Modelling dissection of the arterial wall

Wang, Lei (2016) Modelling dissection of the arterial wall. PhD thesis, University of Glasgow.

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Arteries are the highways through which oxygen-rich blood flows toward oxygen-hungry organs, such as the kidneys, heart, and brain. An arterial dissection is an axial tear within the arterial wall, which may create a false lumen by the action of blood flow through the tear. Propagation of the tear can quickly lead to death as a result of decreased blood supply to other organs, damage to the aortic valve, and sometimes rupture of the artery.

This thesis aims to develop computational models to simulate the inflation and propagation of a tear in the arterial wall and to investigate the mechanical issues in arterial dissection, with mainly focusing on the effects of the fibre orientation, geometry of the tear and residual stress on dissection propagation. The numerical methods used in our models include both the finite element method and the extended finite element method. We assume the mechanical response of the arterial wall is nonlinear, hyperelastic and anisotropic, and use the Holzapfel-Gasser-Ogden (HGO) strain energy function as the constitutive law.

A finite element computational framework, for the calculation of the energy release rate for a fibre-reinforced soft tissue subject to internal pressure, is developed. This model extends the Griffith failure theory such that we can consider pressure-driven tear propagation subject to a large nonlinear deformation of the arterial wall. Using this model to simulate the tear propagation in strips from the arterial wall, we found the increase in the length of a tear elevates the likelihood of propagation, and if the tissues surrounding the tear are stiff enough this leads to arrest.

Simulations of peeling- and pressure-driven tear propagation are performed through the extended finite element method. Peeling-driven propagation is caused by a displacement boundary condition, while pressure-driven propagation is due to pressure loading. We found the tear is likely to propagate along the material axis with the maximum stiffness, which is determined by the fibre orientation in the arterial wall. In models of pressure-driven tear propagation, we investigate the effect of the radial depth and circumferential length of a tear in the cross-section of a two-layer (media and adventitia) arterial wall model. The results show that a shallow and long tear leads to buckling of the inner wall (material section between tear and lumen), while a deep tear tends to propagate. Several shapes of deformed arterial wall with a tear predicted from our simulations are similar to CT images of arterial dissections. The critical pressure for propagation increases with the depth for a very short tear, but decreases for a long tear.

Two methods of introducing residual stress, quantified by an opening angle, into a finite element model for the arterial wall are proposed. The computational programs, of using programming languages including Linux shell script, sed, AWK, Python and Matlab, to automatically build finite element models with both methods are developed. We have used them to investigate the effect of residual stress on the critical pressure for tear propagation in the cross-section of the two-layer arterial wall model. The first method is to import the analytical residual stress into a finite element model as an initial stress field, while the second method is to use a residual stress computed numerically. The first method is illustrated with the neo-Hookean material model, and the second method is used with the HGO material model. We find a similar trend of the critical pressure against the opening angles: the critical pressure increases with the opening angle. However, the increase of the critical pressure is less steep in the HGO model compared to the neo-Hooken model. This is presumably due to the interaction of the fibres. When more fibres are stretched, the loading bearing is shifted more towards the fibre structure, and the influence of the residual stress becomes less.

The implementation of an anisotropic hyperelastic material model with growth, for a living fibrous soft tissue, in a finite element program is presented. The problem of loss of anisotropy in the conventional approach when using the volumetric-isochoric decomposition of deformation gradient is analysed. A possible solution is suggested: avoiding use of this decomposition in the parts associated with anisotropy in the strain energy function. This suggestion is demonstrated through several examples using the Fung-type and HGO material models. The essential derivation of the HGO material model is presented for its finite element implementation with both the conventional approach and our suggestion. The corresponding user-subroutines used in a finite element program FEAP are included. In addition, the growth of tissue is also considered in this subroutine by introducing a growth tensor as a material parameter. The method on how to update this subroutine to consider a stress-, strain- or energy-driven growth law is discussed, which could be used to model the tear propagation in a living fibrous tissue.

In summary, this thesis presents computational techniques for modelling dissection of the arterial wall. These models characterise the mechanical factors in the arterial dissection, which could be adapted for other damage and failure of soft tissue. A prediction from these models opens a window to the mechanical issues of this disease and other injuries.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: Arterial dissection, finite element, buckling, tear propagation, energy release rate, cohesive zone model, residual stress, critical pressure
Subjects: Q Science > QA Mathematics
Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
Supervisor's Name: Luo, Prof. Xiaoyu and Roper, Dr. Steven and Hill, Prof. Nicholas
Date of Award: 2016
Depositing User: Mr Lei Wang
Unique ID: glathesis:2016-7066
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 05 Feb 2016 16:06
Last Modified: 17 Feb 2016 09:06

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