Mathematical modelling of aortic dissection

Li, Beibei (2013) Mathematical modelling of aortic dissection. PhD thesis, University of Glasgow.

Abstract

An aortic dissection is a tear of the intima of the aortic wall that spreads into the media
or between the media and adventitia. In addition to the original lumen for blood flow,
the dissection creates a new flow channel, the `false' lumen that may cause the artery to
narrow or even close over entirely. Aortic dissection is a medical emergency and can quickly
lead to death.
The mechanical property of the aorta has been described by the strain energy function
given by Holzapfel et al. [2000]. The aorta is idealized as an elastic axisymmetric thickwalled
tube with 3 layers. We focus on the dissection in media, which is considered as
a composite reinforced by two families of fibres. We assume the dissection in the media
is axisymmetric. The mathematical model for the dissection is presented. The 2D plane
crack problem in linear elastic infinity plane and 2D strip, the axisymmetric crack problem
in linear elastic compressible and incompressible tube, the axisymmetric crack problem in
an incompressible axisymmetric aorta are applied to obtain solutions to three different
problems. And the fluid flow inside the crack has been studied.
The 2D plane crack problem in linear elastic infinity plane has been solved analytically.
The 2D plane crack problem in linear elastic compressible and incompressible strip is modelled respectively and solved numerically.
The models for axisymmetric crack problem in linear elastic compressible and incompressible tube are presented respectively. The numerical solutions for the crack problems are expressed, and the results are analyzed.
The mathematical model of the incompressible aorta axisymmetric dissection is given,
and the solutions are found numerically. The results change along with the different parameters in the strain energy function, which are analyzed and compared.
The fluid flow inside the tear is assumed very thin which is expressed as the lubrication
theory. We use the implicit method to model the Stokes equation numerically, and
test the crack opening change along with time.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: Hill, Prof. Nicholas and Roper, Dr. Steven
• Date of Award: 2013
• Depositing User: Miss Beibei Li
• Unique ID: glathesis:2013-3968
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 25 Feb 2013 11:13
• Last Modified: 25 Feb 2013 11:24
• URI: https://theses.gla.ac.uk/id/eprint/3968