A planar biaxial constitutive relation for the luminal layer of intra-luminal thrombus in abdominal aortic aneurysms

The rupture risk of abdominal aortic aneurysms (AAAs) is thought to be associated with increased levels of wall stress. Finite element analysis (FEA) allows the prediction of wall stresses in a patient-specific, non-invasive manner. We have recently shown that it is important to include the intra-luminal thrombus (ILT), present in approximately 70% of AAA, into FEA simulations of AAA. All FEA simulations to date assume an isotropic, homogeneous material behavior for this material. The purpose of this work was to investigate the multi-axial biomechanical behavior of ILT and to derive an appropriate constitutive relation. We performed planar biaxial testing on the luminal layer of nine ILT specimens obtained fresh in the operating room (9 patients, mean age 71±4.5 years, mean diameter 5.9±0.4 cm), and a constitutive relation was derived from this data. Peak stretch and maximum tangential modulus (MTM) values were recorded for the equibiaxial protocol in both the circumferential (θ) and longitudinal (L) directions. Stress contour plots were used to investigate the presence of mechanical anisotropy, after which an appropriate strain energy function was fit to each of the specimen datasets. The peak stretch values for the luminal layer of the ILT were (mean±SEM) 1.18±0.02 and 1.13±0.02 in the θ and L directions, respectively (p = 0.14). The MTM values were 20±2 and 23±3 N/cm² in the θ and L directions, respectively (p = 0.37). From these results and our observation of the symmetry of the stress contour plots for each specimen, we concluded that the use of an isotropic strain energy function for ILT is appropriate. Each specimen data set was then fit to a second-order polynomial strain energy function of the first invariant of the left Cauchy-Green strain tensor, resulting in an accurate fit (average R² = 0.92 ± 0.02; range 0.80-0.99). Comparison of our previously reported, uniaxially derived constitutive relation with the biaxially derived relation derived here shows large differences in the predicted mechanical response, underscoring the importance of the appropriate experimental methods used to derive constitutive relations. Further work is merited in an effort to produce more accurate predictions of wall stresses in patient-specific AAA, and viscoelastic behaviors of the ILT.