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Space–Time and ALE-VMS Techniques for Patient-Specific Cardiovascular Fluid–Structure Interaction Modeling

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Abstract

This is an extensive overview of the core and special space–time and Arbitrary Lagrangian–Eulerian (ALE) techniques developed by the authors’ research teams for patient-specific cardiovascular fluid–structure interaction (FSI) modeling. The core techniques are the ALE-based variational multiscale (ALE-VMS) method, the Deforming-Spatial-Domain/Stabilized Space–Time formulation, and the stabilized space–time FSI technique. The special techniques include methods for calculating an estimated zero-pressure arterial geometry, prestressing of the blood vessel wall, 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, the Sequentially-Coupled Arterial FSI technique and its multiscale versions, techniques for the projection of fluid–structure interface stresses, calculation of the wall shear stress and oscillatory shear index, arterial-surface extraction and boundary condition techniques, and a scaling technique for specifying a more realistic volumetric flow rate. With results from earlier computations, we show how these core and special FSI techniques work in patient-specific cardiovascular simulations.

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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

  1. Humphrey J (2002) Cardiovascular solid mechanics, cells, tissues, and organs. Springer, New York

    Google Scholar 

  2. Holzapfel G (2000) Nonlinear solid mechanics, a continuum approach for engineering. Wiley, Chichester

    MATH  Google Scholar 

  3. Holzapfel G, Ogden R (2010) Constitutive modelling of arteries. Proc R Soc A 466:1551–1596

    MathSciNet  MATH  Google Scholar 

  4. 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. doi:10.1016/j.cma.2004.09.014

    MathSciNet  MATH  Google Scholar 

  5. 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. doi:10.1016/j.cma.2005.08.023

    MathSciNet  MATH  Google Scholar 

  6. 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. doi:10.1002/fld.1430

    MathSciNet  MATH  Google Scholar 

  7. Förster C, Wall W, Ramm E (2007) Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Comput Methods Appl Mech Eng 196:1278–1293

    MATH  Google Scholar 

  8. 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 Ser A 70:1224–1231 (in Japanese)

    Google Scholar 

  9. 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. doi:10.1016/j.cma.2005.05.050

    MathSciNet  MATH  Google Scholar 

  10. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Influence of wall elasticity in patient-specific hemodynamic simulations. Comput Fluids 36:160–168. doi:10.1016/j.compfluid.2005.07.014

    MATH  Google Scholar 

  11. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2008) Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling. Comput Mech 43:151–159. doi:10.1007/s00466-008-0325-8

    MATH  Google Scholar 

  12. 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

    Google Scholar 

  13. 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

    MathSciNet  MATH  Google Scholar 

  14. Bazilevs Y, del Alamo JC, Humphrey JD (2010) From imaging to prediction: emerging non-invasive methods in pediatric cardiology. Prog Pediatr Cardiol 30:81–89

    Google Scholar 

  15. Figueroa C, Baek S, Taylor C, Humphrey J (2009) A computational framework for fluid–solid–growth modeling in cardiovascular simulations. Comput Methods Appl Mech Eng 199:3583–3602

    MathSciNet  Google Scholar 

  16. 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. doi:10.1007/s00466-006-0065-6

    MATH  Google Scholar 

  17. Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322

    MathSciNet  MATH  Google Scholar 

  18. 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. doi:10.1002/fld.1443

    MathSciNet  MATH  Google Scholar 

  19. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Numerical investigation of the effect of hypertensive blood pressure on cerebral aneurysm—dependence of the effect on the aneurysm shape. Int J Numer Methods Fluids 54:995–1009. doi:10.1002/fld.1497

    MathSciNet  MATH  Google Scholar 

  20. Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2007) YZβ discontinuity-capturing for advection-dominated processes with application to arterial drug delivery. Int J Numer Methods Fluids 54:593–608. doi:10.1002/fld.1484

    MathSciNet  MATH  Google Scholar 

  21. 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. doi:10.1002/fld.1633

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  23. Isaksen JG, Bazilevs Y, Kvamsdal T, Zhang Y, Kaspersen JH, Waterloo K, Romner B, Ingebrigtsen T (2008) Determination of wall tension in cerebral artery aneurysms by numerical simulation. Stroke 39:3172–3178

    Google Scholar 

  24. Maynard JP, Nithiarasu P (2008) A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method. Commun Numer Methods Eng 24:367–417

    Google Scholar 

  25. Tezduyar TE, Schwaab M, Sathe S (2009) Sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng 198:3524–3533. doi:10.1016/j.cma.2008.05.024

    MathSciNet  MATH  Google Scholar 

  26. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2009) Fluid–structure interaction modeling of blood flow and cerebral aneurysm: significance of artery and aneurysm shapes. Comput Methods Appl Mech Eng 198:3613–3621. doi:10.1016/j.cma.2008.08.020

    MathSciNet  MATH  Google Scholar 

  27. Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng 198:3534–3550

    MathSciNet  MATH  Google Scholar 

  28. 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. doi:10.1002/cnm.1241

    MATH  Google Scholar 

  29. Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46:17–29. doi:10.1007/s00466-009-0423-2

    MathSciNet  MATH  Google Scholar 

  30. 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. doi:10.1007/s00466-009-0425-0

