Specific-Idealized aortic dissection model
Visceral malperfusion is associated with a tear on the proximal descending thoracic aorta (DTA) in AD23. We created a specific-idealized model that can show visceral malperfusion in AD (Fig. 2a). The model was constructed using a modeling software (SpaceClaim, v.2021 R1, ANSYS, Inc., PA, USA) with nine branches. The model has a large primary entry tear in the proximal DTA, which separates the true lumen and false lumen, and a small re-entry tear in the left common iliac artery (CIA_L), allowing the flow in false lumen to come out as true lumen. The area of primary entry tear was 98.45 mm2, whereas that of the re-entry tear was 3.73 mm2. In addition, the model had a uniform intimal flap, with a thickness of 1 mm (Fig. 2d).
Computational Fluid Dynamics.
The fluid domain was extracted from the model (Fig. 2b and c). The fluid was modelled with a density and dynamic viscosity of 1060 kg/m3 and 0.0035 kg/m‧s (3.5 cP), respectively, similar to our previous study23. The Newtonian fluid property was assumed because of the large diameters and high flow rates involved. Since the cannulation proceeds in the cardiac arrest state, the ascending aorta was treated as a wall. In the AC, the inlet condition was set to a uniform steady flow rate of 3–7 L/min applied to the brachiocephalic trunk (BT), and the flow rate was halved in AFC and applied to the BT and right common iliac artery (CIA_R) (Fig. 2b and c). All the outlets were assumed to have the same constant pressure, considering that the pressure loss through the large aorta was negligible24. The rigid body assumption and no-slip condition were used for the aortic wall. A dynamic mesh function was used for deformation, and surfaces that contacted the structural domains were set as fluid-solid interfaces. A Mesh was selected as 1.6 million tetrahedral cells based on the mesh independence test (Table S1). The simulation was performed using a transient condition, and incompressible RANS equations were solved using the SIMPLE scheme to resolve pressure-velocity coupling. In this study, maximum Reynolds number at the inlet was 4165, and a shear stress transport k-omega turbulence model was used. A second-order upwind scheme was used for the momentum and turbulence equations. The convergence criterion was set to 0.001.
Computational Structural Dynamics.
In our previous study, the intimal flap was made of silicon, a shore 20A material. The Young’s modulus of shore 20A can be estimated at approximately 0.73 MPa25, and its mechanical properties were applied as the Ogden 3rd order hyperelastic model using uniaxial, biaxial, and planar experimental data in this study26. The strain energy function for this model can be calculated as follows:
$$\psi =\frac{{\mu }_{1}}{{\alpha }_{1}}\left({\stackrel{-}{{\lambda }_{1}}}^{{\alpha }_{1}}+{\stackrel{-}{{\lambda }_{2}}}^{{\alpha }_{1}}+{\stackrel{-}{{\lambda }_{3}}}^{{\alpha }_{1}}-3\right)+\frac{{\mu }_{2}}{{\alpha }_{2}}\left({\stackrel{-}{{\lambda }_{1}}}^{{\alpha }_{2}}+{\stackrel{-}{{\lambda }_{2}}}^{{\alpha }_{2}}+{\stackrel{-}{{\lambda }_{3}}}^{{\alpha }_{2}}-3\right)+$$
$$\frac{{\mu }_{3}}{{\alpha }_{3}}\left({\stackrel{-}{{\lambda }_{1}}}^{{\alpha }_{3}}+{\stackrel{-}{{\lambda }_{2}}}^{{\alpha }_{3}}+{\stackrel{-}{{\lambda }_{3}}}^{{\alpha }_{3}}-3\right)+\frac{1}{{d}_{1}}{\left(J-1\right)}^{2}+\frac{1}{{d}_{2}}{\left(J-1\right)}^{4}+\frac{1}{{d}_{3}}{\left(J-1\right)}^{6} \left(1\right)$$
where \({\lambda }_{p}\) denotes the deviatoric principal stretches of the left-Cauchy-Green tensor, \(J\) is the determinant of the elastic deformation gradient, and \({\mu }_{p}\), \({\alpha }_{p}\), and \({d}_{p}\) are the material constants.
A mesh was made of approximately 55,000 20-noded hexahedral elements for hyperelastic material analysis. Under the boundary condition, a fixed support was applied to all surfaces that did not contact the fluid domain, and surfaces that contact fluid domains were set as fluid-solid interfaces. These were performed using a transient and direct sparse solver.
Fluid-Structure Interaction.
