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Journal of Applied Mechanics and Technical Physics

2020 year, number 5

Energy Approach to the Solution of the Hydroelastic Problem of the Growth of a Diverticulum of a Fusiform Aneurysm

M. Yu. Mamatyukov1,2, A. K. Khe1,2, D. V. Parshin1,2, A. P. Chupakhin1,2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk National Research State University, Novosibirsk, 630090, Russia
Keywords: церебральная аневризма, дивертикул, гидроупругость, энергия Уиллмора, гемодинамика, cerebral aneurysm, diverticulum, hydroelasticity, Willmore energy, hemodynamics

Abstract

This paper considers an energy approach to assessing the state of a cerebral aneurysm as a hydroelastic system consisting of an elastic vessel wall and oncoming blood flow. Assuming that the elastic energy of a vessel with an aneurysm in combination with the bending energy and kinetic energy is spent only on viscous flow dissipation in the structure, we performed a series of numerical calculations for model configurations of a fusiform aneurysm in the absence and in the presence of a diverticulum of different sizes relative to the size of the aneurysm body. It is shown that pressure-velocity diagrams are in good agreement with clinical data. Using numerical simulation, it is shown that a diverticulum of small size has a significant effect on hemodynamics inside the body of the aneurysm, and at a large diverticulum size, the vortex induced inside the diverticulum is almost completely localized in it.