The Relationship Between Surface Curvature and Abdominal Aortic Aneurysm Wall Stress

Abstract

The maximum diameter (MD) criterion is the most important factor when predicting risk of rupture of abdominal aortic aneurysms (AAAs). An elevated wall stress has also been linked to a high risk of aneurysm rupture, yet is an uncommon clinical practice to compute AAA wall stress. The purpose of this study is to assess whether other characteristics of the AAA geometry are statistically correlated with wall stress. Using in-house segmentation and meshing algorithms, 30 patient-specific AAA models were generated for finite element analysis (FEA). These models were subsequently used to estimate wall stress and maximum diameter and to evaluate the spatial distributions of wall thickness, cross-sectional diameter, mean curvature, and Gaussian curvature. Data analysis consisted of statistical correlations of the aforementioned geometry metrics with wall stress for the 30 AAA inner and outer wall surfaces. In addition, a linear regression analysis was performed with all the AAA wall surfaces to quantify the relationship of the geometric indices with wall stress. These analyses indicated that while all the geometry metrics have statistically significant correlations with wall stress, the local mean curvature (LMC) exhibits the highest average Pearson's correlation coefficient for both inner and outer wall surfaces. The linear regression analysis revealed coefficients of determination for the outer and inner wall surfaces of 0.712 and 0.516, respectively, with LMC having the largest effect on the linear regression equation with wall stress. This work underscores the importance of evaluating AAA mean wall curvature as a potential surrogate for wall stress.

Engineering analysis of aortic wall stress and root dilatation in the V-shape surgery for treatment of ascending aortic aneurysms

“…It has been shown by Elefteriades et al [ 5 ] that the mean wall tension of the aortic root decreased post-surgery with the reduced root diameter, simply based on the Laplace’s law. However, the change of the wall stress, especially the peak wall stress, of the aortic root may not have a similar simple relation with the reduced diameter, since the wall stress field is usually inhomogeneous and depends not only on the diameter but also on other shape features including the centreline and surface curvatures, as has been shown by Liang et al [ 23 ] and de Galarreta et al [ 28 ]. Thus, a detailed patient-specific biomechanical analysis in this study is essential for a more accurate evaluation for the impact of the novel V-shape surgery on the wall stress of the aortic root.…”

3D-Ultrasound Based Mechanical and Geometrical Analysis of Abdominal Aortic Aneurysms and Relationship to Growth

“…1 C). These local principal curvatures are closely related to the wall stress [ 36 ], indicating regions at risk and in which changes in the aortic wall are expected to happen. From the local principal curvatures, the point-wise mean ( M ) and Gaussian curvatures ( G ) were determined by respectively averaging and multiplying the local values of K 1 and K 2.…”

Predictors of Abdominal Aortic Aneurysm Risks

“…More refined computational models and experimental systems to investigate the effects of blood flow and flow pulsatility (not just blood pressure), and even vascular growth and remodeling have also been implemented [ 85 ]. Geometrical changes have been investigated [ 86 ] as well as geometry-derived indexes, including tortuosity and surface curvature [ 87 , 88 , 89 , 90 ]. However, biomechanical indexes of rupture continue to be elusive and rupture mechanisms are not yet fully understood.…”