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Team for Advanced Flow Simulation and Modeling



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Wall Shear Stress Calculations for a Middle Cerebral Artery Bifurcation with Aneurysm

The Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation was introduced in [1-3] for flow problems with moving boundaries and interfaces and has been applied to a large class of problems, including fluid-structure interactions (FSI). In this joint work with Ryo Torii and Marie Oshima (University of Tokyo), the version of the DSD/SST formulation introduced in [4] is applied to computation of the FSI and wall shear stress for a middle cerebral artery bifurcation with aneurysm. This joint work is described fully in [5]. The computations were carried out by Ryo Torii, using a computer program he wrote with guidance and help from the T*AFSM.

The computer model was extracted from the computed tomography (CT) model of the middle cerebral artery bifurcation of a 59 year-old female patient. In the FSI computation, the arterial walls are assumed to be made of a linearly elastic material, but the geometric nonlinearities are accounted for. A computation was carried out also with a model where the arterial walls are assumed to be rigid, so that we can see the importance of taking into account the FSI between the blood flow and the arterial walls. The computations show that taking such FSI into account makes a significant difference in the predicted values of the wall shear stress.

Fig. 1. Left: Deformation of the arterial walls at the peak systole (colors show the wall displacement in the normal direction). Middle: Wall shear stress distribution at the peak systole for the computational model with elastic wall. This model takes into account the FSI between the blood flow and the arterial walls. Right: Wall shear stress distribution at the peak systole for the computational model with rigid wall. For flow velocities at various cross-sections and other details, see [5].

References

1. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1992) 1-44.

2. T.E. Tezduyar, M. Behr and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces -- The Deforming-Spatial-Domain/Space-Time Procedure: I. The Concept and the Preliminary Numerical Tests", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 339-351.

3. T.E. Tezduyar, M. Behr, S. Mittal and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces -- The Deforming-Spatial-Domain/Space-Time Procedure: II. Computation of Free-surface Flows, Two-liquid Flows, and Flows with Drifting Cylinders", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 353-371.

4. T.E. Tezduyar, "Computation of Moving Boundaries and Interfaces and Stabilization Parameters", International Journal for Numerical Methods in Fluids, 43 (2003) 555-575.

5. R. Torii, M. Oshima, T. Kobayashi, K. Takagi and T.E. Tezduyar, "Influence of Wall Elasticity in Patient-Specific Hemodynamic Simulations", Computers & Fluids, 36 (2007) 160-168.