Computational Modeling of Heart Valves: Understanding and Predicting Disease

  • Ahmed A. Bakhaty
  • Ali Madani
  • Mohammad R. K. MofradEmail author


Computational methods offer a robust means of studying healthy and diseased heart valves. Simulations can shed light on the elusive function of heart valves and allow us to understand the underlying causes of heart valve disease in an effort to develop effective treatments. In comparison to experimental approaches, which either may not be representative in vitro or feasible in vivo, simulations assist in obtaining detailed information on the response of valves in a cost-effective manner.

In this chapter, we take a look at how computational methods have been used to study the varying types of heart valves. In particular, we focus on the modeling of diseased valves, and the simulation of associated therapies. We aim to highlight the work done to date in computationally modeling heart valves and emphasize the need for continued development of these models.


Heart valve Computational modeling Multi-scale Disease prediction 


  1. 1.
    Neumann D, Grbic S, Mansi T. Multi-modal pipeline for comprehensive validation of mitral valve geometry and functional computational models. Comput Model. 2014;15(12):1281–312.Google Scholar
  2. 2.
    Mofrad MRK, Kamm RD. Cellular mechanotransduction: diverse perspectives from molecules to tissues. Cambridge: Cambridge University Press; 2009.CrossRefGoogle Scholar
  3. 3.
    Taylor PM, et al. The cardiac valve interstitial cell. Int J Biochem Cell Biol. 2003;35(2):113–8.CrossRefGoogle Scholar
  4. 4.
    Liu AC, Joag VR, Gotlieb AI. The emerging role of valve interstitial cell phenotypes in regulating heart valve pathobiology. Am J Pathol. 2007;171:1407–18.PubMedPubMedCentralCrossRefGoogle Scholar
  5. 5.
    Holzapfel GA. Nonlinear solid mechanics, vol. 24. Chichester: Wiley; 2000.Google Scholar
  6. 6.
    Zienkiewicz OC, et al. The finite element method, vol. 3. London: McGraw-hill; 1977.Google Scholar
  7. 7.
    Sacks MS, Yoganathan AP. Heart valve function: a biomechanical perspective. Philos Trans R Soc B. 2007;362(1484):1369–91.CrossRefGoogle Scholar
  8. 8.
    Holzapfel GA, Gasser TC, Ogden RW. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elas Phys Sci Solids. 2000;61:1–9.CrossRefGoogle Scholar
  9. 9.
    Balzani D, et al. A polyconvex framework for soft biological tissues. Adjustment to experimental data. Int J Solids Struct. 2006;43(20):6052–70.CrossRefGoogle Scholar
  10. 10.
    Sun W, Sacks MS. Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues. Biomech Model Mechanobiol. 2005;4(2–3):190–9.PubMedCrossRefGoogle Scholar
  11. 11.
    Driessen NJB, et al. Computational analyses of mechanically induced collagen fiber remodeling in the aortic heart valve. J Biomech Eng. 2003;125(4):549–57.PubMedCrossRefGoogle Scholar
  12. 12.
    Saleeb AF, Kumar A, Thomas VS. 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. 2013;35(1):23–35.PubMedCrossRefGoogle Scholar
  13. 13.
    Rim Y, McPherson DD, Kim H. Effect of leaflet-to-chordae contact interaction on computational mitral valve evaluation. Biomed Eng Online. 2014;13(1):31.PubMedPubMedCentralCrossRefGoogle Scholar
  14. 14.
    Sotiropoulos F, et al. Computational techniques for biological fluids: from blood vessel scale to blood cells. In: Image-based computational modeling of the human circulatory and pulmonary systems. New York: Springer; 2011. p. 105–55.Google Scholar
  15. 15.
    Bluestein D, Li YM, Krukenkamp IB. Free emboli formation in the wake of bileaflet mechanical heart valves and the effects of implantation techniques. J Biomech. 2002;35(12):1533–40.PubMedCrossRefGoogle Scholar
  16. 16.
