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An incremental deformation model of arterial dissection

Li, Beibei; Roper, Steven M.; Wang, Lei; Luo, Xiaoyu; Hill, N.A.

An incremental deformation model of arterial dissection Thumbnail


Beibei Li

Steven M. Roper

Lei Wang

Xiaoyu Luo

N.A. Hill


We develop a mathematical model for a small axisymmetric tear in a residually stressed and axially pre-stretched cylindrical tube. The residual stress is modelled by an opening angle when the load-free tube is sliced along a generator. This has application to the study of an aortic dissection, in which a tear develops in the wall of the artery. The artery is idealised as a single-layer thick-walled axisymmetric hyperelastic tube with collagen fibres using a Holzapfel–Gasser–Ogden strain-energy function, and the tear is treated as an incremental deformation of this tube. The lumen of the cylinder and the interior of the dissection are subject to the same constant (blood) pressure. The equilibrium equations for the incremental deformation are derived from the strain energy function. We develop numerical methods to study the opening of the tear for a range of material parameters and boundary conditions. We find that decreasing the fibre angle, decreasing the axial pre-stretch and increasing the opening angle all tend to widen the dissection, as does an incremental increase in lumen and dissection pressure.


Li, B., Roper, S. M., Wang, L., Luo, X., & Hill, N. (2019). An incremental deformation model of arterial dissection. Journal of Mathematical Biology, 78(5), 1277-1298.

Journal Article Type Article
Online Publication Date Nov 19, 2018
Publication Date Apr 30, 2019
Deposit Date Apr 25, 2019
Publicly Available Date Apr 25, 2019
Journal Journal of Mathematical Biology
Print ISSN 0303-6812
Electronic ISSN 1432-1416
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 78
Issue 5
Pages 1277-1298


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© The Author(s) 2018. <br /> This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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