TAFSM

Team for Advanced Flow Simulation and Modeling



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Abdominal Aortic Aneurysm

One of the major computational challenges in cardiovascular fluid mechanics is accurate modeling of the fluid-structure interaction (FSI) between the blood flow and arterial walls. The blood flow depends on the arterial geometry, and the deformation of the arterial wall depends on the blood flow. The mathematical equations governing the blood flow and arterial deformations need to be solved simultaneously, with proper kinematic and dynamic conditions coupling the two physical systems.

The arterial geometry (see Fig. 1) used here was created by making use of the image data found in [1, 2], with the arterial diameter and wall thickness coming from [3] and [4]. The arterial wall (i.e. the structural mechanics part of the problem) is modeled with the membrane element.

The numerical methods used in this computation were introduced and implemented on parallel computing platforms by the T*AFSM. The set of numerical methods introduced by the T*AFSM over the years and used in this computation includes the DSD/SST formulation [5-8], the quasi-direct FSI method [9, 10], the stabilized space-time FSI (SSTFSI) technique [11], and special techniques for arterial FSI computations [12, 13]. The inflow velocity used in the computation during the cardiac cycle has the same form as that shown at Cerebral Aneurysm -- Variable Wall Thickness, High Blood Pressure. The blood pressure profile is similar to the normal blood pressure profile shown at Cerebral Aneurysm -- Variable Wall Thickness, High Blood Pressure. For more details on this computation, see [13].

Fig. 1. Arterial geometry. For details, see [13].


Fig. 2. Blood-flow patterns at an instant during the cardiac cycle. For details, see [13].


Fig. 3. Blood-flow patterns when the inflow velocity is at its minimum and maximum (top), and when the blood pressure is at its maximum and secondary maximum (bottom). For details, see [13].

References

1. http://www.vascularweb.org/_CONTRIBUTION_PAGES/Patient_Information/3_Most_Common_AVA/AorticAneurysms_AVA.html.

2. http://www.slrsurgery.org/divisions/vascular.html.

3. http://www.camsf.com/vasc_aortic.html.

4. A.E. Li, I. Kamel, F. Rando, M. Anderson, B. Kumbasar, J.A.C. Lima and D.A. Bluemke, "Using MRI to Assess Aortic Wall Thickness in the Multiethnic Study of Atherosclerosis: Distribution by Race, Sex, and Age", American Journal of Roentgenology, 182 (2003) 593-597.

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

6. 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.

7. 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.

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

9. T.E. Tezduyar, S. Sathe, R. Keedy and K. Stein, "Space-Time Techniques for Finite Element Computation of Flows with Moving Boundaries and Interfaces", Proceedings of the III International Congress on Numerical Methods in Engineering and Applied Sciences, Monterrey, Mexico, CD-ROM (2004).

10. T.E. Tezduyar, S. Sathe, R. Keedy and K. Stein, "Space-Time Finite Element Techniques for Computation of Fluid-Structure Interactions", Computer Methods in Applied Mechanics and Engineering, 195 (2006) 2002-2027.

11. T.E. Tezduyar and S. Sathe, "Modeling of Fluid-Structure Interactions with the Space-Time Finite Elements: Solution Techniques", International Journal for Numerical Methods in Fluids, 54 (2007) 855-900.

12. T.E. Tezduyar, S. Sathe, T. Cragin, B. Nanna, B.S. Conklin, J. Pausewang and M. Schwaab, "Modeling of Fluid-Structure Interactions with the Space-Time Finite Elements: Arterial Fluid Mechanics", International Journal for Numerical Methods in Fluids, 54 (2007) 901-922.

13. T.E. Tezduyar, S. Sathe, M. Schwaab and B.S. Conklin, "Arterial Fluid Mechanics Modeling with the Stabilized Space-Time Fluid-Structure Interaction Technique", International Journal for Numerical Methods in Fluids, 57 (2008) 601-629.