Three-dimensional flows in a hyperelastic vessel under external pressure

Zhang, S., Luo, X. and Cai, Z. (2018) Three-dimensional flows in a hyperelastic vessel under external pressure. Biomechanics and Modeling in Mechanobiology, 17(4), pp. 1187-1207. (doi:10.1007/s10237-018-1022-y) (PMID:29744606)

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Abstract

We study the collapsible behaviour of a vessel conveying viscous flows subject to external pressure, a scenario that could occur in many physiological applications. The vessel is modelled as a three-dimensional cylindrical tube of nonlinear hyperelastic material. To solve the fully coupled fluid–structure interaction, we have developed a novel approach based on the Arbitrary Lagrangian–Eulerian (ALE) method and the frontal solver. The method of rotating spines is used to enable an automatic mesh adaptation. The numerical code is verified extensively with published results and those obtained using the commercial packages in simpler cases, e.g. ANSYS for the structure with the prescribed flow, and FLUENT for the fluid flow with prescribed structure deformation. We examine three different hyperelastic material models for the tube for the first time in this context and show that at the small strain, all three material models give similar results. However, for the large strain, results differ depending on the material model used. We further study the behaviour of the tube under a mode-3 buckling and reveal its complex flow patterns under various external pressures. To understand these flow patterns, we show how energy dissipation is associated with the boundary layers created at the narrowest collapsed section of the tube, and how the transverse flow forms a virtual sink to feed a strong axial jet. We found that the energy dissipation associated with the recirculation does not coincide with the flow separation zone itself, but overlaps with the streamlines that divide the three recirculation zones. Finally, we examine the bifurcation diagrams for both mode-3 and mode-2 collapses and reveal that multiple solutions exist for a range of the Reynolds number. Our work is a step towards modelling more realistic physiological flows in collapsible arteries and veins.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Luo, Professor Xiaoyu
Authors: Zhang, S., Luo, X., and Cai, Z.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Biomechanics and Modeling in Mechanobiology
Publisher:Springer
ISSN:1617-7959
ISSN (Online):1617-7940
Published Online:09 May 2018
Copyright Holders:Copyright © 2018 The Authors
First Published:First published in Biomechanics and Modeling in Mechanobiology 17(4):1187-1207
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
694461EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - MATHEMATICS
689601The first fully coupled mitral valve - left ventricle computational modelXiaoyu LuoLeverhulme Trust (LEVERHUL)RF-2015-510M&S - MATHEMATICS