    MathSciNet  MATH  Google Scholar 

  31. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2010) Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms. Int J Numer Methods Biomed Eng 26:336–347. doi:10.1002/cnm.1289

    MathSciNet  MATH  Google Scholar 

  32. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2010) Role of 0D peripheral vasculature model in fluid–structure interaction modeling of aneurysms. Comput Mech 46:43–52. doi:10.1007/s00466-009-0439-7

    MATH  Google Scholar 

  33. Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Liang X, Kvamsdal T, Brekken R, Isaksen J (2010) A fully-coupled fluid–structure interaction simulation of cerebral aneurysms. Comput Mech 46:3–16

    MathSciNet  MATH  Google Scholar 

  34. Sugiyama K, Ii S, Takeuchi S, Takagi S, Matsumoto Y (2010) Full Eulerian simulations of biconcave neo-Hookean particles in a Poiseuille flow. Comput Mech 46:147–157

    MathSciNet  MATH  Google Scholar 

  35. Mut F, Aubry R, Lohner R, Cebral JR (2010) Fast numerical solutions of patient-specific blood flows in 3D arterial systems. Int J Numer Methods Biomed Eng 26:73–85

    MATH  Google Scholar 

  36. Bevan RLT, Nithiarasu P, Loon RV, Sazanov I, Luckraz H, Garnham A (2010) Application of a locally conservative Galerkin (LCG) method for modelling blood flow through a patient-specific carotid bifurcation. Int J Numer Methods Fluids. doi:10.1002/fld.2313. Published online

    Google Scholar 

  37. Chitra K, Sundararajan T, Vengadesan S, Nithiarasu P (2010) Non-Newtonian blood flow study in a model cavopulmonary vascular system. Int J Numer Methods Fluids. doi:10.1002/fld.2256. Published online

    MATH  Google Scholar 

  38. Cebral JR, Mut F, Sforza D, Lohner R, Scrivano E, Lylyk P, Putnam C (2010) Clinical application of image-based CFD for cerebral aneurysms. Int J Numer Methods Biomed Eng. doi:10.1002/cnm.1373. Published online

    Google Scholar 

  39. 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. doi:10.1002/fld.2360

    MATH  Google Scholar 

  40. Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2011) Nested and parallel sparse algorithms for arterial fluid mechanics computations with boundary layer mesh refinement. Int J Numer Methods Fluids 65:135–149. doi:10.1002/fld.2415

    MathSciNet  MATH  Google Scholar 

  41. 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 Methods Fluids 65:324–340. doi:10.1002/fld.2448

    MATH  Google Scholar 

  42. 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. doi:10.1002/cnm.1433

    MathSciNet  Google Scholar 

  43. Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid–structure interaction simulations. Finite Elem Anal Des 47:593–599

    MathSciNet  Google Scholar 

  44. 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. doi:10.1115/1.4005071

    Google Scholar 

  45. Moghadam ME, Bazilevs Y, Hsia T-Y, Vignon-Clementel IE, Marsden AL, M. of Congenital Hearts Alliance (MOCHA) (2011) A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations. Comput Mech 48:277–291. doi:10.1007/s00466-011-0599-0

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  47. Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26:27–36. doi:10.1109/2.237441

    Google Scholar 

  48. Behr M, Johnson A, Kennedy J, Mittal S, Tezduyar T (1993) Computation of incompressible flows with implicit finite element implementations on the connection machine. Comput Methods Appl Mech Eng 108:99–118. doi:10.1016/0045-7825(93)90155-Q

    MathSciNet  MATH  Google Scholar 

  49. Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119:157–177. doi:10.1016/0045-7825(94)00082-4

    MATH  Google Scholar 

  50. Mittal S, Tezduyar TE (1994) Massively parallel finite element computation of incompressible flows involving fluid-body interactions. Comput Methods Appl Mech Eng 112:253–282. doi:10.1016/0045-7825(94)90029-9

    MathSciNet  MATH  Google Scholar 

  51. 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. doi:10.1016/0045-7825(94)00077-8

    MATH  Google Scholar 

  52. Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows: fluid-structure interactions. Int J Numer Methods Fluids 21:933–953. doi:10.1002/fld.1650211011

    MATH  Google Scholar 

  53. Aliabadi SK, Tezduyar TE (1995) Parallel fluid dynamics computations in aerospace applications. Int J Numer Methods Fluids 21:783–805. doi:10.1002/fld.1650211003

    MathSciNet  MATH  Google Scholar 

  54. Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18:397–412. doi:10.1007/BF00350249

    MATH  Google Scholar 

  55. Johnson AA, Tezduyar TE (1996) Simulation of multiple spheres falling in a liquid-filled tube. Comput Methods Appl Mech Eng 134:351–373. doi:10.1016/0045-7825(95)00988-4

    MathSciNet  MATH  Google Scholar 

  56. Johnson AA, Tezduyar TE (1997) Parallel computation of incompressible flows with complex geometries. Int J Numer Methods Fluids 24:1321–1340. doi:10.1002/(SICI)1097-0363(199706)24:12<1321::AID-FLD562>3.3.CO;2-C

    MATH  Google Scholar 

  57. Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23:130–143. doi:10.1007/s004660050393

