for piecewise linear curves, surfaces, and triple lines. J Comput Phys 172:99–118
Kuprat AP, Einstein DR (2009) An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data. J Comput Phys 228:619–640
Lorensen W, Cline H (1987) Marching Cubes: A high resolution 3D surface construction algorithm. In: Proc. SIGGRAPH 87. 21:163–169
Maddah M, Soltanian-Zadeh H, Afzali-Kusha A (2003) Snake modeling and distance transform approach to vascular centerline extraction and quantification. Comput Med Imaging Graph (UK) 27(6):503 – 12
Minard KR, Einstein DR, Jacob RE, Kabilan S, Kuprat AP, Timchalk CA, Trease LL, Corley RA (2006) Application of magnetic resonance (MR) imaging for the development and validation of computational fluid dynamic (CFD) models of the rat respiratory system. Inhal Toxicol 18(10):787–94
Molthen RC, Karau KL, A DC (2004) Quantitative models of the rat pulmonary arterial tree morphometry applied to hypoxia-induced arterial remodeling. J Appl Physiol 97(6):2372–84
Newman T, Yi H (2006) A survey of the Marching Cubes algorithm. Comput Graph 30:854–879
Nordsletten DA, Blackett S, Bentley MD, Ritman EL, Smith NP (2006) Structural morphology of renal vasculature. Am J Physiol Heart Circ Physiol 291(1):H296–309
Palagyi K, Kuba A (1999) A parallel 3D 12-subiteration thinning algorithm. Graph Models Image Process (USA) 61(4):199–221
Pennecot J, Krenkel L, Wagner C (2008) Lung automatic reconstruction algroithm for CFD simulations. In: GiD 2008 4th conference on advances and applications of GiD
Shewchuk JR (1996) Triangle: engineering a 2D quality mesh generator and Delaunay triangulator. In: Lecture notes in computer science. 1148:203–222
Spaan JA, ter Wee R, van Teeffelen JW, Streekstra G, Siebes M, Kolyva C, Vink H, Fokkema DS, VanBavel E (2005) CT, MRI and cryomicrotome: visualisation of intramural coronary vasculature by an imaging cryomicrotome suggests compartmentalisation of myocardial perfusion areas. Med Biol Eng Comput 43(4):431–435
Taylor R (1999) An introduction to error analysis: the study of uncertainties in physical measurements. University Science Books, Mill Valley
Wischgoll T, Choy JS, Ritman EL, Kassab GS (2008) Validation of image-based method for extraction of coronary morphometry. Ann Biomed Eng 36(3):356–368
Zhou Y, Toga AW (1999) Efficient skeletonization of volumetric objects. IEEE Trans Vis Comput Graph 5:196–209
Acknowledgements
Research was supported by the National Heart and Blood Institute Award 1RO1HL073598-01A1; by the National Institute of Environmental Health Sciences Award P01 ES011617 and by the National Science Foundation award DMS-0809285. The authors would also like to acknowledge Dr. Ghassan Kassab for graciously providing the coronary CT data, and Dr. Kevin Minard for the lung MR data.
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Jiao, X., Einstein, D.R., Dyedov, V. et al. Automatic identification and truncation of boundary outlets in complex imaging-derived biomedical geometries. Med Biol Eng Comput 47, 989–999 (2009). https://doi.org/10.1007/s11517-009-0501-9
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DOI: https://doi.org/10.1007/s11517-009-0501-9