Abstract: | Recent advances in computational modeling of vascular adaptations and the need for their extension to patient-specific modeling
have introduced new challenges to the path toward abdominal aortic aneurysm modeling. First, the fundamental assumption in
adaptation models, namely the existence of vascular homeostasis in normal vessels, is not easy to implement in a vessel model
built from medical images. Second, subjecting the vessel wall model to the normal pressure often makes the configuration deviate
from the original geometry obtained from medical images. To address those technical challenges, in this work, we propose a
two-step optimization approach; first, we estimate constitutive parameters of a healthy human aorta intrinsic to the material
by using biaxial test data and a weighted nonlinear least-squares parameter estimation method; second, we estimate the distributions
of wall thickness and anisotropy using a 2-D parameterization of the vessel wall surface and a global approximation scheme
integrated within an optimization routine. A direct search method is implemented to solve the optimization problem. The numerical
optimization method results in a considerable improvement in both satisfying homeostatic condition and minimizing the deviation
of geometry from the original shape based on in vivo images. Finally, the utility of the proposed technique for patient-specific
modeling is demonstrated in a simulation of an abdominal aortic aneurysm enlargement. |