Keywords: abdominal aortic aneurysm, fluid-structure interaction, finite volume, mesh motion, non-linear material.

An Abdominal Aortic Aneurysm (AAA) is a local and progressive balloon-like dilation found on the wall of the aorta. The arterial wall is compliant, with non-linear elastic material properties. Due to this, the interaction of the blood flow with the inner arterial wall is believed to play a particularly important role in the initiation, growth and rupture of the aneurysm.

Fluid-structure interaction simulations were performed using OpenFOAM-1.2 which uses the finite volume method to solve both the fluid and solid domains [1]. Fluid and solid mesh motion solvers were implemented to allow both meshes to expand and contract during the cardiac cycle.

The wall of an aneurysm is generally thinner than the arterial wall on either side of it. To represent this, FSI simulations were performed on a straight tube with a localised reduction in wall thickness in the middle of the tube. Initially a linear elastic material model was employed. A constant fluid pressure of 20 MPa was applied at the fluid inlet. This caused the thinner section of the geometry to displace more than the rest of the tube, forming a new geometry. A fluid pressure of 20 MPa was then reapplied to this new geometry, causing the thin-walled section to displace further. This was repeated and a number of different sized aneurysms were created in this way. FSI simulations were performed on each of these geometries using physiologically realistic inlet velocity and outlet pressure boundary conditions.

Following this, a code was implemented in OpenFOAM which allows materials with non-linear properties to be modelled. Initial testing of this code involved applying a fluid pressure of 10 MPa to an aneurysm model and performing FSI simulations modelling the solid as both a linear and non-linear material. A pressure of 30 MPa was also applied in both cases to observe the behaviour of the non-linear material at high stresses and strains.

When the initial pressure was applied to the tube, the fluid and solid meshes moved as the simulation progressed causing an aneurysm to form in the middle of the tube and the mesh motion was considered to have been implemented successfully.

In the FSI simulations on the aneurysm models, the maximum stress and maximum displacement were both found to occur during systolic deceleration. The location of maximum stress was found to depend on the uniformity of the aneurysm wall thickness. In all cases the maximum displacement also occurred in the centre of the aneurysm during systolic deceleration.

Results from the initial testing of the non-linear code show that when a low pressure was applied and low stresses were obtained, the solid displaced by the same amount for the linear and non-linear materials. When a high pressure was applied and high stresses were obtained, the non-linear material displaced more than the linear material. This is as expected from the stress-strain curves for both materials and this code shows good initial results.

1

A. Ivankovic, A. Karac, E. Dendrinos and K. Parker, "Towards Early Diagnosis of Atherosclerosis: The Finite Volume Methods for Fluid-Structure Interaction", Biorheology, 39, pp. 401 - 407, 2002.

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