Life Science Special Report December 2015

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LIFE SCIENCES VIRTUAL ABDOMINAL AORTIC ANEURYSM PRE-PROCESSING Different mesh topologies and grid refinements were assessed (Figure 3) using STAR-CCM+. These were based on polyhedral, nonconformal hexahedral and tetrahedral elements, all with boundary layer extrusion to accurately calculate the velocity gradient near the walls of the vessel. For the sensitivity analysis of the grid, the verification procedure proposed by Roache [1] was followed. The mesh size varied from 300,000 to roughly 1,400,000 cells. In addition, the influence of the boundary layer was taken into account by comparing the solutions obtained with various dimensions of prisms layer, as shown on Figure 4. FIGURE 4: Prism layer infl uence investigation SOLVING The physics and the solver setups had to be determined in order to automate the solving process. Two different types of fluids were compared to model the behavior of the blood: (a) a simple Newtonian fluid with standard properties and (b) a non-Newtonian fluid with Power-law rheology. The influence of the time step and number of inner iterations was assessed using the same systematic approach as adopted for the mesh study. While keeping the physics and the solver parameters unchanged, different numerical schemes were tested and compared: • Solvers: segregated (S), coupled implicit (Ci) and coupled explicit (Ce) • Pressure/velocity coupling: first-order and second-order upwind convection schemes (pv1 and pv2 respectively) • Temporal discretization: first-order and second-order upwind convection scheme (t1 and t2 respectively) Figure 5 shows a comparison of OSI values computed with the different numerical schemes. In Figure 6, the time history for the benchmark model and the final average value of the velocity magnitude inside the vessel are reported. POST-PROCESSING To visualize the numerical solution, scalar plots that show the variations of a number of parameters were drawn on the surface and inside the vessel. Furthermore, by exporting the solution-in-time, it was possible to integrate the Wall Shear Stress (WSS) components and compute the hemodynamic risk indices. Figure 7 shows a sample of post-processing images. FIGURE 3: Example of grid topology. A: tetrahedral based; B: polyhedral based; C: hexahedral based. The investigation about grid generation led to the definition of a discretization strategy which is suitable to represent the physics as realistically as possible. CONCLUSION This study assessed how the choice of grid, solver models and features of the fl uid (blood) affects the computation of some specifi c parameters (such as pressure, fl uid velocity, tension and stress state of the vessel) in the case of an abdominal aortic aneurysm. The investigation about grid generation led to the defi nition of a discretization strategy which is suitable to represent the physics as realistically as possible. Non-conformal hexahedral grids allow the representation of the phenomenon FIGURE 5: Oscillatory Shear Index (OSI) computed using different numerical schemes with fewer numerical discretization errors than the other non-structural grids; as a consequence, the use of a polyhedral or tetrahedral mesh implies a more refi ned grid and therefore a higher number of cells, which in turn requires more computational time and resources . It is also necessary to have a good resolution of the boundary layer to compute the WSS accurately. For the solving phase, a suitable time step and number of inner iterations, numerical scheme and fl uid rheology were extracted as parameters for the automation process. 6 SPECIAL REPORT
VIRTUAL ABDOMINAL AORTIC ANEURYSM LIFE SCIENCES FIGURE 6: Transient solution (a-b-c) and average solution for the benchmark geometry FIGURE 7: Post-processing results and reporting to aid AAA diagnosis and treatments AUTHORS Dr. Simone Bartesaghi, Ph.D in Mechanical Engineering, Milano, Italy. Until 2012, Ph.D candidate at Politecnico di Milano, Department of Mechanics, Italy. email: simone.bartesaghi@alice.it www.simonebartesaghi.com Prof. Giorgio Colombo, Politecnico di Milano, Department of Mechanics, Italy. email: giorgio.colombo@polimi.it REFERENCES: [1] Roache, P.J., “Verifi cation and Validation in Computational <strong>Science</strong> and Engineering,” Hermosa Publishers, pp. 403-412, 1998. SPECIAL REPORT 7
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Life Science Special Report December 2015

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