The FSI simulations were performed using a coupling system in ANSYS workbench (v.2021 R1, ANSYS, Inc., USA) that connected ANSYS Fluent and ANSYS Mechanical on a workstation (Dual Intel Xeon Gold 6148, 2.40 GHz CPU and 128 GB RAM). The ANSYS FSI simulation was based on a 2-way implicit iterative method in a transient coupled system. The forces or stresses on the fluid domain of the interface are converted to the solid domain, and the displacements on the solid domain of the interface are converted to the fluid domain in the coupling method. In this coupling, transferring information involves the calculation of weights and subsequent use in data interpolation. The induced force on the intimal flap was obtained after the flow field was solved using Ansys Fluent. Then, the displacement of the intimal flap was solved using Ansys Mechanical. This process is repeated until the simulation is over.
In this study, the arbitrary Lagrangian-Eulerian (ALE) method was applied to FSI. In the ALE framework, the continuity and momentum equations for the incompressible flow are as follows, respectively:
$$\nabla \bullet {{v}}_{f}=0 \left(2\right)$$
$${\rho }_{f}\frac{\partial {{v}}_{f}}{\partial t}+{\rho }_{f}\left({{v}}_{f}-{{w}}_{f}\right)\bullet \nabla {{v}}_{f}=-\nabla p+\nabla \bullet \mu \left(\nabla {{v}}_{f}+{\nabla }^{T}{{v}}_{f}\right)+{\rho }_{f}{{b}}_{f} \left(3\right)$$
where \({{v}}_{f}\) denotes the fluid velocity vector, \({\rho }_{f}\) is the fluid density, \({{w}}_{f}\) is the moving boundary velocity vector, \(p\) is the pressure, \(\mu\) is the dynamic viscosity, and \({\rho }_{f}{{b}}_{f}\) is the body force vector acting on the fluid.
The momentum equation for structural domain is as follows:
$${\rho }_{s}\frac{\partial {{v}}_{s}}{\partial t}=\nabla \bullet {{\sigma }}_{s}+{\rho }_{s}{{b}}_{s} \left(4\right)$$
where \({{v}}_{s}\) denotes the solid velocity vector, \({\rho }_{s}\) is the solid density, \({{\sigma }}_{f}\) is the solid stress tensor, and \({\rho }_{s}{{b}}_{s}\) is the body force vector acting on the solid.
The boundary conditions at FSI interface for the fluid and structural domain are given as:
$${{u}}_{s}={{u}}_{f} \left(5\right)$$
$${{n}}_{s}{{\sigma }}_{s}={{n}}_{f}{{\sigma }}_{f} \left(6\right)$$
$$\frac{\partial {{u}}_{f}}{\partial t}={{v}}_{f} \left(7\right)$$
where \({u}\) and \({n}\) are the displacement vector and normal vector, respectively, with the subscript \(s\) indicating a property of solid and \(f\) of fluid, \({{n}={n}}_{f}={-{n}}_{s}\) at the interface, and \({{\sigma }}_{f}\) is the fluid stress tensor.
The time step of the coupling system was set to 0.2 ms, and the total time was set to 2 s to stabilize the flow state. To report the simulation results, we used the results of the final time-step. The maximum root-mean-square residuals for both fluid and solid domains had to reach 0.01 to ensure convergence of the solution. The under relaxation factor was set to 1.0. To visualize and calculate data, Ensight (v.2021 R1, ANSYS, Inc., USA) and MATLAB (v.R2020a, The MathWorks Inc., MA USA) were used in this study.
Effect of intimal flap stiffness.
Two additional simulations were performed to investigate the effect of the intimal flap stiffness. First, for AC 7 L/min, CFD in which all bodies were rigid was performed and compared with the FSI simulation. Second, we applied more flexible mechanical properties than shore 20A for AC 4 L/min using the Neo-Hookean model. To validate that the results of the Ogden model and Neo-Hooken model are similar, the Young's modulus of the previously estimated shore 20A (0.74 MPa) was applied to the Neo-Hooken model, and the Poisson’s ratio was set to 0.49. To apply a more flexible material, Young's modulus was set to 0.1 MPa and Poisson's ratio set to 0.49. The strain energy function for this model can be calculated as follows:
$$\psi =\frac{\mu }{2}\left(\stackrel{-}{{I}_{1}}-3\right)+\frac{1}{d}{\left(J-1\right)}^{2} \left(8\right)$$
where \(\stackrel{-}{{I}_{1}}\) denotes the first deviatoric strain invariant, \(J\) is the determinant of the deformation gradient, \(\mu\) is the initial shear modulus of the material, and \(d\) is the material incompressibility parameter.