V.V. Borisenko – Ph.D.(Phys.-Math.), Associate Professor,  Lomonosov Moscow State University

E-mail: vladimir_borisen@mail.ru

T.N. Veselova – Dr.Sc.(Med.), 

National Medical Research Center of Cardiology of the Ministry of Healthcare of Russia (Moscow) E-mail: tnikveselova@gmail.com

S.K. Ternovoi – Academic of RAS, Dr.Sc.(Med.), Head of Department, 

I.M. Sechenov First Moscow State Medical University; 

National Medical Research Center of Cardiology of the Ministry of Healthcare of Russia (Moscow) E-mail: prof_ternovoy@list.ru

A.M. Chepovskiy – Dr.Sc.(Eng.), Professor, 

RUDN Univercity (Moscow); 

HSE (Moscow)

E-mail: achepovskiy@hse.ru

According to computed tomography of the patient’s heart region, a 3D model for the inner surface of the coronary arteries and part of the aorta is being constructed. Recreating the 3D geometry of blood vessels is necessary to build a hydrodynamic model of blood supply to the heart and calculate parameters of blood flow using the Navier–Stokes equations. When constructing the geometric model, special attention is paid to the removal of calcifications from the internal volume of blood vessels, which strongly affect the blood flow.

For computing a 3D model, a combination of a seeded region growing algorithm, which works with voxels of space, and a cellular algorithm for constructing an isosurface triangulation is used. The latter uses the tetrahedral mesh proposed by S. Chan, E. Purisima, and V. Skala, in which tetrahedra are built in a cubic lattice on the common faces of adjacent cubes. Such tetrahedral mesh fits well with the partition of space into a voxel lattice, which makes it possible to combine two different 3D algorithms.

The voxel region growing algorithm allows us to perform three-dimensional segmentation of the circulatory system that separates the coronary arteries from the veins and internal volumes of the heart. Segmentation is performed semi-automatically. At the first stage, the complete model of circulatory system is computed by the region growing algorithm. Then the user manually marks on the axial sections the contours in the upper and lower parts of the aorta and, if necessary, in the coronar arteries. The voxels inside these contours serve as boundaries for the region growth algorithm. After this, the region growth algorithm is launched for the second time. It builds a subset of the initial model inside the established boundaries. The same region growing algorithm is then used to isolate calcifications within the constructed voxel model.

Finally, the voxel model is used in conjunction with the tetrahedral mesh for precise calculating the triangulation of the model surface. The tetrahedral mesh is built only in the neighborhood of the border of voxel model. This allows us to compute a surface triangulation with subpixel accuracy.

Borisenko V.V., Veselova T.N., Ternovoi S.K., Chepovskiy A.M. Building a 3D model of heart vessels with the removal of calcifications. Highly Available Systems. 2020. V. 16. № 3. P. 58−65. DOI: 10.18127/j20729472-202003-06. (In Russian).

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