    Hellums JD, et al. Studies on the mechanisms of shear-induced platelet activation. In: Cerebral ischemia and hemorheology. New York: Springer; 1987. p. 80–9.CrossRefGoogle Scholar
  17. 17.
    Shahriari S, et al. Evaluation of shear stress accumulation on blood components in normal and dysfunctional bileaflet mechanical heart valves using smoothed particle hydrodynamics. J Biomech. 2012;45(15):2637–44.PubMedCrossRefGoogle Scholar
  18. 18.
    Min Yun B, et al. A numerical investigation of blood damage in the hinge area of aortic bileaflet mechanical heart valves during the leakage phase. Ann Biomed Eng. 2012;40(7):1468–85.PubMedCrossRefGoogle Scholar
  19. 19.
    Pozrikidis C. Numerical simulation of cell motion in tube flow. Ann Biomed Eng. 2005;33(2):165–78.PubMedCrossRefGoogle Scholar
  20. 20.
    Chandran KB. Role of computational simulations in heart valve dynamics and design of valvular prostheses. Cardiovasc Eng Technol. 2010;1(1):18–38.PubMedPubMedCentralCrossRefGoogle Scholar
  21. 21.
    Benson DJ. An efficient, accurate, simple ALE method for nonlinear finite element programs. Comput Methods Appl Mech Eng. 1989;72(3):305–50.CrossRefGoogle Scholar
  22. 22.
    Peskin CS. The immersed boundary method. Acta Numerica. 2002;11:479–517.CrossRefGoogle Scholar
  23. 23.
    Glowinski R, et al. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J Comput Phys. 2001;169(2):363–426.CrossRefGoogle Scholar
  24. 24.
    LeVeque RJ. Finite volume methods for hyperbolic problems, vol. 31. Cambridge: Cambridge university press; 2002.CrossRefGoogle Scholar
  25. 25.
    Vigmostad SC, et al. Fluid–structure interaction methods in biological flows with special emphasis on heart valve dynamics. Int J Numer Methods Biomed Eng. 2010;26(3–4):435–70.CrossRefGoogle Scholar
  26. 26.
    Cornell WD, et al. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J Am Chem Soc. 1995;117(19):5179–97.CrossRefGoogle Scholar
  27. 27.
    Brooks BR, et al. CHARMM: a program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem. 1983;4(2):187–217.CrossRefGoogle Scholar
  28. 28.
    Park S, Klein TE, Pande VS. Folding and misfolding of the collagen triple helix: Markov analysis of molecular dynamics simulations. Biophys J. 2007;93(12):4108–15.PubMedPubMedCentralCrossRefGoogle Scholar
  29. 29.
    Sundar Raman S, et al. A molecular dynamics analysis of ion pairs formed by lysine in collagen: Implication for collagen function and stability. J Mol Struct THEOCHEM. 2008;851:299–312.CrossRefGoogle Scholar
  30. 30.
    Sundar Raman S, et al. Role of aspartic acid in collagen structure and stability: A molecular dynamics investigation. J Phys Chem. 2006;110(41):20678–85.CrossRefGoogle Scholar
  31. 31.
    Salsas-Escat R, Stultz CM. The molecular mechanics of collagen degradation: Implications for human disease. Exp Mech. 2009;49(1):65–77.CrossRefGoogle Scholar
  32. 32.
    Madani A, Garakani K, Mofrad MRK. Molecular mechanics of Staphylococcus aureus adhesin, CNA, and the inhibition of bacterial adhesion by stretching collagen. PLoS One. 2017;12(6):e0179601.PubMedPubMedCentralCrossRefGoogle Scholar
  33. 33.
    Hutcheson JD, et al. Serotonin receptors and heart valve disease-It was meant 2B. Pharmacol Ther. 2011;132(2):146–57.PubMedPubMedCentralCrossRefGoogle Scholar
  34. 34.
