Stress analysis method for ascending aortic aneurysm based on unloaded geometry with non-uniform thickness distribution

Using finite element method (FEM) to compute wall stress is now a common way to assess ascending thoracic aortic aneurysms (ATAA) severity. Medical images can provide aortic geometry for FEM, but thickness information is lacked and the geometry is at loaded state. Therefore, in this study, an unloaded geometry with a non-uniform thickness distribution is reconstructed. Measurements of wall thickness are taken from resected tissue to accurately replicate the thickness distribution. Subsequently, a novel method, derived from the existing fixed-point iterative (FPI) approach, is developed and applied to estimate the unloaded aortic geometry. This new method involves updating the relaxation factor at each iteration to improve robustness by constraining it within a threshold and normalizing it. Compared to the traditional FPI method, this novel approach is better tailored to the aortic geometries examined in this study. The study compares stress results obtained from models with uniform and non-uniform aortic wall thickness, both with and without assuming unloaded conditions. Findings indicate that stress distribution of non-uniform geometry matches better to the measured damage extent. Stress distribution of unloaded geometry is similar to that of loaded geometry, while the use of unloaded geometry enhances the stress gradient. The stress analysis reveals variations across different directions and regions, with the second principal stress (SPS) magnitude that is more sensitive to the circumferential region than the first principal stress (FPS) and von Mises stress (VMS). There is an overlap area between the high SPS region and the most expanded region. The most dilated area usually matched with high SPS region for loaded and unloaded geometry or uniform and non-uniform geometry. Thus, although magnitude of SPS is smaller than that of FPS and of VMS, it is suggested to pay more attention to SPS in severity assessment of ATAA aneurysm.