Computational Mechanics

, Volume 55, Issue 6, pp 1211–1225 | Cite as

Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models

  • Ming-Chen HsuEmail author
  • David Kamensky
  • Fei Xu
  • Josef Kiendl
  • Chenglong Wang
  • Michael C. H. Wu
  • Joshua Mineroff
  • Alessandro Reali
  • Yuri Bazilevs
  • Michael S. Sacks


This paper builds on a recently developed immersogeometric fluid–structure interaction (FSI) methodology for bioprosthetic heart valve (BHV) modeling and simulation. It enhances the proposed framework in the areas of geometry design and constitutive modeling. With these enhancements, BHV FSI simulations may be performed with greater levels of automation, robustness and physical realism. In addition, the paper presents a comparison between FSI analysis and standalone structural dynamics simulation driven by prescribed transvalvular pressure, the latter being a more common modeling choice for this class of problems. The FSI computation achieved better physiological realism in predicting the valve leaflet deformation than its standalone structural dynamics counterpart.


Fluid–structure interaction Bioprosthetic heart valve Isogeometric analysis Immersogeometric analysis Arbitrary Lagrangian–Eulerian NURBS and T-splines Kirchhoff–Love shell Fung-type hyperelastic model 



M.S. Sacks was supported by NIH/NHLBI Grant R01 HL108330. D. Kamensky was partially supported by the CSEM Graduate Fellowship. M.-C. Hsu, C. Wang and Y. Bazilevs were partially supported by the ARO Grant No. W911NF-14-1-0296. J. Kiendl and A. Reali were partially supported by the European Research Council through the FP7 Ideas Starting Grant No. 259229 ISOBIO. 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 results reported in this paper.


  1. 1.
    Schoen FJ, Levy RJ (2005) Calcification of tissue heart valve substitutes: progress toward understanding and prevention. Ann Thorac Surg 79(3):1072–1080CrossRefGoogle Scholar
  2. 2.
    Pibarot P, Dumesnil JG (2009) Prosthetic heart valves: selection of the optimal prosthesis and long-term management. Circulation 119(7):1034–1048CrossRefGoogle Scholar
  3. 3.
    Li C-P, Chen S-F, Lo C-W, Lu P-C (2011) Turbulence characteristics downstream of a new trileaflet mechanical heart valve. ASAIO Journal 57(3):188–196CrossRefGoogle Scholar
  4. 4.
    Yun BM, Wu J, Simon HA, Arjunon S, Sotiropoulos F, Aidun CK, Yoganathan AP (2012) A numerical investigation of blood damage in the hinge area of aortic bileaflet mechanical heart valves during the leakage phase. Ann Biomed Eng 40(7):1468–1485CrossRefGoogle Scholar
  5. 5.
    Siddiqui RF, Abraham JR, Butany J (2009) Bioprosthetic heart valves: modes of failure. Histopathology 55:135–144CrossRefGoogle Scholar
  6. 6.
    Sacks MS, Schoen FJ (2002) Collagen fiber disruption occurs independent of calcification in clinically explanted bioprosthetic heart valves. J Biomed Mater Res 62(3):359–371CrossRefGoogle Scholar
  7. 7.
    Sacks MS, Mirnajafi A, Sun W, Schmidt P (2006) Bioprosthetic heart valve heterograft biomaterials: structure, mechanical behavior and computational simulation. Expert Rev Med Devices 3(6):817–834CrossRefGoogle Scholar
  8. 8.
    Sun W, Abad A, Sacks MS (2005) Simulated bioprosthetic heart valve deformation under quasi-static loading. J Biomech Eng 127(6):905–914CrossRefGoogle Scholar
  9. 9.
    Saleeb AF, Kumar A, Thomas VS (2013) The important roles of tissue anisotropy and tissue-to-tissue contact on the dynamical behavior of a symmetric tri-leaflet valve during multiple cardiac pressure cycles. Med Eng Phys 35(1):23–35CrossRefGoogle Scholar
  10. 10.
    Auricchio F, Conti M, Ferrara A, Morganti S, Reali A (2014) Patient-specific simulation of a stentless aortic valve implant: the impact of fibres on leaflet performance. Comput Methods Biomech Biomed Eng 17(3):277–285CrossRefGoogle Scholar
  11. 11.
