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Multiscale Sequentially-Coupled Arterial FSI

We use the multiscale sequentially-coupled fluid-structure interaction (FSI) technique in patient-specific arterial FSI computation of a cerebral aneurysm. The lumen geometry used here was provided by Dr. Ryo Torii (University College London). It was extracted from the computed tomography model of a bifurcating segment of the middle cerebral artery of a 67 year-old female with aneurysm. The arterial wall (i.e. the structural mechanics part of the problem) is modeled with the continuum element made of hyperelastic (Fung) material.

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 [1-4], the quasi-direct FSI method [5, 6], the stabilized space-time FSI (SSTFSI) technique [7], special techniques for arterial FSI computations [8-11], and a multiscale sequentially-coupled arterial FSI technique [12]. The lumen geometry was used earlier in simulations reported in [13, 14]. The inflow volumetric flow rate is calculated (see [11]) from the maximum-velocity waveform used in [13]. The inflow velocity profile (in space and time) is calculated (see [11]) based on this volumetric flow rate by using a special mapping technique introduced in [11]. The traction condition imposed at the outflow boundary during the cardiac cycle is based on a normal blood pressure profile, which is calculated (see [11]) by using the Windkessel model and the inflow volumetric flow rate. The inflow volumetric flow rate and the pressure profile can be seen at Cerebral Aneurysm -- High-Resolution Wall Shear Stress. We use a variation of the "estimated zero-pressure arterial geometry" method that was introduced in [9]. In this variation (see [11]), we use variable wall thickness for the artery. The zero-pressure configuration, the wall thickness normalized by the wall thickness at the inflow, and the structural mechanics mesh can be seen at Cerebral Aneurysm -- High-Resolution Wall Shear Stress. One of the special arterial FSI techniques used in the computation is generating meshes with layered, high-refinement zones in the normal direction near the arterial walls to improve the boundary layer resolution (see [10, 11]). In the computations reported here, two meshes are used: a coarse mesh and a fine mesh with such layered, high-refinement zones. The coarse and fine meshes have the same triangular mesh at the arterial wall, which is shown in Fig. 1. The coarse and fine fluid mechanics meshes at the inflow plane are shown in Fig. 2. We first compute the arterial shape with the (fully) coupled arterial FSI (CAFSI) technique and the coarse mesh. Given the arterial shape as a function of time during a cardiac cycle, we follow with mesh motion and fluid mechanics computations with the refined mesh. We call this approach the Multiscale Sequentially-Coupled Arterial FSI (SCAFSI M1C) technique. For comparison purpose, we also compute with the CAFSI technique and the fine mesh. The layered, high-refinement meshes near the arterial wall give us higher-resolution wall shear stress (WSS) values (see Figs. 3-5), and as can be seen from the figures, the WSS distributions obtained with the SCAFSI M1C technique are close to those obtained with the CAFSI technique and the fine mesh. For more details on these computations, see [12].

Fig. 1. Fluid mechanics mesh at the arterial wall. For details, see [12].


Fig. 2. Coarse and fine fluid mechanics meshes at the inflow plane. For details, see [12].


Fig. 3. WSS distributions from the CAFSI technique and the fine mesh when the volumetric flow rate is maximum (left) and when the outflow pressure is maximum (right). For details, see [12].


Fig. 4. WSS distributions from the SCAFSI M1C technique when the volumetric flow rate is maximum (left) and when the outflow pressure is maximum (right). For details, see [12].


Fig. 5. Time-averaged WSS distributions from the CAFSI technique and the fine mesh (left) and the SCAFSI M1C technique (right). For details, see [12].

References

1. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1992) 1-44, doi: 10.1016/S0065-2156(08)70153-4.

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, doi: 10.1016/0045-7825(92)90059-S.

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, doi: 10.1016/0045-7825(92)90060-W.

4. T.E. Tezduyar, "Computation of Moving Boundaries and Interfaces and Stabilization Parameters", International Journal for Numerical Methods in Fluids, 43 (2003) 555-575, doi: 10.1002/fld.505.

5. 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).

6. 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, doi: 10.1016/j.cma.2004.09.014.

7. 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, doi: 10.1002/fld.1430.

8. 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, doi: 10.1002/fld.1443.

9. 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, doi: 10.1002/fld.1633.

10. T.E. Tezduyar, M. Schwaab and S. Sathe, "Sequentially-Coupled Arterial Fluid-Structure Interaction (SCAFSI) Technique", Computer Methods in Applied Mechanics and Engineering, 198 (2009) 3524-3533, doi: 10.1016/j.cma.2008.05.024.

11. K. Takizawa, J. Christopher, T.E. Tezduyar and S. Sathe, "Space-Time Finite Element Computation of Arterial Fluid-Structure Interactions with Patient-Specific Data", International Journal for Numerical Methods in Biomedical Engineering, 26 (2010) 101-116, doi: 10.1002/cnm.1241.

12. T.E. Tezduyar, K. Takizawa, C. Moorman, S. Wright and J. Christopher, "Multiscale Sequentially-Coupled Arterial FSI Technique", Computational Mechanics, 46 (2010) 17-29, doi: 10.1007/s00466-009-0423-2.

13. R. Torii, M. Oshima, T. Kobayashi, K. Takagi and T.E. Tezduyar, "Numerical Investigation of the Effect of Hypertensive Blood Pressure on Cerebral Aneurysm -- Dependence of the Effect on the Aneurysm Shape", International Journal for Numerical Methods in Fluids, 54 (2007) 995-1009, doi: 10.1002/fld.1497.

14. R. Torii, M. Oshima, T. Kobayashi, K. Takagi and T.E. Tezduyar, "Fluid-Structure Interaction Modeling of a Patient-Specific Cerebral Aneurysm: Influence of Structural Modeling", Computational Mechanics, 43 (2008) 151-159, doi: 10.1007/s00466-008-0325-8.