    Varughese JF, Li Y. Molecular dynamics and docking studies on cardiac troponin C. J Biomol Struct Dyn. 2011;29(1):123–35.CrossRefGoogle Scholar
  35. 35.
    Silva JR, et al. A multiscale model linking ion-channel molecular dynamics and electrostatics to the cardiac action potential. Proc Natl Acad Sci. 2009;106(27):11102–6.PubMedCrossRefPubMedCentralGoogle Scholar
  36. 36.
    DeAzevedo ER, et al. The effects of anticalcification treatments and hydration on the molecular dynamics of bovine pericardium collagen as revealed by 13C solid-state NMR. Magn Reson Chem. 2010;48(9):704–11.PubMedCrossRefPubMedCentralGoogle Scholar
  37. 37.
    Stella JA, et al. Tissue-to-cellular deformation coupling in cell-microintegrated elastomeric scaffolds. In: IUTAM Symposium on cellular, molecular and tissue mechanics. New York: Springer; 2010. p. 81–9.CrossRefGoogle Scholar
  38. 38.
    David Merryman W, et al. Viscoelastic properties of the aortic valve interstitial cell. J Biomech Eng. 2009;131(4):041005.PubMedCrossRefPubMedCentralGoogle Scholar
  39. 39.
    Liu H, Yu S, Simmons CA. Determination of local and global elastic moduli of valve interstitial cells cultured on soft substrates. J Biomech. 2013;46(11):1967–71.PubMedCrossRefPubMedCentralGoogle Scholar
  40. 40.
    Zeng X, Li S. Multiscale modeling and simulation of soft adhesion and contact of stem cells. J Mech Behav Biomed Mater. 2011;4(2):180–9.PubMedCrossRefPubMedCentralGoogle Scholar
  41. 41.
    Unnikrishnan GU, Unnikrishnan VU, Reddy JN. Constitutive material modeling of cell: a micromechanics approach. J Biomech Eng. 2007;129(3):315–23.PubMedCrossRefPubMedCentralGoogle Scholar
  42. 42.
    Huang H-YS, Liao J, Sacks MS. In-situ deformation of the aortic valve interstitial cell nucleus under diastolic loading. J Biomech Eng. 2007;129:880–9.PubMedCrossRefPubMedCentralGoogle Scholar
  43. 43.
    Huang S, Huang H-YS. Virtual experiments of heart valve tissues. Conf Proc IEEE Eng Med Biol Soc. 2012;2012:6645–8.PubMedPubMedCentralGoogle Scholar
  44. 44.
    Huang S, Huang H-YS. Virtualisation of stress distribution in heart valve tissue. Comput Methods Biomech Biomed Engin. 2014;17(15):1696–704.PubMedCrossRefPubMedCentralGoogle Scholar
  45. 45.
    Kouznetsova VG. Computational homogenization for the multi-scale analysis of multi-phase materials. PhD thesis. 2002.Google Scholar
  46. 46.
    Bakhaty AA, Govdindjee S and Mofrad MRK. Coupled tissue and cellular multiscale analysis of aortic valve tissue. 2016.Google Scholar
  47. 47.
    Weinberg EJ, Shahmirzadi D, Mofrad MRK. On the multiscale modeling of heart valve biomechanics in health and disease. Biomech Model Mechanobiol. 2010;9(4):373–87.PubMedCrossRefPubMedCentralGoogle Scholar
  48. 48.
    Ron S, Abdulla T, Schleich J-M. Progress with multiscale systems. Meas Control. 2011;44(6):180–5.CrossRefGoogle Scholar
  49. 49.
    Alan SG, et al. Heart disease and stroke statistics–2014 update: a report from the American Heart Association. Circulation. 2014;129(3):e28–e292.Google Scholar
  50. 50.