    MATH  Google Scholar 

  58. Behr M, Tezduyar T (1999) The shear-slip mesh update method. Comput Methods Appl Mech Eng 174:261–274. doi:10.1016/S0045-7825(98)00299-0

    MATH  Google Scholar 

  59. 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. doi:10.1016/S0045-7825(00)00204-8

    MATH  Google Scholar 

  60. Stein K, Benney R, Kalro V, Tezduyar TE, Leonard J, Accorsi M (2000) Parachute fluid–structure interactions: 3-D computation. Comput Methods Appl Mech Eng 190:373–386. doi:10.1016/S0045-7825(00)00208-5

    MATH  Google Scholar 

  61. Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130. doi:10.1007/BF02897870

    MATH  Google Scholar 

  62. Tezduyar T, Osawa Y (2001) Fluid–structure interactions of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191:717–726. doi:10.1016/S0045-7825(01)00311-5

    MATH  Google Scholar 

  63. Stein K, Benney R, Tezduyar T, Potvin J (2001) Fluid–structure interactions of a cross parachute: numerical simulation. Comput Methods Appl Mech Eng 191:673–687. doi:10.1016/S0045-7825(01)00312-7

    MATH  Google Scholar 

  64. Ohayon R (2001) Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems. Comput Methods Appl Mech Eng 190:3009–3019

    MATH  Google Scholar 

  65. Behr M, Tezduyar T (2001) Shear-slip mesh update in 3D computation of complex flow problems with rotating mechanical components. Comput Methods Appl Mech Eng 190:3189–3200. doi:10.1016/S0045-7825(00)00388-1

    MATH  Google Scholar 

  66. Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70:58–63. doi:10.1115/1.1530635

    MATH  Google Scholar 

  67. Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193:2019–2032. doi:10.1016/j.cma.2003.12.046

    MATH  Google Scholar 

  68. van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid-structure interaction problem. SIAM J Sci Comput 27:599–621

    MathSciNet  MATH  Google Scholar 

  69. Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36:191–206. doi:10.1016/j.compfluid.2005.02.011

    MathSciNet  MATH  Google Scholar 

  70. Brenk M, Bungartz H-J, Mehl M, Neckel T (2006) Fluid–structure interaction on Cartesian grids: flow simulation and coupling environment. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction. Lecture notes in computational science and engineering, vol 53. Springer, Berlin, pp 233–269

    Google Scholar 

  71. Lohner R, Cebral JR, Yang C, Baum JD, Mestreau EL, Soto O (2006) Extending the range of applicability of the loose coupling approach for FSI simulations. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction. Lecture notes in computational science and engineering, vol 53. Springer, Berlin, pp 82–100

    Google Scholar 

  72. Bletzinger K-U, Wuchner R, Kupzok A (2006) Algorithmic treatment of shells and free form-membranes in FSI. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction. Lecture notes in computational science and engineering, vol 53. Springer, Berlin, pp 336–355

    Google Scholar 

  73. Sawada T, Hisada T (2007) Fluid–structure interaction analysis of the two dimensional flag-in-wind problem by an interface tracking ALE finite element method. Comput Fluids 36:136–146

    MATH  Google Scholar 

  74. Takizawa K, Yabe T, Tsugawa Y, Tezduyar TE, Mizoe H (2007) Computation of free–surface flows and fluid–object interactions with the CIP method based on adaptive meshless Soroban grids. Comput Mech 40:167–183. doi:10.1007/s00466-006-0093-2

    MATH  Google Scholar 

  75. Takizawa K, Tanizawa K, Yabe T, Tezduyar TE (2007) Ship hydrodynamics computations with the CIP method based on adaptive Soroban grids. Int J Numer Methods Fluids 54:1011–1019. doi:10.1002/fld.1466

    MATH  Google Scholar 

  76. Yabe T, Takizawa K, Tezduyar TE, Im H-N (2007) Computation of fluid–solid and fluid–fluid interfaces with the CIP method based on adaptive Soroban grids—an overview. Int J Numer Methods Fluids 54:841–853. doi:10.1002/fld.1473

    MathSciNet  MATH  Google Scholar 

  77. Manguoglu M, Sameh AH, Tezduyar TE, Sathe S (2008) A nested iterative scheme for computation of incompressible flows in long domains. Comput Mech 43:73–80. doi:10.1007/s00466-008-0276-0

    MathSciNet  MATH  Google Scholar 

  78. 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. doi:10.1007/s00466-008-0261-7

    MATH  Google Scholar 

  79. Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Fluid–structure interaction modeling of ringsail parachutes. Comput Mech 43:133–142. doi:10.1007/s00466-008-0260-8

    MATH  Google Scholar 

  80. Sathe S, Tezduyar TE (2008) Modeling of fluid–structure interactions with the space–time finite elements: contact problems. Comput Mech 43:51–60. doi:10.1007/s00466-008-0299-6

    MathSciNet  MATH  Google Scholar 

  81. Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction. Comput Mech 43:81–90

    MATH  Google Scholar 

  82. Bazilevs Y, Hughes TJR (2008) NURBS-based isogeometric analysis for the computation of flows about rotating components. Comput Mech 43:143–150

    MathSciNet  MATH  Google Scholar 

  83. Heil M, Hazel AL, Boyle J (2008) Solvers for large-displacement fluid–structure interaction problems: segregated versus monolithic approaches. Comput Mech 43:91–101

