## 2 Materials and Methods
### Establishment of the Constitutive Model  
The determination of material property parameters determines the accuracy of creating the native model. Previous studies have proved that there is no significant difference in the mechanical property constants and elastic modulus between the human aortic wall and the 4-10-month-old porcine aortic wall [23; 24]; so, the porcine aorta was chosen as the test object in this study, and the circumferential and longitudinal stress-strain relationship curves were obtained through longitudinal and circumferential tensile tests; then, the parameter corrections were carried out by using inverse optimization methods to obtain the material mechanical property parameters of the porcine aortic wall, and the material mechanical property parameters of the porcine aortic wall were ultimately constructed based on the results. This parameter is used to construct the HGO model of the human aortic wall. From 5-7-month-old pigs, select the fresh descending aorta, which has a wall thickness of about 2.96 mm. Fix it on a glass plate, cut it into segments of about 120 mm in length from the same location, and divide them into two groups. Use one group to dissect the intima, media, and adventitia; use the other group to create an AD entry at the proximal third and an exit at the distal end symmetrically, with a distance of 30 mm between the two tears. Use forceps to extend the AD and connect it to an in vitro simulation platform [25] for expansion, to ensure its biomechanical properties are closer to those of a real AD. Figure 1b,c show samples of the aorta before and after expansion, respectively. Then, dissect the intimal flap and FL wall. Cut the separated intima, media, adventitia, intimal flap, and FL wall into samples of about 90 \(\times\) 10 mm along the circumferential and longitudinal directions. The MARK-10 ESM 1500S single-column tensile teste (Mark-10 Corporation, Copiague, NY, USA) was used for the biological tissue tensile tests. The fixture was clamped 15 mm from the upper and lower edges of the sample, with an initial distance of 60 mm between fixtures. A preload of 0.5 N was applied to eliminate the viscoelastic effects of the aortic wall. The tester was started, and the sample was stretched at 1.2 mm/min until complete rupture, as shown in Figure 2.  
Uniaxial tensile tests were performed on the adventitia, media, intima, FL wall, and intimal flap to obtain stress-strain curves. This study focuses on the intimal flap group. Eight valid datasets were acquired in the circumferential and longitudinal directions. The results showed the material exhibited distinct linear and nonlinear elastic phases, with directional mechanical variations (Figure 3a,b), consistent with the anisotropic hyperelasticity of the aortic wall. A sample model was built in ABAQUS-ISIGHT with a length of 60 mm and a width of 10 mm. The HGO anisotropic hyperelastic material was selected, with a density of 1100 kg/m\({}^{3}\). Initial parameter values were set based on Fischer [21]: \(C_{10}\) = 0.02918 MPa, \(k_{1}\) = 0.01037 MPa, \(k_{2}\) = 2.03, \(\theta\) = 42.4\({}^{\circ}\), and \(\kappa\) = 0. During the tensile simulation, one end of the sample was fixed, while the other was subjected to a velocity condition of 1.2 mm/min. Experimental data on the tensile force and displacement from circumferential and longitudinal tests were used to compare the experimental and simulation results. The least squares method was applied to fit the experimental data, followed by optimization using a multi-island genetic algorithm. The material parameter inversion and correction method identifies candidate constitutive parameters within a specified range, updating them iteratively during correction to minimize the objective function value, thereby inverting and optimizing the aortic tissue constitutive parameters. In this study, the correction objective is to minimize the error between the experimental and simulation data, quantified by the mean square error (MSE).