    Billiar KL, Sacks MS. Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp – part I: experimental results. J Biomech Eng. 2000;122(1):23–30.PubMedPubMedCentralCrossRefGoogle Scholar
  51. 51.
    Glaire Gloeckner D, Bihir KL, Sacks MS. Effects of mechanical fatigue on the bending properties of the porcine bioprosthetic heart valve. ASAIO J. 1999;45(1):59–63.CrossRefGoogle Scholar
  52. 52.
    Buchanan RM, Sacks MS. Interlayer micromechanics of the aortic heart valve leaflet. Biomech Model Mechanobiol. 2014;13(4):813–26.PubMedPubMedCentralCrossRefGoogle Scholar
  53. 53.
    Haj-Ali R, et al. A general three-dimensional parametric geometry of the native aortic valve and root for biomechanical modeling. J Biomech. Sept. 2012;45(14):2392–7.PubMedCrossRefPubMedCentralGoogle Scholar
  54. 54.
    Thubrikar MJ. The aortic valve. Boca Raton: CRC press; 1989.Google Scholar
  55. 55.
    De Hart J, et al. A two-dimensional fluid-structure interaction model of the aortic value. J Biomech. 2000;33:1079–88.PubMedCrossRefPubMedCentralGoogle Scholar
  56. 56.
    Weinberg EJ, Mofrad MRK. Transient, three-dimensional, multiscale simulations of the human aortic valve. Cardiovasc Eng. 2007;7(4):140–55.PubMedCrossRefPubMedCentralGoogle Scholar
  57. 57.
    Bakhaty AA, Mofrad MRK. Coupled Simulation of Heart Valves: Applications to Clinical Practice. Ann Biomed Eng. 2015;43(7):1626–39.PubMedCrossRefPubMedCentralGoogle Scholar
  58. 58.
    Garcia D, et al. Impairment of coronary flow reserve in aortic stenosis. J Appl Physiol. 2009;106(1):113–21.PubMedCrossRefPubMedCentralGoogle Scholar
  59. 59.
    Weinberg EJ, Schoen FJ, Mofrad MRK. A computational model of aging and calcification in the aortic heart valve. PLoS One. 2009;4(6):e5960.PubMedPubMedCentralCrossRefGoogle Scholar
  60. 60.
    Van Loon R. Towards computational modelling of aortic stenosis. Int J Numer Methods Biomed Eng. 2010;26(3–4):405–20.CrossRefGoogle Scholar
  61. 61.
    Maleki H, et al. A metric for the stiffness of calcified aortic valves using a combined computational and experimental approach. Med Biol Eng Comput. 2014;52(1):1–8.PubMedCrossRefGoogle Scholar
  62. 62.
    David Merryman W. Mechano-potential etiologies of aortic valve disease. J Biomech. 2010;43(1):87–92.PubMedCrossRefGoogle Scholar
  63. 63.
    Li C, Xu S, Gotlieb AI. The progression of calcific aortic valve disease through injury, cell dysfunction, and disruptive biologic and physical force feedback loops. Cardiovasc Pathol. 2013;22(1):1–8.PubMedCrossRefGoogle Scholar
  64. 64.
    Ateshian GA, Ricken T. Multigenerational interstitial growth of biological tissues. Biomech Model Mechanobiol. 2010;9(6):689–702.PubMedPubMedCentralCrossRefGoogle Scholar
  65. 65.
    Fedak PWM, et al. Clinical and pathophysiological implications of a bicuspid aortic valve. Circulation. 2002;106(8):900–4.PubMedPubMedCentralCrossRefGoogle Scholar
  66. 66.
    Viscardi F, et al. Comparative finite element model analysis of ascending aortic flow in bicuspid and tricuspid aortic valve. Artif Organs. 2010;34(12):1114–20.PubMedCrossRefGoogle Scholar
  67. 67.