    MATH  Google Scholar 

  84. Sternel DC, Schaefer M, Heck M, Yigit S (2008) Efficiency and accuracy of fluid–structure interaction simulations using an implicit partitioned approach. Comput Mech 43:103–113

    MATH  Google Scholar 

  85. Mehl M, Brenk M, Bungartz H-J, Daubner K, Muntean IL, Neckel T (2008) An Eulerian approach for partitioned fluid–structure simulations on Cartesian grids. Comput Mech 43:115–124

    MATH  Google Scholar 

  86. Idelsohn SR, Marti J, Souto-Iglesias A, Onate E (2008) Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM. Comput Mech 43:125–132

    MATH  Google Scholar 

  87. Idelsohn SR, Marti J, Limache A, Onate E (2008) Unified Lagrangian formulation for elastic solids and incompressible fluids: application to fluid–structure interaction problems via the PFEM. Comput Methods Appl Mech Eng 197:1762–1776

    MathSciNet  MATH  Google Scholar 

  88. Manguoglu M, Sameh AH, Saied F, Tezduyar TE, Sathe S (2009) Preconditioning techniques for nonsymmetric linear systems in computation of incompressible flows. J Appl Mech 76:021204. doi:10.1115/1.3059576

    Google Scholar 

  89. Idelsohn SR, Pin FD, Rossi R, Onate E (2009) Fluid-structure interaction problems with strong added-mass effect. Int J Numer Methods Eng 80:1261–1294

    MATH  Google Scholar 

  90. Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2010) Solution of linear systems in arterial fluid mechanics computations with boundary layer mesh refinement. Comput Mech 46:83–89. doi:10.1007/s00466-009-0426-z

    MATH  Google Scholar 

  91. Mayer UM, Popp A, Gerstenberger A, Wall WA (2010) 3D fluid–structure–contact interaction based on a combined XFEM FSI and dual mortar contact approach. Comput Mech 46:53–67

    MathSciNet  MATH  Google Scholar 

  92. Calderer R, Masud A (2010) A multiscale stabilized ALE formulation for incompressible flows with moving boundaries. Comput Mech 46:185–197

    MathSciNet  MATH  Google Scholar 

  93. 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. doi:10.1002/fld.2221

    MATH  Google Scholar 

  94. 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

    MATH  Google Scholar 

  95. Ryzhakov PB, Rossi R, Idelsohn SR, Onate E (2010) A monolithic Lagrangian approach for fluid–structure interaction problems. Comput Mech 46:883–899

    MathSciNet  MATH  Google Scholar 

  96. Bazilevs Y, Hsu M-C, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar TE (2011) 3D simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Methods Fluids 65:207–235. doi:10.1002/fld.2400

    MATH  Google Scholar 

  97. 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

    MATH  Google Scholar 

  98. Takizawa K, Moorman C, Wright S, Spielman T, Tezduyar TE (2011) Fluid–structure interaction modeling and performance analysis of the Orion spacecraft parachutes. Int J Numer Methods Fluids 65:271–285. doi:10.1002/fld.2348

    MATH  Google Scholar 

  99. Takizawa K, Wright S, Moorman C, Tezduyar TE (2011) Fluid–structure interaction modeling of parachute clusters. Int J Numer Methods Fluids 65:286–307. doi:10.1002/fld.2359

    MATH  Google Scholar 

  100. Takizawa K, Tezduyar TE (2011) Multiscale space–time fluid–structure interaction techniques. Comput Mech 48:247–267. doi:10.1007/s00466-011-0571-z

    MathSciNet  MATH  Google Scholar 

  101. Takizawa K, Spielman T, Tezduyar TE (2011) Space–time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters. Comput Mech 48:345–364. doi:10.1007/s00466-011-0590-9

    MATH  Google Scholar 

  102. Takizawa K, Spielman T, Moorman C, Tezduyar TE (2012) Fluid–structure interaction modeling of spacecraft parachutes for simulation-based design. J Appl Mech 79:010907. doi:10.1115/1.4005070

    Google Scholar 

  103. Takizawa K, Henicke B, Puntel A, Spielman T, Tezduyar TE (2012) Space–time computational techniques for the aerodynamics of flapping wings. J Appl Mech 79:010903. doi:10.1115/1.4005073

    Google Scholar 

  104. Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Numerical-performance studies for the stabilized space–time computation of wind-turbine rotor aerodynamics. Comput Mech 48:647–657. doi:10.1007/s00466-011-0614-5

    MATH  Google Scholar 

  105. Sawada T, Tezuka A (2011) LLM and X-FEM based interface modeling of fluid–thin structure interactions on a non-interface-fitted mesh. Comput Mech 48:319–332. doi:10.1007/s00466-011-0600-y

    MathSciNet  MATH  Google Scholar 

  106. Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2011) A parallel sparse algorithm targeting arterial fluid mechanics computations. Comput Mech 48:377–384. doi:10.1007/s00466-011-0619-0

    MATH  Google Scholar 

  107. Onate E, Celigueta MA, Idelsohn SR, Salazar F, Suarez B (2011) Possibilities of the particle finite element method for fluid–soil–structure interaction problems. Comput Mech 48:307–318. doi:10.1007/s00466-011-0617-2