    Kamensky D, Hsu M-C, Schillinger D, Evans JA, Aggarwal A, Bazilevs Y, Sacks MS, Hughes TJR (2015) An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves. Comput Methods Appl Mech Eng 284:1005–1053MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hsu M-C, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJR (2014) Fluid-structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech 54:1055–1071zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Peskin CS (1972) Flow patterns around heart valves: a numerical method. J Comput Phys 10(2):252–271zbMATHCrossRefGoogle Scholar
  14. 14.
    Peskin CS (2002) The immersed boundary method. Acta Numer 11:479–517zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Mittal R, Iaccarino G (2005) Immersed boundary methods. Annu Rev Fluid Mech 37:239–261MathSciNetCrossRefGoogle Scholar
  16. 16.
    Sotiropoulos F, Yang X (2014) Immersed boundary methods for simulating fluid-structure interaction. Prog Aerosp Sci 65:1–21Google Scholar
  17. 17.
    Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, ChichesterCrossRefGoogle Scholar
  19. 19.
    Hsu M-C, Wang C, Herrema AJ, Schillinger D, Ghoshal A, Bazilevs Y (2015) An interactive geometry modeling and parametric design platform for isogeometric analysis. Computers & Mathematics with Applications. doi: 10.1016/j.camwa.2015.04.002
  20. 20.
    Kiendl J, Bletzinger K-U, Linhard J, Wüchner R (2009) Isogeometric shell analysis with Kirchhoff–Love elements. Comput Methods Appl Mech Eng 198:3902–3914zbMATHCrossRefGoogle Scholar
  21. 21.
    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 199:2403–2416zbMATHCrossRefGoogle Scholar
  22. 22.
    Kiendl J, Hsu M-C, Wu MCH, Reali A (2015) Isogeometric Kirchhoff-Love shell formulations for general hyperelastic materials. Computer Methods in Applied Mechanics and Engineering. doi: 10.1016/j.cma.2015.03.010
  23. 23.
    Rhinoceros (2015).
  24. 24.
    Autodesk T-Splines Plug-in for Rhino (2015).
  25. 25.
    Piegl L, Tiller W (1997) The NURBS Book (Monographs in Visual Communication), 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  26. 26.
    Scott MA, Hughes TJR, Sederberg TW, Sederberg MT (2014) An integrated approach to engineering design and analysis using the Autodesk T-spline plugin for Rhino3d. ICES REPORT 14–33, The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Sept 2014Google Scholar
  27. 27.
    Li X, Zheng J, Sederberg TW, Hughes TJR, Scott MA (2012) On linear independence of T-spline blending functions. Comput Aided Geom Des 29(1):63–76zbMATHMathSciNetCrossRefGoogle Scholar
  28. 28.
    Li X, Scott MA (2014) Analysis-suitable T-splines: Characterization, refineability, and approximation. Mathematical Models and Methods in Applied Sciences 24:1141–1164zbMATHMathSciNetCrossRefGoogle Scholar
  29. 29.
    Grasshopper (2015).
  30. 30.
    Rhino Developer Tools (2015).
  31. 31.
    Kim H, Lu J, Sacks MS, Chandran KB (2008) Dynamic simulation of bioprosthetic heart valves using a stress resultant shell model. Ann Biomed Eng 36(2):262–275CrossRefGoogle Scholar
  32. 32.
    Sederberg TW, Cardon DL, Finnigan GT, North NS, Zheng J, Lyche T (2004) T-spline simplification and local refinement. ACM Trans Graph 23(3):276–283CrossRefGoogle Scholar
  33. 33.
    Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, ChichesterGoogle Scholar
  34. 34.
    Scott MA, Borden MJ, Verhoosel CV, Sederberg TW, Hughes TJR (2011) Isogeometric finite element data structures based on Bézier extraction of T-splines. Int J Numer Methods Eng 88:126–156zbMATHMathSciNetCrossRefGoogle Scholar
  35. 35.
    Kamensky D, Evans JA, Hsu M-C (2015) Stability and conservation properties of collocated constraints in immersogeometric fluid-thin structure interaction analysis. Communications in Computational Physics. AcceptedGoogle Scholar
  36. 36.
    Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349zbMATHMathSciNetCrossRefGoogle Scholar
  37. 37.
    Donea J, Giuliani S, Halleux JP (1982) An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comput Methods Appl Mech Eng 33(1–3):689–723zbMATHCrossRefGoogle Scholar
  38. 38.
