On the optimal structure of the arterial wall

Багаев, С. Н.; Zakharov, V.N.; Markel, A. L.; Медведев, А. Е.; Orlov, V. A.; Самсонов, В. И.; Фомин, В. М.

doi:10.1134/1.1810580

Cited by 5 publications

(2 citation statements)

References 1 publication

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“…According to Ref. [2], the ratio between the wall width and the radius of blood vessels is relatively constant and it lays between 0.15 and 0.20 . Then, ε varies from 0.05 to 0.07 .…”

Section: Asymptotic Analysis Of Problem (315)mentioning

confidence: 99%

A mathematical model of the atherosclerosis development in thin blood vessels and its asymptotic approximation

Mel'nyk

2017

Preprint

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Some existing models of the atherosclerosis development are discussed and a new improved mathematical model, which takes into account new experimental results about diverse roles of macrophages in atherosclerosis, is proposed. Using technic of upper and lower solutions, the existence and uniqueness of its positive solution are justified. After the nondimensionalisation, small parameters are found. Then asymptotic approximation for the solution is constructed and justified with the help of asymptotic methods for boundary-value problems in thin domains. The results argue for the possibility to replace the complex 3D (dimensional) mathematical model with the corresponding simpler 2D model with sufficient accuracy measured by these small parameters.

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“…According to Ref. [2], the ratio between the wall width and the radius of blood vessels is relatively constant and it lays between 0.15 and 0.20 . Then, ε varies from 0.05 to 0.07 .…”

Section: Asymptotic Analysis Of Problem (315)mentioning

confidence: 99%

A mathematical model of the atherosclerosis development in thin blood vessels and its asymptotic approximation

Mel'nyk

2017

Preprint

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“…This fact was first documented in the early 1930s [ 1 ] and has recently been repeatedly proved using modern diagnostic tools [ 2 , 3 , 4 , 5 ]. A number of research groups have addressed this phenomenon; however, the results of their studies have not made it possible to identify the mechanisms of generation of a blood flow swirl or propose reliable quantitative criteria for assessing the quality of a swirling blood jet [ 6 , 7 ]. The benefits of a flow swirl stated in these studies have been formulated rather vaguely and are confined to a size reduction of the detachment and congestion zones and prevention of boundary layer thickening as the blood flow evolves [ 8 ].…”

Section: Introductionmentioning

confidence: 99%

The Hydrodynamics of a Swirling Blood Flow in the Left Heart and Aorta

et al. 2021

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This paper proposes a new approach to the quantitative analysis of the hydrodynamic structure of a blood flow in the flow channel running from the left atrium to the end of the aorta. This approach is based on the concept of the structural organization of tornado-like swirling jets in channels with a given geometric configuration. Considering the large amount of experimental data in our possession, it was shown that along the entire length of the flow channel, conditions exist for the generation and maintenance of a swirling structure of the jet throughout the entire cardiac cycle. This study has given rise to a new direction in research in fundamental physiology and medicine, which is of great practical importance for diagnosing and treating circulatory disorders accompanied by changes in the geometric configuration and biomechanical characteristics of the heart and great vessels.

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Unsteady motion of a viscous incompressible fluid in a tube with a deformable wall

Медведев

2013

J Appl Mech Tech Phy

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On the optimal structure of the arterial wall

Cited by 5 publications

References 1 publication

A mathematical model of the atherosclerosis development in thin blood vessels and its asymptotic approximation

A mathematical model of the atherosclerosis development in thin blood vessels and its asymptotic approximation

The Hydrodynamics of a Swirling Blood Flow in the Left Heart and Aorta

Unsteady motion of a viscous incompressible fluid in a tube with a deformable wall

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