    MathSciNet  MATH  Google Scholar 

  108. Takase S, Kashiyama K, Tanaka S, Tezduyar TE (2011) Space–time SUPG finite element computation of shallow-water flows with moving shorelines. Comput Mech 48:293–306. doi:10.1007/s00466-011-0618-1

    MathSciNet  MATH  Google Scholar 

  109. Nagaoka S, Nakabayashi Y, Yagawa G, Kim YJ (2011) Accurate fluid–structure interaction computations using elements without mid-side nodes. Comput Mech 48:269–276. doi:10.1007/s00466-011-0620-7

    MathSciNet  MATH  Google Scholar 

  110. Takizawa K, Tezduyar TE (2012) Computational methods for parachute fluid–structure interactions. Arch Comput Methods Eng 19:125–169. doi:10.1007/s11831-012-9070-4

    Google Scholar 

  111. Gerbeau J, Vidrascu M, Frey P (2005) Fluid-structure interaction in blood flows on geometries based on medical images. Comput Struct 83:155–165

    Google Scholar 

  112. Fernandez M, Moubachir M (2005) A Newton method using exact jacobians for solving fluid-structure coupling. Comput Struct 83:127–142

    Google Scholar 

  113. Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44. doi:10.1016/S0065-2156(08)70153-4

    MathSciNet  MATH  Google Scholar 

  114. 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 94:339–351. doi:10.1016/0045-7825(92)90059-S

    MathSciNet  MATH  Google Scholar 

  115. 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 94:353–371. doi:10.1016/0045-7825(92)90060-W

    MathSciNet  MATH  Google Scholar 

  116. Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575. doi:10.1002/fld.505

    MathSciNet  MATH  Google Scholar 

  117. 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

    MathSciNet  MATH  Google Scholar 

  118. 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. doi:10.1016/0045-7825(92)90141-6

    MATH  Google Scholar 

  119. 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

    MathSciNet  MATH  Google Scholar 

  120. Hughes TJR, Hulbert GM (1988) Space–time finite element methods for elastodynamics: formulations and error estimates. Comput Methods Appl Mech Eng 66:339–363

    MathSciNet  MATH  Google Scholar 

  121. 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. ASME, New York, pp 7–24

    Google Scholar 

  122. 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. Fluids, vol 3. Wiley, New York. Chapter 17

    Google Scholar 

  123. Tezduyar TE, Takizawa K, Christopher J (2009) Multiscale sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. In: Hartmann S, Meister A, Schaefer M, Turek S (eds) International workshop on fluid–structure interaction—theory, numerics and applications. Kassel University Press, Kassel, pp 231–252

    Google Scholar 

  124. Tezduyar TE, Cragin T, Sathe S, Nanna B (2007) 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

    Google Scholar 

  125. Tezduyar TE, Schwaab M, Sathe S (2007) Arterial fluid mechanics with the sequentially-coupled arterial FSI technique. In: Onate E, Papadrakakis M, Schrefler B (eds) Coupled problems 2007. CIMNE, Barcelona

    Google Scholar 

  126. Wells RE Jr, Merrill EW (1961) Shear rate dependence of the viscosity of whole blood and plasma. Science 133:763–764

    Google Scholar 

  127. Simo J, Hughes T (1998) Computational inelasticity. Springer, New York

    MATH  Google Scholar 

  128. Betsch P, Gruttmann F, Stein E (1996) A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains. Comput Methods Appl Mech Eng 130:57–79

    MathSciNet  MATH  Google Scholar 

  129. Stuparu M (2002) Human heart valves. Hyperelastic material modeling. In: Proceedings of the X-th conference on mechanical vibrations. Timisoara, Romania

    Google Scholar 

  130. 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

    MATH  Google Scholar 

  131. Johnson C (1987) Numerical solution of partial differential equations by the finite element method. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  132. 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. doi:10.1016/0045-7825(84)90157-9

    MathSciNet  MATH  Google Scholar 

  133. Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput Methods Appl Mech Eng 59:307–325. doi:10.1016/0045-7825(86)90003-4

    MATH  Google Scholar 

  134. Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190:411–430. doi:10.1016/S0045-7825(00)00211-5

    MATH  Google Scholar 

  135. Hughes T, Scovazzi G, Franca L (2004) Multiscale and stabilized methods. In: Stein E, de Borst R, Hughes T (eds) Encyclopedia of computational mechanics. Fluids, vol 3. Wiley, New York. Chapter 2

    Google Scholar 

  136. 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

    MATH  Google Scholar 

  137. Hughes TJR, Feijóo G, Mazzei L, Quincy JB (1998) The variational multiscale method—a paradigm for computational mechanics. Comput Methods Appl Mech Eng 166:3–24

    MATH  Google Scholar 

  138. 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

    MathSciNet  MATH  Google Scholar 

  139. Akin JE, Tezduyar T, Ungor M, Mittal S (2003) Stabilization parameters and Smagorinsky turbulence model. J Appl Mech 70:2–9. doi:10.1115/1.1526569

    MATH  Google Scholar 

  140. Akin JE, Tezduyar TE (2004) Calculation of the advective limit of the SUPG stabilization parameter for linear and higher-order elements. Comput Methods Appl Mech Eng 193:1909–1922. doi:10.1016/j.cma.2003.12.050