    Formaggia L, Gerbeau JF, 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 191:561–582zbMATHMathSciNetCrossRefGoogle Scholar
  39. 39.
    Gerbeau J-F, Vidrascu M, Frey P (2005) Fluid-structure interaction in blood flows on geometries based on medical imaging. Comput Struct 83:155–165CrossRefGoogle Scholar
  40. 40.
    Nobile F, Vergara C (2008) An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions. SIAM J Sci Comput 30:731–763zbMATHMathSciNetCrossRefGoogle Scholar
  41. 41.
    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 46:3–16zbMATHMathSciNetCrossRefGoogle Scholar
  42. 42.
    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 9:481–498CrossRefGoogle Scholar
  43. 43.
    Perego M, Veneziani A, Vergara C (2011) A variational approach for estimating the compliance of the cardiovascular tissue: an inverse fluid-structure interaction problem. SIAM J Sci Comput 33:1181–1211zbMATHMathSciNetCrossRefGoogle Scholar
  44. 44.
    Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid-structure interaction simulations. Finite Elem Anal Des 47:593–599MathSciNetCrossRefGoogle Scholar
  45. 45.
    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 19:171–225MathSciNetCrossRefGoogle Scholar
  46. 46.
    Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014) ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling. Math Models Methods Appl Sci 24:2437–2486zbMATHMathSciNetCrossRefGoogle Scholar
  47. 47.
    Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44zbMATHMathSciNetGoogle Scholar
  48. 48.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575zbMATHMathSciNetCrossRefGoogle Scholar
  49. 49.
    Tezduyar TE, Sathe S (2007) Modelling of fluid-structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54(6–8):855–900zbMATHMathSciNetCrossRefGoogle Scholar
  50. 50.
    Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid-structure interaction techniques. Comput Mech 48:247–267zbMATHMathSciNetCrossRefGoogle Scholar
  51. 51.
    Takizawa K, Tezduyar TE (2012) Space-time fluid-structure interaction methods. Math Models Methods Appl Sci 22:1230001MathSciNetCrossRefGoogle Scholar
  52. 52.
    Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2013) Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. Comput Mech 51:1061–1073zbMATHMathSciNetCrossRefGoogle Scholar
  53. 53.
    Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time interface-tracking with topology change (ST-TC). Comput Mech 54:955–971zbMATHMathSciNetCrossRefGoogle Scholar
  54. 54.
    Takizawa K, Torii R, Takagi H, Tezduyar TE, Xu XY (2014) Coronary arterial dynamics computation with medical-image-based time-dependent anatomical models and element-based zero-stress state estimates. Comput Mech 54:1047–1053zbMATHCrossRefGoogle Scholar
  55. 55.
    Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time fluid mechanics computation of heart valve models. Comput Mech 54:973–986zbMATHMathSciNetCrossRefGoogle Scholar
  56. 56.
    Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322zbMATHMathSciNetCrossRefGoogle Scholar
  57. 57.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37zbMATHMathSciNetCrossRefGoogle Scholar
  58. 58.
    Bazilevs Y, Hsu M-C, 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 22:1230002CrossRefGoogle Scholar
  59. 59.
    Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Øiseth O, Mathisen KM, Kostov N, McIntyre S (2014) Engineering analysis and design with ALE-VMS and Space-Time methods. Arch Comput Methods Eng 21:481–508MathSciNetCrossRefGoogle Scholar
  60. 60.
    Bazilevs Y, Takizawa K, Tezduyar TE, Hsu M-C, Kostov N, McIntyre S (2014) Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods. Arch Comput Methods Eng 21:359–398MathSciNetCrossRefGoogle Scholar
  61. 61.
    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 32:199–259zbMATHMathSciNetCrossRefGoogle Scholar
  62. 62.
    Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190:411–430zbMATHCrossRefGoogle Scholar
  63. 63.
    Hughes TJR, Mazzei L, Jansen KE (2000) Large eddy simulation and the variational multiscale method. Comput Vis Sci 3:47–59zbMATHCrossRefGoogle Scholar
  64. 64.
    Hughes TJR, Mazzei L, Oberai AA, Wray A (2001) The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence. Phys Fluids 13:505–512CrossRefGoogle Scholar
  65. 65.
    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, chap. 2. Wiley, HobokenGoogle Scholar
  66. 66.
    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 197:173–201zbMATHCrossRefGoogle Scholar
  67. 67.
