Computational estimation of haemodynamics and tissue stresses in abdominal aortic aneurysms

Abstract

Abdominal aortic aneurysm is a vascular disease involving a focal dilation of the aorta. The exact cause is unknown but possibilities include infection and weakening of the connective tissue. Risk factors include a history of atherosclerosis, current smoking and a close relative with the disease. Although abdominal aortic aneurysm can affect anyone, it is most often seen in older men, and may be present in up to 5.9% of the population aged 80 years. Biomechanical factors such as tissue stresses and shear stresses have been shown to play a part in aneurysm progression, although the specific mechanisms are still to be determined. The growth rate of the abdominal aortic aneurysm has been found to correlate with the peak stress in the aneurysm wall and the blood flow is thought to influence disease development. In order to resolve the connections between biology and biomechanics, accurate estimations of the forces involved are required.

The first part of this thesis assesses the use of computational fluid dynamics for modelling haemodynamics in abdominal aortic aneurysms. Boundary conditions from the literature on healthy patients are used, along with patient specific aneurysm geometries, to obtain a first estimate of blood flow patterns and haemodynamic wall parameters within the aneurysms. The use of healthy patient boundary conditions is difficult to justify as the presence of the aneurysm is likely to alter the flow rate in the aorta. This is investigated with a Doppler ultrasound study of blood velocities in the normal and aneurysmal aorta. Archetypal waveforms reveal a significant difference in the diastolic maximum of young healthy volunteers and AAA patients. The archetypal aortic velocity wave for patients with abdominal aortic aneurysm is used to calculate the haemodynamics in a group of patients and these calculations are compared with those obtained using patient specific boundary conditions, and with phase-contrast magnetic resonance imaging measurements of blood velocity. With the correct z-velocity profile at the entrance to a short inlet section proximal to the aneurysm, the calculated velocities agreed qualitatively with the measured velocities. However, the velocities calculated using the correct inlet flow rate, but a simple velocity profile, are quite different from the measurements. These results show that the correct velocity profile at the aneurysm entrance is required to predict velocities within the aneurysm cavity.

In reality the blood and the artery wall interact: the blood flow domain continually dilates and contracts, altering the flow patterns; the flow controls the pressure on the wall and therefore the stresses within it. The influence of this fluid-structure interaction on the blood flow and tissue stresses is investigated in axially symmetric models of abdominal aortic aneurysm. Modelling of the complete fluid-structure interaction reveals how the pressure and flow waves are distorted by the aneurysm geometry. This distortion, which is absent from both static pressure and one way coupled models, accounts for the small errors in tissue and wall shear stresses obtained when using these models with lower computational complexity. These errors vary with the type of modelling as well as the aneurysm diameter and elasticity. A one dimensional, lumped parameter model of the aneurysm is developed to elucidate the effect of aneurysm geometry on the propagation of pressure and flow waves. It reveals interesting consequences of the diameter of the aneurysm on its inductance and resistance, and its use in improving the outlet pressure boundary condition is investigated.