On the Energy of a Hydroelastic System: Blood Flow in an Artery with Cerebral Aneurysm
M. Yu. Mamatyukov1,2, A. K. Khe1,2, D. V. Parshin1,2, P. I. Plotnikov1,2, A. P. Chupakhin1,2
1Lavrent'ev Institute for Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk National Research State University, Novosibirsk, 630090, Russia
Keywords: функционал Уиллмора, кривизна поверхности, церебральные аневризмы, гидроупругость, численный расчет, Willmore functional, surface curvature, cerebral aneurysms, hydroelasticity, numerical calculation
Abstract
An energy approach to the study of a hydroelastic system consisting of an elastic blood vessel, viscous fluid flow, and an aneurysm anomaly is developed to evaluate the various energy components of the system: viscous flow dissipation energy, tensile energy and bending energy of the aneurysm wall. To calculate the total energy of the system, we have developed a computing complex including commercial and free software and self-developed modules. The performance of the complex has been tested on model geometric configurations and configurations corresponding to blood vessels with cerebral aneurysms of real patients and those reconstructed by angiographic images. The calculated values of the Willmore functional characterizing the shell bending energy are consistent with theoretical data.
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