    MATH  Google Scholar 

  141. Catabriga L, Coutinho ALGA, Tezduyar TE (2005) Compressible flow SUPG parameters computed from element matrices. Commun Numer Methods Eng 21:465–476. doi:10.1002/cnm.759

    MathSciNet  MATH  Google Scholar 

  142. Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZβ shock-capturing. Comput Mech 38:469–481. doi:10.1007/s00466-005-0025-6

    MATH  Google Scholar 

  143. Tezduyar TE, Sathe S (2006) Enhanced-discretization selective stabilization procedure (EDSSP). Comput Mech 38:456–468. doi:10.1007/s00466-006-0056-7

    MATH  Google Scholar 

  144. Onate E, Valls A, Garcia J (2006) FIC/FEM formulation with matrix stabilizing terms for incompressible flows at low and high Reynolds numbers. Comput Mech 38:440–455

    MATH  Google Scholar 

  145. Corsini A, Rispoli F, Santoriello A, Tezduyar TE (2006) Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation. Comput Mech 38:356–364. doi:10.1007/s00466-006-0045-x

    MathSciNet  MATH  Google Scholar 

  146. Catabriga L, Coutinho ALGA, Tezduyar TE (2006) Compressible flow SUPG parameters computed from degree-of-freedom submatrices. Comput Mech 38:334–343. doi:10.1007/s00466-006-0033-1

    MATH  Google Scholar 

  147. Rispoli F, Corsini A, Tezduyar TE (2007) Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD). Comput Fluids 36:121–126. doi:10.1016/j.compfluid.2005.07.004

    MATH  Google Scholar 

  148. Corsini A, Iossa C, Rispoli F, Tezduyar TE (2010) A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors. Comput Mech 46:159–167. doi:10.1007/s00466-009-0441-0

    MathSciNet  MATH  Google Scholar 

  149. 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. doi:10.1016/j.cma.2009.06.019

    MathSciNet  MATH  Google Scholar 

  150. Corsini A, Rispoli F, Tezduyar TE (2011) Stabilized finite element computation of NOx emission in aero-engine combustors. Int J Numer Methods Fluids 65:254–270. doi:10.1002/fld.2451

    MathSciNet  MATH  Google Scholar 

  151. Shakib F, Hughes TJR, Johan Z (1991) A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations. Comput Methods Appl Mech Eng 89:141–219

    MathSciNet  Google Scholar 

  152. Lo A (1982) Nonlinear dynamic analysis of cable and membrane structure. Ph.D. thesis, Department of Civil Engineering, Oregon State University

  153. Benney RJ, Stein KR, Leonard JW, Accorsi ML (1997) Current 3-D structural dynamic finite element modeling capabilities. In: Proceedings of AIAA 14th aerodynamic decelerator systems technology conference. San Francisco, California. AIAA Paper 97-1506

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  155. Fujisawa T, Inaba M, Yagawa G (2003) Parallel computing of high-speed compressible flows using a node-based finite element method. Int J Numer Methods Fluids 58:481–511

    MathSciNet  MATH  Google Scholar 

  156. Tezduyar TE (2007) Finite elements in fluids: special methods and enhanced solution techniques. Comput Fluids 36:207–223. doi:10.1016/j.compfluid.2005.02.010

    MathSciNet  MATH  Google Scholar 

  157. Johan Z, Mathur KK, Johnsson SL, Hughes TJR (1995) A case study in parallel computation: Viscous flow around an Onera M6 wing. Int J Numer Methods Fluids 21:877–884

    MATH  Google Scholar 

  158. Tezduyar TE, Liou J, Ganjoo DK (1990) Incompressible flow computations based on the vorticity-stream function and velocity-pressure formulations. Comput Struct 35:445–472. doi:10.1016/0045-7949(90)90069-E

    MATH  Google Scholar 

  159. Tezduyar TE, Mittal S, Shih R (1991) Time-accurate incompressible flow computations with quadrilateral velocity-pressure elements. Comput Methods Appl Mech Eng 87:363–384. doi:10.1016/0045-7825(91)90014-W

    MATH  Google Scholar 

  160. Hilber HM, Hughes TJR, Taylor RL (1977) Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Eng Struct Dyn 5:283–292

    Google Scholar 

  161. 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

    MathSciNet  Google Scholar 

  162. Green AE, Naghdi PM (1976) A derivation of equations for wave propagation in water of variable depth. J Fluid Mech 78:237–246

    MATH  Google Scholar 

  163. McPhail T, Warren J (2008) An interactive editor for deforming volumetric data. In: International Conference on Biomedical Engineering 2008, Singapore, pp 137–144

    Google Scholar 

  164. Chung J, Hulbert G (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. J Appl Mech 60:371–375

    MathSciNet  MATH  Google Scholar 

  165. 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

    Google Scholar 

  166. 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

    Google Scholar 

  167. Frank O (1899) Die Grundform des arteriellen Pulses. Z Biol 37:483–586

    Google Scholar 

  168. Formaggia L, Gerbeau J-F, Nobile F, Quarteroni A (2001) On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comput Methods Appl Mech Eng 191:561–582

