Uncertainty Quantification for Abdominal Aortic Aneurysms

For the accurate prediction of rupture risk of abdominal aortic aneurysms (AAAs) using finite element models, patient specific data is needed. This includes the geometry of the AAA and of course patient specific material properties of the aneurysmatic wall. Using modern CT scanners it is possible to obtain the overall shape of the AAA. The local wall thickness, however, can not be detected. In addition, it is impossible to estimate the parameters of a patient specific constitutive law in vivo. Excision of AAA tissue specimens for tensile testing and determination of a patient specific material properties can only be performed during open surgical repair, thus rendering a computational rupture risk prediction obsolete.

Since prior to surgery some patient specific parameters are subject to uncertainty, our approach is to include this uncertainty into the computational model to get a more reliable estimate of the rupture risk. We are using and developing Bayesian multi-fidelity schemes to efficiently propagate the input uncertainty through the nonlinear system to obtain response statistics.  

The figure on the right shows three different possible distributions of one constitutive parameter in a model of an AAA.