Non-invasive in vivo time-dependent strain measurement method in human abdominal aortic aneurysms: Towards a novel approach to rupture risk estimation

We aim to introduce a novel, inverse method for in vivo material parameter identification of human abdominal aortic aneurysms (AAA), which could overcome one of the greatest sources of uncertainty in patient-specific simulations, and could also serve as a rapid, patient-calibrated, novel measure of aneurysm rupture risk. As an initial step, the determination of the kinematic fields is presented here. Images of the AAA lumen, acquired in 10 discrete time-steps through a stabilized cardiac cycle by electrocardiogram-gated computer tomography angiography, are used to approximate the in vivo, time dependent kinematic fields of the arterial wall using a novel, incompressible Kirchhoff-Love shell element implemented into the isogeometric analysis framework. Defining a smoothing parametric surface via 2D bicubic spline fitting in the spatial, and by harmonic regression in the temporal domain, we are able to adequately mitigate the measurement inaccuracy. The ill-posedness of the problem requires certain assumptions on the displacement. In our case, based on numerical fluid structure interaction simulation observations, we hypothesized the incremental displacement vector of the reference surface to coincide with its corrected normal; hence the periodic movement was assured. Finally, we present two examples: an AAA and an undilated calcificated aorta. Strains in the diseased part were compared to those in a healthy arterial section of the same patient and found to have significant differences in both specimens. In the case of AAAs, high spatial gradients surrounding the dilated part indicate abrupt changes in material properties, a phenomenon less significant for the atherosclerotic case.