Mathematical modeling of flows in blood vessels of complex shape

Cardiometry

article

Yuri Y. Gromov¹  Aleksei V. Gorbunov¹  Viacheslav M. Tyutyunnik¹  Sergey A. Kopylov¹ 

[1]Tambov State Technical University Russia

关键词: Blood vessels;    Complex shape;    Blood flows;    Mathematical modeling;   

DOI  :  10.18137/cardiometry.2022.24.145158

学科分类：环境科学（综合）

来源: Russian New University

【 摘 要 】

A study of the structure and topography of the cerebral arterialbed of 156 virtually healthy individuals verified 17 variants ofthe arterial circle of the great brain, most of which are shownin actual photographs. An analysis of various approaches tomodeling of cerebral vessels was carried out and it is shownthat all of them are based on the representation of a bloodvessel in the form of a linear cylinder. In reality, in the blood system of the brain, such sections are only rare short elements ofvessels that vary in diameter and direction. Cylindrical coordinates have been most commonly used to construct mathematical models of cerebral vessels, but they are not applicable tobending vessels. The aim of this work: to build a mathematicalapparatus allowing to adequately describe various types of vessels containing sections with complex geometry (bends, especially U-shaped ones, spirals, etc.). Four typical sections of thevascular system were identified, in correspondence with whichmathematical surfaces were introduced, and the correspondingmathematical description was selected for each of them. Themathematical apparatus introduced into consideration allowedus to build a description of hydrodynamic processes occurringin vessels of complex shape. The results of geometrical modeling in the Mathlab system and the corresponding fragments ofthe script are presented. The developed mathematical softwaremade it possible to construct a system of transfer equations forvessels of complex shape.

【 授权许可】

CC BY