The haemodynamics of aneurysms: a spectral element analysis of the effects of wall stiffness

The prevalence of abdominal aortic aneurysms is increasing with an ageing population. Aneurysms present a major health risk; in the event of aneurysm rupture, patients exhibit a mortality rate of 70-95% (Lindholt et al. 2005). Treatment of aneurysms involves invasive surgery, which carries an inherent risk, therefore it is preferable to intervene only when the aneurysm is close to rupture. Currently, the aneurysm initiation, growth and rupture mechanisms are not fully understood and accurate predictions of aneurysm growth-rate and rupture time cannot be made. Research in this field has identified haemodynamic stimuli as the principal factor in aneurysm growth. As such, in-depth fluid-dynamic investigations can contribute greatly to developing appropriate models for patient prognosis and treatment. Previous investigations into aneurysm haemodynamics have largely been focused on blood flows with rigid-wall dynamics. To realistically model the flow, a moving boundary condition must be applied to account for the elasticity of the aneurysm wall. A fluid-structure interaction was studied in the context of abdominal aortic aneurysms. The effects of an elastic wall were modelled using a numerical technique. To this end, a new coupling scheme is proposed based around an Arbitrary Lagrangian-Eulerian (ALE) algorithm. The monolithic ALE solver uses a modified iterative over unequal time step coupling routine. The use of an ALE algorithm for modelling aneurysm flows maximises the accuracy of flow field data in the near-wall region where the haemodynamic environment is most pertinent. The biological material that comprises the artery wall is highly complex in nature. To accurately model the wall response, the wall is modelled as a multi-layered, hyper-elastic and heterogeneous material. A novel time stepping algorithm was developed and tested to model the wall response in the aneurysm. Spectral elements were used for the spatial discretisation while a backward differencing time stepping scheme was proposed for the temporal evolution. A two-step operator splitting scheme was proposed in order to implicitly solve for the displacement at the next time step. This algorithm is capable of modelling both the inertial and non-linear response of the wall, which is important in the context of biological applications. Once formulated, two fluid-structure interaction studies were conducted. The first investigated the effects of heterogeneous wall properties, such as those formed around lesions and calcification, on the haemodynamics in arteries. It was found that previous models based on a rigid-wall assumption misrepresent the flow conditions in aneurysms. Furthermore, it was shown that local variations in wall elasticity can affect the wall shear stress environment both locally and downstream of the lesion or calcification. Weakening of the aneurysm wall was shown to increase the wall shear stress downstream. This occurred as the greater wall motion led to higher variations in flow rate. In terms of the local effects, local variations in wall stiffness led to additional variations in aneurysm geometry and wall velocity. These changes led to a local change in boundary layer thickness which in turn affected the local wall shear stress distribution. In cases when the wall was weakened the wall shear stress decreased locally. Conversely the stiffer wall case corresponded to an increase in local wall shear stress. Finally an investigation into the effect of wall stiffness on established aneurysm geometries was conducted. Using an elastic-wall model, the wall motion was shown to cause significant flow reversal in the boundary layer. As a result, in addition to the vortex ring shed from the proximal neck, a distal vortex ring formed. The proximity of these vortices to the aneurysm wall affects the shear layer at the wall and consequently the wall shear stresses. In cases where there was large motion, the shear layer is drawn into a secondary distal vortex ring. At intermediate levels of wall motion, the formation of this secondary distal vortex ring is suppressed. The presence of the primary distal vortex ring protects the wall from the impact of the strong proximal vortex ring. Local variations in wall stiffness were investigated at three locations in the aneurysm bulge. All weakened wall cases exhibited similar changes in wall dynamics compared to the uniformly stiff case. However, it has been shown that a weakened region upstream of the distal neck provided the greatest change in wall shear stress distribution. The case of a weakened central region represents the least favourable haemodynamic conditions for healthy endothelial wall function. In terms of the stiffened cases, the least protective distribution was the stiffening at the distal neck. These results indicate that aneurysms that feature a weakened wall region upstream of the distal neck present the greatest risk of rupture.