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. 
@article{FPM_2020_23_2_a2,
     author = {V. V. Borisenko and T. N. Veselova and S. K. Ternovoy and A. M. Chepovskiy},
     title = {Reconstruction of {3D} geometry of coronary arteries},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {37--56},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2020},
     language = {ru},
     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/