Geodesic
Reconstruction of 3D geometry of coronary arteries
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 2, pp. 37-56.

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We consider the problem of 3D reconstruction for the internal surface of aorta and coronary arteries. This is needed for the creation of a hydrodynamic model of blood supply to the heart. The initial data are transverse tomographic sections of the heart of a particular patient with a thickness of 0.5 mm. Triangulation of the aorta and coronary arteries is to be used to calculate a blood flow in the software package FlowVision, designed for modeling three-dimensional flows of liquid and gas. The simulation results are planned to be applied in practical medicine for the diagnosis of myocardial ischemia. Triangulation is calculated using a three-dimensional Seeded Region Growing algorithm that creates a set of voxels. Then the triangulation of the surface of this set is constructed and smoothed by the Subdivision Surface method. We also describe a semi-automatic procedure to define a Region of Interest used to separate the aorta and coronary arteries from the inner volume of heart, veins and other structures that should not be included in the constructed triangulation. 
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     title = {Reconstruction of {3D} geometry of coronary arteries},
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     url = {http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a2/}
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V. V. Borisenko; T. N. Veselova; S. K. Ternovoy; A. M. Chepovskiy. Reconstruction of 3D geometry of coronary arteries. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 2, pp. 37-56. http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a2/

[1] Aksenov A. A., “FlowVision: industrialnaya vychislitelnaya gidrodinamika”, Kompyut. issled. i modelirovanie, 9:1 (2017), 5–20

[2] Aksenov A. A., Gudzovskii A. V., “Paket prikladnykh programm FlowVision”, Tr. MFTI. Ser. Aerofizika i prikl. matem., 1998, 45–56

[3] Bonchkovskii R. N., “Zapolnenie prostranstva tetraedrami”, Matem. prosv. Ser. 1, 4, 1935, 26–40

[4] Veselova T. N., Merkulova I. N., Barysheva N. A., Ternovoi S. K., Shariya M. A., Ruda M. Ya., “Sravnenie osobennostei ateroskleroticheskikh blyashek v koronarnykh arteriyakh u bolnykh s ostrym koronarnym sindromom i stabilnoi formoi ishemicheskoi bolezni serdtsa po dannym multispiralnoi kompyuternoi tomografii”, Kardiologiya, 53:12 (2013), 14–20

[5] Veselova T. N., Merkulova I. N., Yarovaya E. B., Ternovoi S. K., Ruda M. Ya., “Rol multispiralnoi kompyuternoi tomografii v otsenke zhiznesposobnosti miokarda i prognozirovanii razvitiya remodelirovaniya levogo zheludochka serdtsa u bolnykh infarktom miokarda s pod'emom segmenta ST na EKG”, Kardiologiya, 53:2 (2013), 10–18

[6] Vinberg E. B., “Kaleidoskopy i gruppy otrazhenii”, Matem. prosv., 7, 2003, 45–63

[7] Kallinger W., Borisenko V. V., Dizhevskii A. Yu., “Raspoznavanie sharovidnykh osobennostei po serii tomograficheskikh snimkov”, Tr. 18-i Mezhdunar. konf. po kompyut. grafike i zreniyu, Grafikon'2008, GraphiSon, M., 2008, 312 pp.

[8] Kokster G. S. M., Vvedenie v geometriyu, Nauka, M., 1966 | MR

[9] Ternovoi S. K., Shabanova M. S., Gaman S. A., Merkulova I. N., Shariya M. A., “Rol kompyuternoi tomografii v vyyavlenii nestabilnykh ateroskleroticheskikh blyashek koronarnykh arterii: sopostavlenie rezultatov kompyuternoi tomografii i vnutrisosudistogo ultrazvukovogo issledovaniya”, Ros. elektr. zhurn. luch. diagn., 6:3 (2016), 68–79 http://rejr.ru/

[10] Carneiro B. P., Kaufman A. E., “Tetra-Cubes: An algorithm to generate 3D isosurfaces based upon tetrahedra”, SIGGRAPH'96, 205–210

[11] Catmull E., Clark J., “Recursively generated B-spline surfaces on arbitrary topological meshes”, Computer-Aided Design., 10:6 (1978), 350–355 | DOI

[12] Chernyaev E. V., Marching Cubes 33: Construction of Topologically Correct Isosurfaces, Inst. for High Energy Phys., Protvino, 1995

[13] Gueziec A., “Exploiting triangulated surface extraction using tetrahedral decomposition”, IEEE Trans. Visualization Comput. Graphics, 1:4 (1995), 328–342 | DOI

[14] Justice R. K., Stokely E. M., Strobel J. S., Ideker R. E., Smith W. M., “Medical image segmentation using 3D seeded region growing”, Medical Imaging 1997: Image Processing, Proc. SPIE, 3034, 1997

[15] Kallinger W., Fischer R., Borisenko V., Porteder H., Santha G., Springer E., “Dental planning and patient safety”, Wiener Klinische Wochenschrift, 120, suppl. 3 (2008), 52–54

[16] Kallinger W., Fischer R., Borisenko V., Santha G., Springer E., “Computer aided detection of lung nodules in the view of patient safety”, Wiener Klinische Wochenschrift, 120, suppl. 3 (2008), 49–52 | DOI

[17] Loop Ch., Smooth Subdivision Surfaces Based on Triangles, M. S. Math. Thesis, Univ. of Utah, 1987

[18] Lorensen W. E., Cline H. E., “Marching Cubes: A high resolution 3D surface construction algorithm”, Computer Graphics, 21:4 (1987), 163–169 | DOI

[19] Serra J., Image Analysis and Mathematical Morphology, Academic Press, 1982 | MR | Zbl

[20] Skala V., “Precision of isosurface extraction from volume data and visualization”, Conf. on Sci. Comput., 2000, 368–378

[21] Pavlidis G., Algorithms for Graphics and Image Processing, Comput. Sci. Press, Rockville, 1982 | MR | Zbl

[22] Bui Tuong Phong, Illumination of Computer-Generated Images, UTEC-CSs-73-129, Univ. of Utah, 1973