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Fluid–structure interaction simulation of pulsatile ventricular assist devices

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Abstract

In this paper we present a collection of fluid–structure interaction (FSI) computational techniques that enable realistic simulation of pulsatile Ventricular Assist Devices (VADs). The simulations involve dynamic interaction of air, blood, and a thin membrane separating the two fluids. The computational challenges addressed in this work include large, buckling motions of the membrane, the need for periodic remeshing of the fluid mechanics domain, and the necessity to employ tightly coupled FSI solution strategies due to the very strong added mass effect present in the problem. FSI simulation of a pulsatile VAD at realistic operating conditions is presented for the first time. The FSI methods prove to be robust, and may be employed in the assessment of current, and the development of future, pulsatile VAD designs.

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References

  1. Akkerman I, Bazilevs Y, Benson DJ, Farthing MW, Kees CE (2012) Free-surface flow and fluid-object interaction modeling with emphasis on ship hydrodynamics. J Appl Mech 79:010905

    Article  Google Scholar 

  2. Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230:4137–4152

    Article  MathSciNet  MATH  Google Scholar 

  3. Akkerman I, Dunaway J, Kvandal J, Spinks J, Bazilevs Y (2012) Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS. Comput Mech 50:719–727

    Article  MATH  Google Scholar 

  4. Amodeo A, Brancaccio G, Michielon G, Filippelli S, Ricci Z, Morelli S, Gagliardi MG, Iacobelli R, Pongiglione G, Di Donato RM (November 2010) Pneumatic pulsatile ventricular assist device as a bridge to heart transplantation in pediatric patients. Artif Organs 34(11):1017–1022

    Google Scholar 

  5. Arabia FA, Tsau PH, Smith RG, Nolan PE, Paramesh V, Bose RK, Woolley DS, Sethi GK, Rhenman BE, Copeland J (2006) Pediatric bridge to heart transplantation: application of the berlin heart, medos, and the thoratec ventricular assist devices. J Heart Lung Transplant 25(1):16–21

    Article  Google Scholar 

  6. Bazilevs Y, Akkerman I (2010) Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method. J Comput Phys 229:3402–3414

    Article  MathSciNet  MATH  Google Scholar 

  7. Bazilevs Y, Calo VM, Cottrel JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197:173–201

    Article  MATH  Google Scholar 

  8. Bazilevs Y, Calo VM, Cottrell JA, Evans JA, Hughes TJR, Lipton S, Scott MA, Sederberg TW (2010) Isogeometric analysis using T-splines. Comput Methods Appl Mech Eng 199:229–263

    Article  MathSciNet  MATH  Google Scholar 

  9. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37

    Article  MathSciNet  MATH  Google Scholar 

  10. 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

    Google Scholar 

  11. Bazilevs Y, Hsu M-C, Kiendl J, Benson DJ (2012) A computational procedure for prebending of wind turbine blades. Int J Numer Methods Eng 89:323–336

    Article  MATH  Google Scholar 

  12. Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II: Fluid-structure interaction modeling with composite blades. Int J Numer Methods Fluids 65:236–253

    Article  MATH  Google Scholar 

  13. Bazilevs Y, Hsu M-C, Scott MA (2012) Isogeometric fluid-structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Comput Methods Appl Mech Eng. doi:10.1016/j.cma.2012.03.028

  14. Bazilevs Y, Ming-Chen H, Takizawa K, Tezduyar TE (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction. Math Models Methods Appl Sci 22(supp 02):1230002

    Article  Google Scholar 

  15. Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36: 12–26

    Google Scholar 

  16. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng 196:4853–4862

    Article  MathSciNet  MATH  Google Scholar 

  17. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2010) Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes. Comput Methods Appl Mech Eng 199:780–790

    Article  MathSciNet  MATH  Google Scholar 

  18. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid-structure interaction: methods and applications. Wiley, Chichester

    Book  Google Scholar 

  19. Benson DJ, Bazilevs Y, De Luycker E, Hsu M-C, Scott M, Hughes TJR, Belytschko T (2010) A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM. Int J Numer Methods Eng 83:765–785