    MathSciNet  MATH  Google Scholar 

  169. Vignon-Clementel I, Figueroa C, Jansen K, Taylor C (2006) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Methods Appl Mech Eng 195:3776–3796

    MathSciNet  MATH  Google Scholar 

  170. Tezduyar TE, Takizawa K, Christopher J (2009) Sequentially-coupled FSI technique. In: Kvamsdal T, Pettersen B, Bergan P, Onate E, Garcia J (eds) Marine 2009. CIMNE, Barcelona,

    Google Scholar 

  171. Tezduyar TE, Takizawa K, Christopher J, Moorman C, Wright S (2009) Interface projection techniques for complex FSI problems. In: Kvamsdal T, Pettersen B, Bergan P, Onate E, Garcia J (eds) Marine 2009. CIMNE, Barcelona

    Google Scholar 

  172. Jansen K, Whiting C, Hulbert G (1999) A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190:305–319

    MathSciNet  Google Scholar 

  173. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195

    MathSciNet  MATH  Google Scholar 

  174. Zhang Y, Bazilevs Y, Goswami S, Bajaj C, Hughes TJR (2007) Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Comput Methods Appl Mech Eng 196:2943–2959

    MathSciNet  MATH  Google Scholar 

  175. Zhang Y, Wang W, Liang X, Bazilevs Y, Hsu M-C, Kvamsdal T, Brekken R, Isaksen J (2009) High-fidelity tetrahedral mesh generation from medical imaging data for fluid-structure interaction analysis of cerebral aneurysms. Comput Model Eng Sci 42:131–150

    Google Scholar 

  176. Fontan F, Baudet E (1971) Surgical repair of tricuspid atresia. Thorax 26:240–248

    Google Scholar 

  177. Petrossian E, Reddy VM, Collins KK, Culbertson CB, MacDonald MJ, Lamberti JJ, Reinhartz O, Mainwaring RD, Francis PD, Malhotra SP, Gremmels DB, Suleman S, Hanley FL (2006) The extracardiac conduit Fontan operation using minimal approach extracorporeal circulation: early and midterm outcomes. J Thorac Cardiovasc Surg 132:1054–1063

    Google Scholar 

  178. Ensley A, Ramuzat A, Healy T, Chatzimavroudis G, Lucas C, Sharma S, Pettigrew R, Yoganathan A (2000) Fluid mechanic assessment of the total cavopulmonary connection using magnetic resonance phase velocity mapping and digital particle image velocimetry. Ann Biomed Eng 28:1172–1183

    Google Scholar 

  179. Khunatorn Y, Mahalingam S, DeGroff C, Shandas R (2002) Influence of connection geometry and SVC-IVC flow rate ratio on flow structures within the total cavopulmonary connection: a numerical study. J Biomech Eng 124:364–377

    Google Scholar 

  180. Bove E, de Leval M, Migliavacca F, Guadagni G, Dubini G (2003) Computational fluid dynamics in the evaluation of hemodynamic performance of cavopulmonary connections after the Norwood procedure for hypoplastic left heart syndrome. J Thorac Cardiovasc Surg 126:1040–1047

    Google Scholar 

  181. Migliavacca F, Dubini G, Bove E, de Leval M (2003) Computational fluid dynamics simulations in realistic 3-D geometries of the total cavopulmonary anastomosis: the influence of the inferior caval anastomosis. J Biomech Eng 125:805–813

    Google Scholar 

  182. Marsden A, Bernstein A, Reddy V, Shadden S, Spilker R, Chan F, Taylor C, Feinstein J (2009) Evaluation of a novel Y-shaped extracardiac Fontan baffle using computational fluid dynamics. J Thorac Cardiovasc Surg 137:394–403

    Google Scholar 

  183. Marsden A, Vignon-Clementel I, Chan F, Feinstein J, Taylor C (2007) Effects of exercise and respiration on hemodynamic efficiency in CFD simulations of the total cavopulmonary connection. Ann Biomed Eng 35:250–263

    Google Scholar 

  184. de Leval MR, Dubini G, Migliavacca F, Jalali H, Camporini G, Redington A, Pietrabissa R (1996) Use of computational fluid dynamics in the design of surgical procedures: application to the study of competitive flows in cavo-pulmonary connections. J Thorac Cardiovasc Surg 111:502–513

    Google Scholar 

  185. Dubini G, de Leval MR, Pietrabissa R, Montevecchi FM, Fumero R (1996) A numerical fluid mechanical study of repaired congenital heart defects: application to the total cavopulmonary connection. J Biomech 29:111–121

    Google Scholar 

  186. Migliavacca F, Dubini G, Pietrabissa R, de Leval MR (1997) Computational transient simulations with varying degree and shape of pulmonic stenosis in models of the bidirectional cavopulmonary anastomosis. Med Eng Phys 19:394–403

    Google Scholar 

  187. Sahni O, Muller J, Jansen K, Shephard M, Taylor C (2006) Efficient anisotropic adaptive discretization of the cardiovascular system. Comput Methods Appl Mech Eng 195:5634–5655

    MathSciNet  MATH  Google Scholar 

  188. Shachar G, Fuhrman B, Wang Y, Lucas R Jr, Lock J (1982) Rest and exercise hemodynamics after the Fontan procedure. Circulation 65:1043–1048

