An incremental deformation model of arterial dissection

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

Abstract

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.

Citation

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. https://doi.org/10.1007/s00285-018-1309-8

• 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
• DOI: https://doi.org/10.1007/s00285-018-1309-8
• Public URL: https://durham-repository.worktribe.com/output/1303268