    MATH  Google Scholar 

  20. Benson DJ, Bazilevs Y, Hsu M-C, Hughes TJR (2010) Isogeometric shell analysis: the Reissner-Mindlin shell. Comput Methods Appl Mech Eng 199:276–289

    Article  MathSciNet  MATH  Google Scholar 

  21. Benson DJ, Bazilevs Y, Hsu M-C, Hughes TJR (2011) A large deformation, rotation-free, isogeometric shell. Comput Methods Appl Mech Eng 200:1367–1378

    Article  MathSciNet  MATH  Google Scholar 

  22. 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

    Article  MathSciNet  MATH  Google Scholar 

  23. Cavanaugh JL, Miyamoto SD, da Cruz E, Pietra BA, Campbell DN, Mitchell MB, Peyton CE, Gruenwald J, Darst JR (2010) Predicting recovery: successful explant of a ventricular assist device in a child with dilated cardiomyopathy. J Heart Lung Transplant 29(1):105–108

    Article  Google Scholar 

  24. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics withimproved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–375

    Article  MathSciNet  MATH  Google Scholar 

  25. Cirak F, Ortiz M (2001) Fully \({C}^1\)-conforming subdivision elements for finite deformation thin shell analysis. Int J Numer Methods Eng 51:813–833

    Article  MATH  Google Scholar 

  26. Cirak F, Ortiz M, Schröder P (2000) Subdivision surfaces: a new paradigm for thin shell analysis. Int J Numer Methods Eng 47:2039–2072

    Article  MATH  Google Scholar 

  27. Cirak F, Scott MJ, Antonsson EK, Ortiz M, Schröder P (2002) Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision. Computer-Aided Des 34:137–148

    Article  Google Scholar 

  28. Dörfel MR, Jüttler B, Simeon B (2010) Adaptive isogeometric analysis by local h-refinement with T-splines. Comput Methods Appl Mech Eng 199:264–275

    Article  MATH  Google Scholar 

  29. Haut Donahue TL, Dehlin W, Gillespie J, Weiss WJ, Rosenberg G (2009) Finite element analysis of stresses developed in the blood sac of a left ventricular assist device. Med Eng Phys 31: 454–460

    Google Scholar 

  30. Doyle MG, Vergniaud J-B, Tavoularis S, Bourgault Y (2008) Numerical simulations of blood flow in artificial and natural hearts with fluid-structure interaction. Artif Organs 32(11):870–879

    Article  Google Scholar 

  31. Esmaily-Moghadam M, Migliavacca F, Vignon-Clementel IE, Hsia TY, Marsden AL (2012) Optimization of shunt placement for the norwood surgery using multi-domain modeling. J Biomed Eng 134: 5

    Google Scholar 

  32. Farhat C, Lesoinne M, Le Tallec P (1998) Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Comput Methods Appl Mech Eng 157:95–114

    Article  MATH  Google Scholar 

  33. Hetzer R, Potapov EV, Stiller B et al (2006) Improvement in survival after mechanical circulatory support with pneumatic ventricula assist devices in pediatric patients. Annals Thorac Surg 82:917–925

    Article  Google Scholar 

  34. Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE-VMS: validation and the role of weakly enforced boundary conditions. Comput Mech. doi:10.1007/s00466-012-0686-x

  35. Hsu M-C, Akkerman I, Bazilevs Y (2013) Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment. Wind Energy. doi:10.1002/we.1599

  36. Hsu M-C, Bazilevs Y (2012) Fluid-structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50:821–833

    Article  MathSciNet  MATH  Google Scholar 

  37. Hsu M-C, Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2010) Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. Comput Methods Appl Mech Eng 199:828–840