    Google Scholar 

  189. Giardini A, Balducci A, Specchia S, Gaetano G, Bonvicini M, Picchio FM (2008) Effect of sildenafil on haemodynamic response to exercise capacity in Fontan patients. Eur Heart J 29:1681–1687

    Google Scholar 

  190. Hjortdal VE, Emmertsen K, Stenbog E, Frund T, Rahbek Schmidt M, Kromann O, Sorensen K, Pedersen EM (2003) Effects of exercise and respiration on blood flow in total cavopulmonary connection: a real-time magnetic resonance flow study. Circulation 108:1227–1231

    Google Scholar 

  191. Pedersen EM, Stenbog EV, Frund T, Houlind K, Kromann O, Sorensen KE, Emmertsen K, Hjortdal VE (2002) Flow during exercise in the total cavopulmonary connection measured by magnetic resonance velocity mapping. Heart 87:554–558

    Google Scholar 

  192. Hetzer R, Jurmann MJ, Potapov EV, Hennig E, Stiller B, Muller JH, Weng Y (2002) Heart assist systems: current status. Hertz 20:407

    Google Scholar 

  193. Wootton DM, Ku DN (1999) Fluid mechanics of vascular systems, diseases, and thrombosis. Annu Rev Biomed Eng 1:299

    Google Scholar 

  194. Liu SQ, Zhong L, Goldman J (2002) Control of the shape of a thrombus-neointima-like structure by blood shear stress. J Biomech Eng 124:30

    Google Scholar 

  195. Kar B, Delgado RM III, Frazier OH, Gregoric I, Harting MT, Wadia Y, Myers T, Moser R, Freund J (2005) The effect of LVAD aortic outflow-graft placement on hemodynamics and flow. Texas Heart Inst J 32:294–298

    Google Scholar 

  196. Gohean JR (2007) A closed-loop multi-scale model of the cardiovascular system for evaluation of ventricular devices. Master’s thesis, University of Texas, Austin, May 2007

  197. Calo V, Brasher N, Bazilevs Y, Hughes T (2008) Multiphysics model for blood flow and drug transport with application to patient-specific coronary artery flow. Comput Mech 43:161–177

    MATH  Google Scholar 

  198. Olufsen MS (1988) Modeling of the arterial system with reference to an anesthesia simulator. Ph.D. thesis, Roskilde University, 1998

  199. Kilner PJ, Yang GZ, Mohiaddin RH, Firmin DN, Longmore DB (1993) Helical and retrograde secondary flow patterns in the aortic arch studied by three-directional magnetic resonance velocity mapping. Circulation 88:2235–2247

    Google Scholar 

  200. Glagov S, Zarins C, Giddens DP, Ku DN (1988) Hemodynamics and atherosclerosis: insights and perspectives gained from studies of human arteries. Arch Pathol Lab Med 112:1018–1031

    Google Scholar 

  201. Shaaban AM, Duerinckx AJ (2000) Wall shear stress and early atherosclerosis: a review. Am J Roentgenol 174:1657–1665

    Google Scholar 

  202. Levesque MJ, Nerem R (1985) The elongation and orientation of cultured endothelial cells in response to shear stress. J Biomech Eng 107:341–347

    Google Scholar 

  203. Levesque MJ, Liepsch D, Moravec S, Nerem R (1986) Correlation of endothelial cell shape and wall shear stress in a stenosed dog aorta. Arteriosclerosis 6:220–229

    Google Scholar 

  204. Okano M, Yoshida Y (1994) Junction complexes of endothelial cells in atherosclerosis-prone and atherosclerosis-resistant regions on flow dividers of brachiocephalic bifurcations in the rabbit aorta. Biorheology 31:155–161

    Google Scholar 

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Acknowledgements

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. This work was also partially supported by the UC San Diego Chancellor’s grant. We thank the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing HPC resources that have contributed to the research reported. We also thank SINTEF, ICT for partially supporting this work. Prof. Tor Ingebrigtsen and Dr. Jorgen Isaksen of the Institute for Clinical Medicine, University of Tromsø, Norway and the Department of Neurosurgery, the University Hospital of Northern Norway provided us with patient-specific cerebral aneurysm data. Prof. Jessica Zhang and Wenyan Wang at Carnegie Mellon University provided us with meshes of the aneurysm models employed in this work. We would like to thank Fred Nugen for segmenting the thoracic aorta model. We would also like to thank Rebecca Boon of TACC for her help with visualization. Finally, we thank Dr. Ryo Torii (Imperial College) for the inflow velocity waveform used in the computations and the arterial geometry used in Sects. 11.1–11.3.

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Authors and Affiliations

  1. Department of Modern Mechanical Engineering and Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Kenji Takizawa

  2. Structural Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA

    Yuri Bazilevs

  3. Mechanical Engineering, Rice University—MS 321, 6100 Main Street, Houston, TX, 77005, USA

    Tayfun E. Tezduyar

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  1. Kenji Takizawa
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Correspondence to Kenji Takizawa.

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Takizawa, K., Bazilevs, Y. & Tezduyar, T.E. Space–Time and ALE-VMS Techniques for Patient-Specific Cardiovascular Fluid–Structure Interaction Modeling. Arch Computat Methods Eng 19, 171–225 (2012). https://doi.org/10.1007/s11831-012-9071-3

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