J24 - On the Use of Nonlinear Elastic Membrane Analysis for Estimating Abdominal Aortic Aneurysm Wall Stress

Introduction: : The dilatation of the abdominal aorta due to weakening of the wall results in an abdominal aortic aneurysm (AAA); it is a common disease affecting approximately 9% of the population in the United States 65 years of age and older. Since the condition is primarily asymptomatic, it is diagnosed by means of abdominal imaging for an unrelated condition. The current clinical standard of care to recommend repair is a maximum diameter greater or equal than 5.0 cm for women and 5.5 cm for men, which may not be suitable for all patients. A biomechanics-based approach may be justified as an alternative rupture risk assessment strategy. To this end, we performed finite element analysis (FEA) and nonlinear elastic membrane analysis (NEMA) of 10 AAA geometries from asymptomatic patients. A comparison of the 99th percentile wall stress (99thWS) was completed with the objective of benchmarking the NEMA-based wall stress with the gold standard FEA-based wall stress.

Materials and

Methods: : Abdominal, contrast-enhanced computed tomography (CT) images from ten AAA patients were acquired retrospectively from Allegheny General Hospital (Pittsburgh, PA) following IRB approval. The images were segmented using an in-house code (AAAVasc) to obtain binary masks of the outer wall, inner wall, and lumen boundaries of each AAA. The wall volume meshes were created with another in-house code (AAAMesh) and consisted of quadratic hexahedral elements. The wall was assumed to have a uniform thickness of 1.5 mm. The volume mesh for the intraluminal thrombus (ILT) was generated using Solidworks (Dassault Systemes Simulia Corp., Providence, RI) and Hypermesh (Altair Engineering Inc., Troy, MI) and consisted of linear tetrahedral elements. A mesh sensitivity analysis revealed an optimal number of 500,000 elements for the combined wall and ILT volume meshes. The FEA solver Abaqus (Dassault Systemes Simulia Corp.) was used to assign wall and ILT constitutive material properties, boundary conditions (intraluminal mean arterial pressure), and execute the FEA simulations. As shown in Table 1, we used constitutive material models (1)-(3) for the wall, and (1) and (4) for the ILT, considering all possible constitutive constants reported in the literature and using all possible combinations of wall and ILT materials. The latter yielded a total of 420 FEA simulations for the ten AAA geometries. Surface meshes for the wall were created with AAAMesh and consisted of triangular elements with a prescribed wall thickness. These meshes were used to compute the first principal wall stress using a NEMA-based approach, which is devoid of constitutive material properties.

Results, Conclusions, and Discussions:: Figure 1 shows an exemplary comparison of the 99th percentile wall stress (99thWS) for each of the AAA NEMA and FEA models. The latter used constitutive material (1) for the wall with constants C_10 and C_20 as 21.9 N/cm^2 and 117.6 N/cm^2, respectively, and constitutive material (4) for the ILT with C = 0.211 N/cm^2 and λ_i = 4. An incompressibility constraint was assumed for all constitutive material models. While the FEA- and NEMA-based estimations of 99thWS are similar for each AAA, large differences were observed for AAA3 and AAA8. Overall, the average percentage difference in 99thWS between the two stress analysis methods was 15%. NEMA is based on the assumption that the AAA wall is a relatively thin membrane and exhibits no bending stresses or stress gradients across it. In addition, it is based on the deformed configuration of the AAA, which we have assumed is the geometry reconstructed from the CT images at a standard mean arterial pressure. To this end, it has the advantage of a fast computational processing time and does not require specifying material properties for the wall or ILT, which yields high translational potential for clinical implementation. FEA requires specification of constitutive material properties, which are unknown on an individual basis, and the derivation of an unpressurized AAA geometry. The latter was generated based on the assumption that all CT exams were taken at the mean arterial pressure. FEA is the gold standard for estimation of the spatial distribution of wall stress in AAAs. While the ground truth for patient-specific AAA wall stress is never known, additional benchmarking is necessary before NEMA can be readily applicable in a clinical setting.

Acknowledgements and/or References (Optional):: This work was funded in part by NIH award 1R01HL159300 and the Zachry Endowed Chair of Mechanical Engineering.

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