    Article  MathSciNet  MATH  Google Scholar 

  38. Hughes TJR (1995) Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods. Comput Methods Appl Mech Eng 127:387–401

    Article  MATH  Google Scholar 

  39. Hughes TJR, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Eng 59:85–99

    Article  MathSciNet  MATH  Google Scholar 

  40. Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349

    Article  MathSciNet  MATH  Google Scholar 

  41. Hughes TJR, Sangalli G (2007) Variational multiscale analysis: the fine-scale Green’s function, projection, optimization, localization, and stabilized methods. SIAM J Numer Anal 45:539–557

    Article  MathSciNet  MATH  Google Scholar 

  42. Hughes TJR, Scovazzi G, Franca LP (2004) Multiscale and stabilized methods. In: Stein E, de Borst R, Hughes TJR (eds) Encyclopedia of Computational Mechanics, vol. 3, Fluids chapter 2. Wiley, New York

    Google Scholar 

  43. Hughes TJR, Tezduyar TE (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 45:217–284

    Article  MathSciNet  MATH  Google Scholar 

  44. Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190:305–319

    Article  MathSciNet  MATH  Google Scholar 

  45. 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

    Article  MATH  Google Scholar 

  46. Johnson AA, Tezduyar TE (1996) Simulation of multiple spheres falling in a liquid-filled tube. Comput Methods Appl Mech Eng 134:351–373

    Article  MathSciNet  MATH  Google Scholar 

  47. Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid-structure interactions in parachute systems. Comput Methods Appl Mech Eng 190:321–332

    Article  MATH  Google Scholar 

  48. Kiendl J, Bazilevs Y, Hsu M-C, Wüchner R, Bletzinger K-U (2010) The bending strip method for isogeometric analysis of Kirchhoff-Love shell structures comprised of multiple patches. Comput Methods Appl Mech Eng 199:2403–2416

    Article  MATH  Google Scholar 

  49. Kiendl J, Bletzinger K-U, Linhard J, Wüchner R (2009) Isogeometric shell analysis with Kirchhoff-Love elements. Comput Methods Appl Mech Eng 198:3902–3914

    Article  MATH  Google Scholar 

  50. Konig CS, Clark C, Mokhtarzadeh-Dehghan MR (1999) Investigation of unsteady flow in a model of a ventricular assist device by numerical modeling and comparison with experiment. Mech Eng Phys 21(1):53–64

    Article  Google Scholar 

  51. Kuttler U, Forster C, Wall WA (2006) A solution for the incompressibility dilemma in partitioned fluid-structure interaction with pure Dirichlet fluid domains. Comput Mech 38:417–429

    Article  Google Scholar 

  52. Long CC, Hsu M-C, Bazilevs Y, Feinstein JA, Marsden AL (2012) Fluid-structure interaction simulations of the Fontan procedure using variable wall properties. Int J Numer Methods Biomed Eng 28:512–527

    Article  MathSciNet  Google Scholar 

  53. Marsden AL, Bernstein AD, Reddy VM, Shadden S, Spilker R, Chan FP, Taylor CA, Feinstein JA (2008) Evaluation of a novel Y-shaped extracardiac fontan baffle using computational fluid dynamics. J Thorac Cardiovasc Surg. doi:10.1016/j.jtcvs.2008.06.043

  54. Marsden AL, Feinstein JA, Taylor CA (2008) A computational framework for derivative-free optimization of cardiovascular geometries. Comput Methods Appl Mech Eng 197(21–24):1890–1905

    Article  MathSciNet  MATH  Google Scholar 

  55. Marsden AL, Wang M, Dennis JE Jr, Moin P (2007) Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation. J Fluid Mech 572:13–36

    Article  MathSciNet  MATH  Google Scholar 

  56. Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows—Fluid-structure interactions. Int J Numer Methods Fluids 21:933–953

    Article  MATH  Google Scholar 

  57. Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, Wüchner R, Bletzinger KU, Bazilevs Y, Rabczuk T (2011) Rotation-free isogeometric thin shell analysis using PHT-splines. Comput Methods Appl Mech Eng 200:3410–3424

