Geodesic
Construction of complex three-dimensional structures of the aorta of a particular patient using finite analytical formulas
Matematičeskaâ biologiâ i bioinformatika, Tome 17 (2022) no. 2, pp. 312-324.

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We have developed a method for constructing the geometry of a morphologically realistic human aorta, including the aortic root (Valsalva sinus), thoracic aorta, aortic arch with branches, abdominal aorta with bifurcation vessels. The creation of a three-dimensional model of the human aorta is necessary when planning surgical interventions, when performing numerical modeling of blood flow in the aorta. The anatomical structure of the aorta differs in different patients, especially in the presence of various pathologies (aneurysms, stenoses, aortic dissection). Creation of an individual human aorta model based on MRI, CT images requires time-consuming manual work of a highly computer skilled specialist. Presented is a simple method of building a 3D model of the human aorta. Initially, a 3D model of the aorta (or selected section of the aorta) of one patient is created. For this purpose, an analytical 3D model of this aorta is constructed from the raw model of the aorta. To build such an analytical aorta, it is necessary to divide the aorta into characteristic sections and specify defining parameters for each section. To build a model of another patient's aorta, a base model is taken and adjusted based on the individual features of the patient's aorta structure. At that, areas of pathology (stenoses and aneurysms) are added if necessary. Correction of the basic model requires much less time and effort than creating an aortic model of a particular patient from scratch. One of the key features of the technique is ease of use, eliminating the monotonous manual labor of building an individual patient's aorta. The resulting three-dimensional model of the aorta is fully ready for 3D modeling and printing on a 3D printer. Sections of the aorta are docked with the second order of smoothness (continuous second derivative between sections of the constructed aorta). 
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     author = {A. E. Medvedev},
     title = {Construction of complex three-dimensional structures of the aorta of a particular patient using finite analytical formulas},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
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A. E. Medvedev. Construction of complex three-dimensional structures of the aorta of a particular patient using finite analytical formulas. Matematičeskaâ biologiâ i bioinformatika, Tome 17 (2022) no. 2, pp. 312-324. http://geodesic.mathdoc.fr/item/MBB_2022_17_2_a11/

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