# Heterogeneity of Ex Vivo and In Vivo Properties along the Length of the Abdominal Aortic Aneurysm
## 3 Results
### Ex Vivo Analysis  
#### 3.1.1 Biaxial Mechanical Response of the Aortic Tissue  
With approximately 30% of the specimens failing due to rupture during experimental set-up or during the initial testing protocol before reaching the 40% displacement protocol, a complete biaxial test was feasible for 24 aortic samples from 7 aneurysms. The average LTM characterizing the linear region of the tissue's response for the analysed specimens was 298.3 \(\pm\) 267.3 KPa and 359.8 \(\pm\) 380.7 KPa in the circumferential (11) and longitudinal (22) direction respectively, with an average anisotropic index of 1.73 \(\pm\) 4.31. The average HTM was found to be 3121.0 \(\pm\) 1666.1 KPa in the circumferential direction and 3381.3 \(\pm\) 2605.4 KPa in the longitudinal direction, with an average anisotropic index of 2.27 \(\pm\) 5.43. The tangential modulus at both low and high strain was not significantly different in the circumferential versus longitudinal direction. The LTM did not present a significant effect of position along the aortic length, but showed a statistically significant effect of position along the circumference (Figure 2a,b). Samples collected from the left regions of the aorta exhibited higher LTM in the circumferential direction (\(p\) = 0.039 for left-posterior versus right-posterior) and higher LTM in the longitudinal direction (\(p\) = 0.044 for left-anterior versus right-anterior; \(p\) = 0.027 for left-anterior versus right-posterior). Of note, a statistically significant effect of position along the aneurysm length was observed for the circumferential HTM (Figure 3a). In particular, the aneurysm neck region in position 1 exhibited higher circumferential HTM compared to the aneurysmal sac regions corresponding to position 3 (\(p\) = 0.001), position 4 (\(p\) = 0.053), and position 5 (\(p\) = 0.010). An effect of position was also observed for the HTM anisotropic index. The index was transformed through an exponential function to obtain a normal distribution. Thus, a positive number indicates a preferred fiber directionality in the circumference direction while a negative number is associated with axially oriented fibers. As these numbers approach 0, the material behaves more isotropically. The samples collected from regions in position 3 showed lower anisotropy and reached statistical significance when compared to the mechanical response characterizing position 2 or 4 (\(p\) < 0.05) (Figure 3b). Figure 3: Heterogeneity of the selected ex vivo biaxial mechanical properties along the length of the AAA. (**a**) High tangential modulus (HTM) in the circumferential direction (11). (**b**) High tangential modulus anisotropy. (**c**) Transition zone onset (TZo) in the circumferential direction (11). (**d**) Transition zone end (TZe) in the circumferential direction (11). * indicates \(p\) value < 0.05, ** indicates \(p\) value < 0.01 and *** indicates \(p\) value < 0.001. Figure 2: Heterogeneity of the selected ex vivo biaxial mechanical properties along the circumference of the AAA. (**a**) Low tangential modulus (LTM) in the circumferential direction (11). (**b**) Low tangential modulus (LTM) in the longitudinal direction (22). * indicates \(p\) value < 0.05. The non-linear transition zone of the stress-stretch curve for each AAA sample was described by means of TZo and TZe. The average TZo for the analyzed specimens was 5.3 \(\pm\) 5.1 KPa in the circumferential direction and 6.1 \(\pm\) 4.6 KPa in the longitudinal direction, with an average anisotropic index of 2.31 \(\pm\) 6.36. The average TZe was found to be 27.8 \(\pm\) 13.8 KPa and 35.0 \(\pm\) 28.4 KPa respectively in the circumferential and longitudinal direction (average anisotropic index was 1.52 \(\pm\) 1.84). The effect of position along the length of the artery on the parameters describing the transition zone was observed for the circumferential direction (Figure 3c,d), with samples in the central region in position 3 showing lower TZo (\(p\)! 0.001 compared to position 2 and 4; \(p\) = 0.06 compared to position 6) and TZe (\(p\)!