    Marom G, et al. Fully coupled fluid-structure interaction model of congenital bicuspid aortic valves: effect of asymmetry on hemodynamics. Med Biol Eng Comput. 2013;51(8):839–48.PubMedCrossRefPubMedCentralGoogle Scholar
  68. 68.
    Katayama S, et al. Bicuspid aortic valves undergo excessive strain during opening: a simulation study. J Thorac Cardiovasc Surg. June 2013;145(6):1570–6.PubMedCrossRefPubMedCentralGoogle Scholar
  69. 69.
    Weinberg EJ, Kaazempur Mofrad MR. A multiscale computational comparison of the bicuspid and tricuspid aortic valves in relation to calcific aortic stenosis. J Biomech. 2008;41(16):3482–7.PubMedCrossRefPubMedCentralGoogle Scholar
  70. 70.
    Atkins SK, et al. Bicuspid aortic valve hemodynamics induces abnormal medial remodeling in the convexity of porcine ascending aortas. Biomech Model Mechanobiol. 2014;13(6):1209–25.PubMedCrossRefGoogle Scholar
  71. 71.
    Wang Q, Sirois E, Sun W. Patient-specific modeling of biomechanical interaction in transcatheter aortic valve deployment. J Biomech. 2012;45(11):1965–71.PubMedPubMedCentralCrossRefGoogle Scholar
  72. 72.
    Genereux P, et al. Clinical outcomes after transcatheter aortic valve replacement using valve academic research consortium definitions: a weighted meta-analysis of 3,519 patients from 16 studies. J Am Coll Cardiol. 2012;59(25):2317–26.PubMedCrossRefGoogle Scholar
  73. 73.
    Auricchio F, et al. A computational tool to support pre-operative planning of stentless aortic valve implant. Med Eng Phys. 2011;33(10):1183–92.PubMedCrossRefGoogle Scholar
  74. 74.
    Auricchio F, et al. Patient-specific simulation of a stentless aortic valve implant: the impact of fibres on leaflet performance. Comput Methods Biomech Biomed Engin. 2014b;17(3):277–85.PubMedCrossRefGoogle Scholar
  75. 75.
    Auricchio F, et al. Simulation of transcatheter aortic valve implantation: a patient-specific finite element approach. Comput Methods Biomech Biomed Engin. 2014a;17(12):1347–57.PubMedCrossRefGoogle Scholar
  76. 76.
    Labrosse MR, et al. Modeling leaflet correction techniques in aortic valve repair: A finite element study. J Biomech. 2011;44(12):2292–8.PubMedCrossRefGoogle Scholar
  77. 77.
    Boodhwani M, et al. Repair of aortic valve cusp prolapse. Multimed Man Cardiothorac Surg. 2009;2009(702):mmcts.2008.003806.PubMedGoogle Scholar
  78. 78.
    Kunzelman KS, Cochran R. Stress/strain characteristics of porcine mitral valve tissue: parallel versus perpendicular collagen orientation. J Card Surg. 1992;7(1):71–8.PubMedPubMedCentralCrossRefGoogle Scholar
  79. 79.
    Kunzelman KS, et al. Finite element analysis of the mitral valve. J Heart Valve Dis. 1993;2(3):326–40.PubMedPubMedCentralGoogle Scholar
  80. 80.
    Kunzelman K, et al. Replacement of mitral valve posterior chordae tendineae with expanded polytetrafluoroethylene suture: a finite element study. J Card Surg. 1996;11(2):136–45.PubMedCrossRefGoogle Scholar
  81. 81.
    Kunzelman KS, Reimink MS, Cochran RP. Flexible versus rigid ring annuloplasty for mitral valve annular dilatation: a finite element model. J Heart Valve Dis. 1998a;7(1):108–16.PubMedGoogle Scholar
  82. 82.
    Kunzelman KS, Quick DW, Cochran RP. Altered collagen concentration in mitral valve leaflets: biochemical and finite element analysis. Ann Thorac Surg. 1998b;66(6):S198–205.PubMedCrossRefGoogle Scholar
  83. 83.
