Abstract
We provide an overview of the special techniques developed earlier by the Team for Advanced Flow Simulation and Modeling (T★AFSM) for fluid–structure interaction (FSI) modeling of patient-specific cerebral aneurysms. The core FSI techniques are the Deforming-Spatial-Domain/Stabilized Space–Time formulation and the stabilized space–time FSI technique. The special techniques include techniques for calculating an estimated zero-pressure arterial geometry, a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, techniques for using variable arterial wall thickness, mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, a recipe for pre-FSI computations that improve the convergence of the FSI computations, techniques for calculation of the wall shear stress and oscillatory shear index, and arterial-surface extraction and boundary condition techniques. We show, with results from earlier computations, how these techniques work. We also describe the arterial FSI techniques developed and implemented recently by the T★AFSM and present a sample from a wide set of patient-specific cerebral-aneurysm models we computed recently.
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Notes
- 1.
In some cases where the outflow diameters significantly differ, the solution obtained from the Laplace’s equation for shrinking amount and wall thickness for the aneurysm/bifurcation area could have an undesirable distribution. The need for specifying values at a set of inter-patch points comes from seeking a better distribution in that area.
References
Bazilevs Y, Hsu M-C, Benson D, Sankaran S, Marsden A (2009) Computational fluid–structure interaction: methods and application to a total cavopulmonary connection. Comput Mech 45:77–89
Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Kvamsdal T, Hentschel S, Isaksen J (2010) Computational fluid–structure interaction: methods and application to cerebral aneurysms. Biomech Model Mechanobiol 9:481–498
Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32:199–259
Frank O (1899) Die grundform des arteriellen pulses. Zeitung fur Biologie 37:483–586
Green AE, Naghdi PM (1976) A derivation of equations for wave propagation in water of variable depth. J Fluid Mech 78:237–246
Huang H, Virmani R, Younis H, Burke AP, Kamm RD, Lee RT (2001) The impact of calcification on the biomechanical stability of atherosclerotic plaques. Circulation 103:1051–1056
Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349
Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119:73–94
McPhail T, Warren J (2008) An interactive editor for deforming volumetric data. International conference on biomedical engineering 2008, Singapore, pp 137–144
Saad Y, Schultz M (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856–869
Takizawa K, Brummer T, Tezduyar TE, Chen PR (2012) A comparative study based on patient-specific fluid–structure interaction modeling of cerebral aneurysms. J Appl Mech 79:010908
Takizawa K, Christopher J, Tezduyar TE, Sathe S (2010a) Space–time finite element computation of arterial fluid–structure interactions with patientspecific data. Int J Numer Methods Biomed Eng 26:101–116
Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2010b) Wall shear stress calculations in space–time finite element computation of arterial fluid–structure interactions. Comput Mech 46:31–41
Takizawa K, Moorman C, Wright S, Purdue J, McPhail T, Chen PR, Warren J, Tezduyar TE (2011) Patient-specific arterial fluid–structure interaction modeling of cerebral aneurysms. Int J Numer Meth Fluids 65:308–323
Taylor CA, Hughes TJR, Zarins CK (1998) Finite element modeling of three-dimensional pulsatile flow in the abdominal aorta: relevance to atherosclerosis. Ann Biomed Eng 158:975–987
Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10):27–36
Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44
Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, Borst RD, Hughes TJR (eds) Encyclopedia of computational mechanics, vol 3: Fluids, Chap. 17. John Wiley & Sons, New York
Tezduyar TE, Cragin T, Sathe S, Nanna B (2007a) FSI computations in arterial fluid mechanics with estimated zero-pressure arterial geometry. In: Onate E, Garcia J, Bergan P, Kvamsdal T (eds) Marine 2007. CIMNE, Barcelona
Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space–time finite elements: Solution techniques. Int J Numer Meth Fluids 54:855–900
Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007b) Modeling of fluid–structure interactions with the space–time finite elements: arterial fluid mechanics. Int J Numer Meth Fluids 54:901–922
Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195:2002–2027
Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2008) Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique. Int J Numer Meth Fluids 57:601–629
Tezduyar TE, Schwaab M, Sathe S (2007c) Arterial fluid mechanics with the sequentially-coupled arterial FSI technique. In: Onate E, Papadrakakis M, Schrefler B (eds) Coupled problems 2007. CIMNE, Barcelona
Tezduyar TE, Schwaab M, Sathe S (2009) Sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng 198:3524–3533
Tezduyar TE, Takizawa K, Brummer T, Chen PR (2011) Space–time fluid–structure interaction modeling of patient-specific cerebral aneurysms. Int J Numer Methods Biomed Eng 27:1665–1710
Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46:17–29
Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2004) Influence of wall elasticity on image-based blood flow simulation. Jpn Soc Mech Eng J A 70:1224–1231 (in Japanese)
Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2011) Influencing factors in image-based fluid–structure interaction computation of cerebral aneurysms. Int J Numer Meth Fluids 65:324–340
Womersley JR (1955) Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Physiol 127:553–563
Acknowledgments
This work was supported in part by a seed grant from the Gulf Coast Center for Computational Cancer Research funded by John & Ann Doerr Fund for Computational Biomedicine. It was also supported in part by the Rice Computational Research Cluster funded by NSF Grant CNS-0821727. The 3DRA research at the Memorial Hermann Hospital University of Texas Medical School at Houston was supported by generous a funding from the Weatherhead Foundation. We thank Dr. Ryo Torii (University College London) for the inflow velocity data used in the computations and the arterial geometry used in Sect. 6.1.
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Takizawa, K., Tezduyar, T.E. (2014). Fluid–Structure Interaction Modeling of Patient-Specific Cerebral Aneurysms. In: Lima, R., Imai, Y., Ishikawa, T., Oliveira, M. (eds) Visualization and Simulation of Complex Flows in Biomedical Engineering. Lecture Notes in Computational Vision and Biomechanics, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7769-9_2
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