    Article  MATH  Google Scholar 

  58. Nordbeck S, Rystedt B (1967) Computer cartography point-in-polygon programs. BIT Numer Math 7:39–64

    Article  MATH  Google Scholar 

  59. Oñate E, Flores FG (2005) Advances in the formulation of the rotation-free basic shell triangle. Comput Methods Appl Mech Eng 194:2406–2443

    Article  MATH  Google Scholar 

  60. Oñate E, Zarate F (2000) Rotation-free triangular plate and shell elements. Int J Numer Methods Eng 47:557–603

    Article  MATH  Google Scholar 

  61. Piegl L, Tiller W (1997) The NURBS book (monographs in visual communication), 2nd edn. Springer, Berlin

    Book  Google Scholar 

  62. Roszelle BN, Deutsch S, Weiss WJ, Manning KB (2011) Flow visualization of a pediatric ventricular assist device during stroke volume reductions related to weaning. J Biomech Eng 39(7):2046–2058

    Google Scholar 

  63. Saad Y, Schultz M (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856–869

    Article  MathSciNet  MATH  Google Scholar 

  64. Sankaran S, Audet C, Marsden AL (2010) A method for stochastic constrained optimization using derivative-free surrogate pattern search and collocation. J Comput Phys 229(12):4664–4682

    Article  MATH  Google Scholar 

  65. Sankaran S, Esmaily-Moghadam M, Kahn AM, Guccione J, Tseng E, Marsden AL (2012) Patient-specific multiscale modeling of blood flow for coronary artery bypass graft surgery. Annals Biomed Eng 40(1):2228–2242

    Article  Google Scholar 

  66. Sankaran S, Marsden AL (2011) A stochastic collocation method for uncertainty quantification in cardiovascular simulations. J Biomech Eng 133(3):031001

    Article  Google Scholar 

  67. San Diego Supercomputing Center (SDSC). http://www.sdsc.edu/. Accessed 15 April 2013

  68. Sengupta D, Kahn AM, Burns JC, Sankaran S, Shadden S, Marsden AL (2012) Image-based modeling of hemodynamics and coronary artery aneurysms caused by kawasaki disease. Biomech Model Mechanobiol 11(6):915–932

    Article  Google Scholar 

  69. Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space-time and ALE-VMS techniques for patient-specific cardiovascular fluid-structure interaction modeling. Arch Comput Methods Eng 19:171–225

    Article  MathSciNet  Google Scholar 

  70. 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

    Article  Google Scholar 

  71. Takizawa K, Christopher J, Tezduyar TE, Sathe S (2010) Space-time finite element computation of arterial fluid-structure interactions with patient-specific data. Int J Numer Methods Biomed Eng 26:101–116

    Article  MATH  Google Scholar 

  72. Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2010) Wall shear stress calculations in space-time finite element computation of arterial fluid-structure interactions. Comput Mech 46:31–41

    Article  MathSciNet  MATH  Google Scholar 

  73. 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 Methods Fluids 65:308–323

    Article  MATH  Google Scholar 

  74. Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid-structure interaction techniques. Comput Mech 48:247–267

    Article  MathSciNet  MATH  Google Scholar 

  75. Takizawa K, Tezduyar TE (2012) Computational methods for parachute fluid-structure interactions. Arch Comput Methods Eng 19:125–169

    Article  MathSciNet  Google Scholar 

  76. Takizawa K, Tezduyar TE (2012) Space-time fluid-structure interaction methods. Math Models Methods Appl Sci. doi: 10.1142/S0218202512300013

  77. Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10):27–36

    Article  Google Scholar 

  78. Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44

    Google Scholar 

  79. Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130

    Article  MATH  Google Scholar 

  80. Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575

    Article  MathSciNet  MATH  Google Scholar 

  81. Tezduyar TE (2007) Finite elements in fluids: special methods and enhanced solution techniques. Comput Fluids 36:207–223

    Article  MathSciNet  MATH  Google Scholar 

  82. Tezduyar TE, Behr M, Liou J (1992) 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. Comput Methods Appl Mech Eng 94(3):339–351