    Kunzelman KS, Einstein DR, Cochran RP. Fluid-structure interaction models of the mitral valve: function in normal and pathological states. Philos Trans R Soc Lond Ser B Biol Sci. 2007;362(1484):1393–406.CrossRefGoogle Scholar
  84. 84.
    Prot V, Skallerud B. Nonlinear solid finite element analysis of mitral valves with heterogeneous leaflet layers. Comput Mech. 2008;43(3):353–68.CrossRefGoogle Scholar
  85. 85.
    Skallerud B, Prot V, Nordrum IS. Modeling active muscle contraction in mitral valve leaflets during systole: a first approach. Biomech Model Mechanobiol. 2011;10(1):11–26.PubMedCrossRefGoogle Scholar
  86. 86.
    Hunter PJ, Nash MP, Sands GB. Computational electromechanics of the heart. Comput Biol Heart. 1997;12:347–407.Google Scholar
  87. 87.
    Rachev A, Hayashi K. Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries. Ann Biomed Eng. 1999;27(4):459–68.PubMedCrossRefGoogle Scholar
  88. 88.
    Einstein DR and Del Pin F. Int. J. 2010;17(6):950–5.Google Scholar
  89. 89.
    Avanzini A. A computational procedure for prediction of structural effects of edge-to-edge repair on mitral valve. J Biomech Eng. 2008;130(3):031015.PubMedCrossRefGoogle Scholar
  90. 90.
    Pham T, Sun W. Material properties of aged human mitral valve leaflets. J Biomed Mater Res A. 2014;102(8):2692–703.PubMedPubMedCentralCrossRefGoogle Scholar
  91. 91.
    Lee C-H, et al. An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment. J Biomech. 2014;47(9):2055–63.PubMedCrossRefGoogle Scholar
  92. 92.
    Tang D, et al. Two-layer passive/active anisotropic FSI models with fiber orientation: MRI-based patient-specific modeling of right ventricular response to pulmonary valve insertion surgery. Mol Cell Biomech. 2007;4(3):159–76.PubMedGoogle Scholar
  93. 93.
    Mansi T, et al. Virtual pulmonary valve replacement interventions with a personalised cardiac electromechanical model. In: Recent Advances in the 3D Physiological Human. New York: Springer; 2009. p. 75–90.CrossRefGoogle Scholar
  94. 94.
    Wafae N, et al. Anatomical study of the human tricuspid valve. Surg Radiol Anat. 1990;12(1):37–41.PubMedCrossRefGoogle Scholar
  95. 95.
    Dumont K, et al. Comparison of the hemodynamic and thrombogenic performance of two bileaflet mechanical heart valves using a CFD/FSI model. J Biomech Eng. 2007;129(4):558–65.PubMedCrossRefGoogle Scholar
  96. 96.
    Borazjani I, Ge L, Sotiropoulos F. High-resolution fluid-structure interaction simulations of flow through a bi-leaflet mechanical heart valve in an anatomic aorta. Ann Biomed Eng. 2010;38(2):326–44.PubMedCrossRefGoogle Scholar
  97. 97.
    Choi YJ, Vedula V, Mittal R. Computational study of the dynamics of a bileaflet mechanical heart valve in the mitral position. Ann Biomed Eng. 2014;42(8):1668–80.PubMedCrossRefGoogle Scholar
  98. 98.
    Sotiropoulos F, Borazjani I. A review of state-of-the-art numerical meth- ods for simulating flow through mechanical heart valves. Med Biol Eng Comput. 2009;47(3):245–56.PubMedPubMedCentralCrossRefGoogle Scholar
  99. 99.
    Guivier-Curien C, Deplano V, Bertrand E. Validation of a numerical 3-D fluid-structure interaction model for a prosthetic valve based on experimental PIV measurements. Med Eng Phys. 2009;31(8):986–93.PubMedCrossRefGoogle Scholar
  100. 100.
