An abdominal aortic aneurysm is a localised progressive dilation of the abdominal aorta. Growth of the aneurysm is associated with a weakening of the wall and the possibility of rupture. Mathematical models of aneurysms may lead to a greater understanding of the pathogenesis of the disease and improved criteria for the prediction of rupture.
A microstructural model of the arterial wall is constructed. The principal load bearing components are elastin and collagen. The wall remodels in response to changes in stress and strain. The dilation of the aneurysm is driven by degradation of elastin and it is believed that collagen remodels to maintain an equilibrium value of strain in the collagen fibres. These features are incorporated into a three-dimensional membrane model that includes the the helical geometry of collagen fibres in the arterial wall and their local structural properties. The governing equations are formulated as a variational problem which is solved by a finite element method.
Three-dimensional deformations are analysed with and without spinal contact. The predicted stress and strain fields can be used to develop criteria for rupture. The model also predicts increased dilation rates in hypertensive conditions and the retraction of the aneurysm that follows a stent bypass operation.