    Article  MathSciNet  MATH  Google Scholar 

  83. Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the finite element methods — space-time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis PVP-vol. 246/AMD-vol. 143, pp 7–24, ASME, New York

  84. Tezduyar TE, Behr M, Mittal S, Liou J (1992) 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. Comput Methods Appl Mech Eng 94(3):353–371

    Article  MathSciNet  MATH  Google Scholar 

  85. Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95:221–242

    Article  MATH  Google Scholar 

  86. Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190:411–430

    Article  MATH  Google Scholar 

  87. Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput Methods Appl Mech Eng 59:307–325

    Google Scholar 

  88. Tezduyar TE, Sathe S (2007) Modeling of fluid-structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54:855–900

    Article  MathSciNet  MATH  Google Scholar 

  89. Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modeling of fluid-structure interactions with the space-time finite elements: arterial fluid mechanics. Int J Numer Methods Fluids 54:901–922

    Article  MathSciNet  MATH  Google Scholar 

  90. Tezduyar TE, Sathe S, Keedy R, Stein K (2004) Space-time techniques for finite element computation of flows with moving boundaries and interfaces. In: Gallegos S, Herrera I, Botello S, Zarate F, Ayala G (eds) Proceedings of the III International Congress on Numerical Methods in Engineering and Applied Science. CD-ROM, Monterrey, Mexico

    Google Scholar 

  91. 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

    Article  MathSciNet  MATH  Google Scholar 

  92. Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid-structure interaction modeling with moving-mesh methods. Comput Mech 43:39–49

    Article  MATH  Google Scholar 

  93. 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 Methods Fluids 57:601–629

    Article  MathSciNet  MATH  Google Scholar 

  94. Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully-discretized equations in computation of fluid-structure interactions with the space-time formulations. Comput Methods Appl Mech Eng 195:5743–5753

    Article  MathSciNet  MATH  Google Scholar 

  95. Tezduyar TE, Schwaab M, Sathe S (2009) Sequentially-coupled arterial fluid-structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng 198:3524–3533

    Article  MathSciNet  MATH  Google Scholar 

  96. 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

    Article  MathSciNet  MATH  Google Scholar 

  97. Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46:17–29

    Article  MathSciNet  MATH  Google Scholar 

  98. Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Space-time finite element computation of complex fluid-structure interactions. Int J Numer Methods Fluids 64:1201–1218

    Article  MATH  Google Scholar 

  99. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Computer modeling of cardiovascular fluid-structure interactions with the deforming-spatial-domain/stabilized space-time formulation. Comput Methods Appl Mech Eng 195:1885–1895

    Google Scholar 

  100. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Fluid-structure interaction modeling of aneurysmal conditions with high and normal blood pressures. Comput Mech 38:482–490

    Article  MATH  Google Scholar 

  101. Zhiliang X, Chen N, Malgorzata MK, Elliot DR, Mark A (2008) A multiscale model of thrombus development. J R Soc Interface 5:705–722

    Article  Google Scholar 

  102. Zhiliang X, Chen N, Shadden SC, Marsden JE, Malgorzata MK, Elliot DR, Mark A (2009) Study of blood flow impact on growth of thrombi using a multiscale model. Soft Matter 5(4):769–779

    Article  Google Scholar 

  103. Yang W, Feinstein JA, Marsden AL (2010) Constrained optimization of an idealized y-shaped baffle for the fontan surgery at rest and exercise. Comput Methods Appl Mech Eng 199:2135–2149

    Article  MATH  Google Scholar 

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Acknowledgments

The support of the AFOSR Award No. FA9550-12-1-0005 and a Burroughs Wellcome Fund Career Award at the Scientific Interface is gratefully acknowledged. We also thank the San Diego Supercomputing Center (SDSC) at the University of California, San Diego for providing HPC resources that have contributed to the research results reported in this paper.

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Long, C.C., Marsden, A.L. & Bazilevs, Y. Fluid–structure interaction simulation of pulsatile ventricular assist devices. Comput Mech 52, 971–981 (2013). https://doi.org/10.1007/s00466-013-0858-3

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