    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 199:828–840zbMATHMathSciNetCrossRefGoogle Scholar
  68. 68.
    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 249–252:28–41MathSciNetCrossRefGoogle Scholar
  69. 69.
    Wriggers P (2006) Comput Contact Mech, 2nd edn. Springer, Berlin HeidelbergCrossRefGoogle Scholar
  70. 70.
    Laursen TA (2003) Computational contact and impact mechanics: fundamentals of modeling interfacial phenomena in nonlinear finite element analysis. Springer, Berlin HeidelbergCrossRefGoogle Scholar
  71. 71.
    Morganti S, Auricchio F, Benson DJ, Gambarin FI, Hartmann S, Hughes TJR, Reali A (2015) Patient-specific isogeometric structural analysis of aortic valve closure. Comput Methods Appl Mech Eng 284:508–520MathSciNetCrossRefGoogle Scholar
  72. 72.
    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 198:3534–3550zbMATHMathSciNetCrossRefGoogle Scholar
  73. 73.
    Esmaily-Moghadam M, Bazilevs Y, Hsia T-Y, Vignon-Clementel IE, MOCHA (2011) A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations. Comput Mech 48:277–291zbMATHMathSciNetCrossRefGoogle Scholar
  74. 74.
    Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–375zbMATHMathSciNetCrossRefGoogle Scholar
  75. 75.
    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 190:305–319zbMATHMathSciNetCrossRefGoogle Scholar
  76. 76.
    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 195:5743–5753zbMATHMathSciNetCrossRefGoogle Scholar
  77. 77.
    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 195:2002–2027zbMATHMathSciNetCrossRefGoogle Scholar
  78. 78.
    Tezduyar TE, Sathe S (2007) Modeling of fluid-structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54:855–900zbMATHMathSciNetCrossRefGoogle Scholar
  79. 79.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid-structure interaction: methods and applications. Wiley, ChichesterCrossRefGoogle Scholar
  80. 80.
    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– 1218zbMATHCrossRefGoogle Scholar
  81. 81.
    Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130zbMATHCrossRefGoogle Scholar
  82. 82.
    Akin JE, Tezduyar TE, Ungor M (2007) Computation of flow problems with the mixed interface-tracking/interface-capturing technique (MITICT). Comput Fluids 36:2–11zbMATHCrossRefGoogle Scholar
  83. 83.
    Cruchaga MA, Celentano DJ, Tezduyar TE (2007) A numerical model based on the mixed interface-tracking/interface-capturing technique (MITICT) for flows with fluid-solid and fluid-fluid interfaces. Int J Numer Methods Fluids 54:1021–1030zbMATHCrossRefGoogle Scholar
  84. 84.
    Akkerman I, Bazilevs Y, Benson DJ, Farthing MW, Kees CE (2011) Free-surface flow and fluid-object interaction modeling with emphasis on ship hydrodynamics. Journal of Applied Mechanics, accepted for publicationGoogle Scholar
  85. 85.
    Wick T (2014) Flapping and contact FSI computations with the fluid-solid interface-tracking/interface-capturing technique and mesh adaptivity. Comput Mech 53(1):29–43zbMATHMathSciNetCrossRefGoogle Scholar
  86. 86.
    Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10): 27–36CrossRefGoogle Scholar
  87. 87.
    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 119:73–94zbMATHCrossRefGoogle Scholar
  88. 88.
    Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid-structure interactions with large displacements. J Appl Mech 70:58–63zbMATHCrossRefGoogle Scholar
  89. 89.
    Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193:2019–2032zbMATHCrossRefGoogle Scholar
  90. 90.
    Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36: 12–26zbMATHMathSciNetCrossRefGoogle Scholar
  91. 91.
    Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng 196:4853–4862zbMATHMathSciNetCrossRefGoogle Scholar
  92. 92.
    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 199:780–790zbMATHMathSciNetCrossRefGoogle Scholar
  93. 93.
    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 50:499–511zbMATHMathSciNetCrossRefGoogle Scholar
  94. 94.
    Tong P, Fung Y-C (1976) The stress-strain relationship for the skin. J Biomech 9(10):649–657CrossRefGoogle Scholar
  95. 95.
    Fung YC (1993) Biomechanics: mechanical properties of living tissues, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  96. 96.
    Sun W, Sacks MS, Sellaro TL, Slaughter WS, Scott MJ (2003) Biaxial mechanical response of bioprosthetic heart valve biomaterials to high in-plane shear. J Biomech Eng 125(3):372–380CrossRefGoogle Scholar
  97. 97.
