Continuum-Mechanical modeling of aneurysm formation

An aneurysm is a bulge (dilation) in the wall of an artery, usually the aorta. An aneurysm that grows and becomes large enough can burst, causing dangerous, often fatal, bleeding inside thebody. Information from mathematical modeling of aneurysm formation can help doctors make the difficult decision about which course of action to take once an aneurysm has been diagnosed (whether to carry out a surgery, to prescribe appropriate drugs to reduce the risk of aneurysm bursting or to simply put the patient under observation). Previous studies have focused on modeling the evolution of aneurysms numerically by assuming that a seriously enough inhomogeneous weakening of the artery has taken place. We aim to model aneurysm formation from a different perspective: we view the initiation of an aneurysm as a bifurcation problem; it can occur even if the material properties are homogeneous along the artery. We hope to establish a theoretical framework under which the initiation of an aneurysm can be predicted, and once an operation to remove or repair an aneurysm has been carried out the integrity of the operated section can be assessed. This will involve the following two tasks: (i) derivation of appropriate constitutive models for healthy and pathological arteries, and (ii) given a particular material model, describing precisely whether an aneurysm can form or not and how it will form (e.g. whether it will grow axi-symmetrically or from the side).