    Nobili M, et al. Numerical simulation of the dynamics of a bileaflet prosthetic heart valve using a fluid-structure interaction approach. J Biomech. 2008;41(11):2539–50.PubMedCrossRefGoogle Scholar
  101. 101.
    De Hart J, et al. A computational fluid-structure interaction analysis of a fiber- reinforced stentless aortic valve. J Biomech. 2003;36(5):699–712.PubMedCrossRefGoogle Scholar
  102. 102.
    Haj-Ali R. Structural simulations of prosthetic tri-leaflet aortic heart valves. J Biomech. 2008;41:1510.PubMedCrossRefGoogle Scholar
  103. 103.
    Sirois E, Sun W. Computational evaluation of platelet activation induced by a bioprosthetic heart valve. Artif Organs. 2010;35(2):157.PubMedGoogle Scholar
  104. 104.
    Martin C, Sun W. Simulation of long-term fatigue damage in bioprosthetic heart valves: effects of leaflet and stent elastic properties. Biomech Model Mechanobiol. 2014;13(4):759–70.PubMedCrossRefGoogle Scholar
  105. 105.
    Kim H, et al. Dynamic simulation of bioprosthetic heart valves using a stress resultant shell model. Ann Biomed Eng. 2008;36:262–75.PubMedCrossRefGoogle Scholar
  106. 106.
    Tzamtzis S, et al. Numerical analysis of the radial force produced by the Medtronic- CoreValve and Edwards-SAPIEN after transcatheter aortic valve implantation (TAVI). Med Eng Phys. 2013;35(1):125–30.PubMedCrossRefGoogle Scholar
  107. 107.
    Sun W, Li K, Sirois E. Simulated elliptical bioprosthetic valve deformation: implications for asymmetric transcatheter valve deployment. J Biomech. 2010;43(16):3085–90.PubMedCrossRefGoogle Scholar
  108. 108.
    Wang L, et al. Computational simulation of oxygen diffusion in aortic valve leaflet for tissue engineering applications. J Heart Valve Dis. 2008;17(6):700.PubMedGoogle Scholar
  109. 109.
    Driessen NJB, et al. Modeling the mechanics of tissue-engineered human heart valve leaflets. J Biomech. 2007;40(2):325–34.PubMedCrossRefGoogle Scholar
  110. 110.
    Hasan A, et al. Biomechanical properties of native and tissue engineered heart valve constructs. J Biomech. 2014;47(9):1949–63.CrossRefGoogle Scholar
  111. 111.
    Nørgaard BL, et al. Diagnostic performance of noninvasive fractional flow reserve derived from coronary computed tomography angiography in suspected coronary artery disease: the NXT trial (Analysis of Coronary Blood Flow Using CT Angiography: Next Steps). J Am Coll Cardiol. 2014;63(12):1145–55.PubMedCrossRefGoogle Scholar
  112. 112.
    Xu C, et al. A novel approach to in vivo mitral valve stress analysis. Am J Phys Heart Circ Phys. 2010;299(6):H1790–4.Google Scholar
  113. 113.
    Luo Z, et al. Intra-operative 2-D ultrasound and dynamic 3-D aortic model registration for magnetic navigation of transcatheter aortic valve implantation. IEEE Trans Med Imaging. 2013;32(11):2152–65.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ahmed A. Bakhaty
    • 1
    • 2
    • 3
  • Ali Madani
    • 4
  • Mohammad R. K. Mofrad
    • 5
    Email author
  1. 1.Department of Civil and Environmental EngineeringUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of Electrical Engineering and Computer ScienceUniversity of CaliforniaBerkeleyUSA
  3. 3.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  4. 4.Department of Applied Science and Technology and Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA
  5. 5.Department of Mechanical and BioengineeringUniversity of CaliforniaBerkeleyUSA

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