Numerical Simulation

Numerical simulations were performed in two steps: pre-stress of the aortic dissection model and virtual deployment of SG. Several assumptions and constraints were adopted in the simulation.

The motion of the aortic root and ascending aorta was neglected in this study. Therefore, the nodes at the proximal ascending aorta, supra-aortic branches and distal descending aorta were fixed with zero displacement. Rayleigh damping was applied to the aorta to account for the viscoelastic tissue support on the outer arterial wall. As the descending aorta is tethered to the spine by paired intercostal arteries, this attachment was modelled by defining four pairs of fixed spots along the descending aorta, effectively preventing any excessive rigid body movement.

The pre-TEVAR aortic dissection geometry was obtained at mid-diastole and could not be assumed as stress-free due to the intraluminal blood pressure. The calculation of pre-stress of aortic dissection was performed by modifying the method reported by Votta et al. (2017). The intraluminal blood pressure was assumed to be constant at 80 mmHg and distributed uniformly in the TL and FL. The aortic dissection model was first pressurised by increasing the internal pressure from 0 to 80 mmHg. Then, the Cauchy stress tensor calculated from the previous simulation was defined as the initial condition for the next simulation in Abaqus. The pre-stress iteration looped until the deformation of the geometry was less than 0.72 mm (the pixel resolution of pre-TEVAR CTA scan) under the 80 mmHg intraluminal pressure loading. After the iteration loop stopped, the pre-stress tensor corresponding to the mid-diastolic phase was obtained and then applied in the following virtual SG deployment simulation.

The virtual SG deployment was performed within the pre-TEVAR aortic dissection geometry with the pre-stress tensor as the initial condition. The virtual SG deployment, including crimp, delivery and release of SG, was attained by applying nodal-specific displacement boundary conditions on the virtual sheath. In the first step, the diameter of the tubular virtual sheath was reduced from 44 mm to 8.5 mm (the diameter of introducer sheath from the manufacturer database); therefore, the SG within was compressed from its stress-free state to the crimped state (Figure 3B; Cook Medical, 2019). The contact between SG and virtual sheath was modelled by using Abaqus explicit general contact algorithm with penalty formulation. Then, the SG was bended to follow the local centreline extracted from the TL of pre-TEVAR geometry and delivered to the target landing position selected on the centreline by referring to the 3-month follow-up scan. Finally, the contact between SG and aorta was activated with the friction coefficient of 0.1 (Vad et al., 2010), and followed by the deployment of SG by expanding the virtual sheath radially to a diameter wider than the local aorta (Figure 3B). The virtual SG deployment simulation continued until mechanical equilibrium was reached. Simulations of the SG with three different lengths were performed separately with the targeting SG proximal landing position being fixed at the same location.