    Fan R, Sacks MS (2014) Simulation of planar soft tissues using a structural constitutive model: finite element implementation and validation. J Biomech 47(9):2043–2054CrossRefGoogle Scholar
  98. 98.
    Mirnajafi A, Raymer J, Scott MJ, Sacks MS (2005) The effects of collagen fiber orientation on the flexural properties of pericardial heterograft biomaterials. Biomaterials 26(7):795–804Google Scholar
  99. 99.
    Kim H, Chandran KB, Sacks MS, Lu J (2007) An experimentally derived stress resultant shell model for heart valve dynamic simulations. Ann Biomed Eng 35(1):30–44CrossRefGoogle Scholar
  100. 100.
    Li K, Sun W (2010) Simulated thin pericardial bioprosthetic valve leaflet deformation under static pressure-only loading conditions: implications for percutaneous valves. Ann Biomed Eng 38(8):2690–2701CrossRefGoogle Scholar
  101. 101.
    Burriesci G, Howard IC, Patterson EA (1999) Influence of anisotropy on the mechanical behaviour of bioprosthetic heart valves. J Med Eng Technol 23(6):203–215CrossRefGoogle Scholar
  102. 102.
    Huynh VL, Nguyen T, Lam HL, Guo XG, Kafesjian R (2003) Cloth-covered stents for tissue heart valves, US Patent 6,585,766Google Scholar
  103. 103.
    Piazza N, Bleiziffer S, Brockmann G, Hendrick R, Deutsch MA, Opitz A, Mazzitelli D, Tassani-Prell P, Schreiber C, Lange R (2011) Transcatheter aortic valve implantation for failing surgical aortic bioprosthetic valve. JACC 4(7):721–732CrossRefGoogle Scholar
  104. 104.
    Gao ZB, Pandya S, Hosein N, Sacks MS, Hwang NHC (2000) Bioprosthetic heart valve leaflet motion monitored by dual camera stereo photogrammetry. J Biomech 33(2):199–207CrossRefGoogle Scholar
  105. 105.
    Gao BZ, Pandya S, Arana C, Hwang NHC (2002) Bioprosthetic heart valve leaflet deformation monitored by double-pulse stereo photogrammetry. Ann Biomed Eng 30(1):11–18CrossRefGoogle Scholar
  106. 106.
    Iyengar AKS, Sugimoto H, Smith DB, Sacks MS (2001) Dynamic in vitro quantification of bioprosthetic heart valve leaflet motion using structured light projection. Ann Biomed Eng 29(11): 963–973CrossRefGoogle Scholar
  107. 107.
    Bellhouse BJ, Bellhouse FH (1968) Mechanism of closure of the aortic valve. Nature 217(5123):86–87CrossRefGoogle Scholar
  108. 108.
    Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New YorkzbMATHGoogle Scholar
  109. 109.
    Kenner T (1989) The measurement of blood density and its meaning. Basic Res Cardiol 84(2):111–124CrossRefGoogle Scholar
  110. 110.
    Rosencranz R, Bogen SA (2006) Clinical laboratory measurement of serum, plasma, and blood viscosity. Am J Clin Pathol 125: S78–S86Google Scholar
  111. 111.
    Yap CH, Saikrishnan N, Tamilselvan G, Yoganathan AP (2011) Experimental technique of measuring dynamic fluid shear stress on the aortic surface of the aortic valve leaflet. J Biomech Eng 133(6):061007CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ming-Chen Hsu
    • 1
    Email author
  • David Kamensky
    • 2
  • Fei Xu
    • 1
  • Josef Kiendl
    • 3
  • Chenglong Wang
    • 1
  • Michael C. H. Wu
    • 1
  • Joshua Mineroff
    • 1
  • Alessandro Reali
    • 3
  • Yuri Bazilevs
    • 4
  • Michael S. Sacks
    • 2
  1. 1.Department of Mechanical EngineeringIowa State UniversityAmesUSA
  2. 2.Center for Cardiovascular Simulation, Institute for Computational Engineering and SciencesThe University of Texas at AustinAustinUSA
  3. 3.Department of Civil Engineering and ArchitectureUniversity of PaviaPaviaItaly
  4. 4.Department of Structural EngineeringUniversity of CaliforniaLa JollaUSA

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