Team for Advanced Flow Simulation and Modeling

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Fluid-Structure Interaction Modeling of Aneurysmal Conditions with High Blood Pressure

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 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 aneurysmal conditions with high blood pressure. 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 with normal blood pressure, so that we can see the influence of hypertension. The computations show that hypertension makes a significant difference in the predicted values of not only the mechanical stress in the aneurysmal wall but also the wall shear stress.

Fig. 1. Normal and high blood pressure profiles.

Fig. 2. Deformation of the arterial walls at the peak systole (colors show the wall displacement in the normal direction). Left: Normal blood pressure. Right: High blood pressure. For more details, see [5].

Fig. 3. Wall shear stress distribution at the peak systole. Left: Normal blood pressure. Right: High blood pressure. For wall shear stress distributions at other instants during the cardiac cycle and for flow velocities at various cross-sections, 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, "Fluid-Structure Interaction Modeling of Aneurysmal Conditions with High and Normal Blood Pressures", Computational Mechanics, 38 (2006) 482-490.