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. 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 fluid-structure interactions 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 fluid-structure interaction 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 fluid-structure interactions between the blood flow and the arterial walls. The computations show that taking such fluid-structure interactions into account makes a significant difference in the predicted values of the wall shear stress.
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, published online, December 2005.
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| Fig 1. Deformation of the arterial walls at the peak systole (colors show the wall displacement in the normal direction). |
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| Fig 2. Wall shear stress distribution at the peak systole for the computational model with elastic wall. This model takes into account the fluid-structure interactions between the blood flow and the arterial walls. Top: Lateral view. Bottom: Superior view. For flow velocities at various cross-sections, see Reference [5].
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| Fig 3. Wall shear stress distribution at the peak systole for the computational model with rigid wall. Top: Lateral view. Bottom: Superior view. For flow velocities at various cross-sections, see Reference [5].
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