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Emerging Trends in Heart Valve Engineering: Part IV. Computational Modeling and Experimental Studies

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Abstract

In this final portion of an extensive review of heart valve engineering, we focus on the computational methods and experimental studies related to heart valves. The discussion begins with a thorough review of computational modeling and the governing equations of fluid and structural interaction. We then move onto multiscale and disease specific modeling. Finally, advanced methods related to in vitro testing of the heart valves are reviewed. This section of the review series is intended to illustrate application of computational methods and experimental studies and their interrelation for studying heart valves.

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References

  1. Affeld, K., P. Walker, and K. Schichl. The use of image processing in the investigation of artificial heart valve flow. ASAIO J. 35:294–297, 1989.

    Article  CAS  Google Scholar 

  2. Agathos, E. A., M. Shen, M. Katsiboulas, P. Koutsoukos, and G. Gloustianou. In vivo calcification of glutaraldehyde-fixed cardiac valve and pericardium of phoca groenlandica. ASAIO J. 57(328–332):3, 2011. doi:10.1097/MAT.1090b1013e3182179a3182189.

    Google Scholar 

  3. Alavi, S. H., V. Ruiz, T. Krasieva, E. Botvinick, and A. Kheradvar. Characterizing the collagen fiber orientation in pericardial leaflets under mechanical loading conditions. Ann. Biomed. Eng. 41:547–561, 2013.

    Article  PubMed  Google Scholar 

  4. Alavi, S. H., A. Sinha, E. Steward, J. C. Milliken, and A. Kheradvar. Load-dependent extracellular matrix organization in atrioventricular heart valves: differences and similarities. Am. J. Physiol. Heart Circ. Physiol. 309(2):H276–H284, 2015. doi:10.1152/ajpheart.00164.2015.

    Article  CAS  PubMed  Google Scholar 

  5. Alemu, Y., and D. Bluestein. Flow-induced platelet activation and damage accumulation in a mechanical heart valve: numerical studies. Artif. Organs 31:677–688, 2007.

    Article  PubMed  Google Scholar 

  6. Amatya, D., D. Troolin, and E. Longmire. 3d3c velocity measurements downstream of artificial heart valves. Methods 7:9, 2009.

    Google Scholar 

  7. Antman, S. S. Nonlinear Problems of Elasticity, Volume 107 of Applied Mathematical Sciences. New York: Springer-Verlag, 2005.

  8. Arjunon, S., P. H. Ardana, N. Saikrishnan, S. Madhani, B. Foster, A. Glezer, and A. P. Yoganathan. Design of a pulsatile flow facility to evaluate thrombogenic potential of implantable cardiac devices. J. Biomech. Eng. 137:045001, 2015.

    Article  PubMed  Google Scholar 

  9. Azadani, A. N., S. Chitsaz, P. B. Matthews, N. Jaussaud, J. Leung, T. Tsinman, L. Ge, and E. E. Tseng. Comparison of mechanical properties of human ascending aorta and aortic sinuses. Ann. Thorac. Surg. 93:87–94, 2012.

    Article  PubMed  Google Scholar 

  10. Bellhouse, B. J., and F. H. Bellhouse. Fluid mechanics of the mitral valve. Nature 224:615–616, 1969.

    Article  CAS  PubMed  Google Scholar 

  11. Belytschko, T., W. K. Liu, B. Moran, and K. Elkhodary. Nonlinear Finite Elements for Continua and Structures. New York: Wiley, 2013.

    Google Scholar 

  12. Bernacca, G. M., A. C. Fisher, T. G. Mackay, and D. J. Wheatley. A dynamic in vitro method for studying bioprosthetic heart valve calcification. J. Mater. Sci. Mater. Med. 3:293–298, 1992.

    Article  CAS  Google Scholar 

  13. Billiar, K. L., and M. S. Sacks. Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp—part I: experimental results. J. Biomech. Eng. 122:23–30, 1999.

    Article  Google Scholar 

  14. Billiar, K. L., and M. S. Sacks. Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp—part I: experimental results. J. Biomech. Eng. 122:23–30, 2000.

    Article  CAS  PubMed  Google Scholar 

  15. Billiar, K. L., and M. S. Sacks. Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: Part II—a structural constitutive model. J. Biomech. Eng. 122:327–335, 2000.

    Article  CAS  PubMed  Google Scholar 

  16. Bischoff, J. E., E. A. Arruda, and K. Grosh. A microstructurally based orthotropic hyperelastic constitutive law. J. Appl. Mech. 69:570–579, 2002.

    Article  CAS  Google Scholar 

  17. Bluestein, D., E. Rambod, and M. Gharib. Vortex shedding as a mechanism for free emboli formation in mechanical heart valves. Trans. Am. Soc. Mech. Eng. J. Biomech. Eng. 122:125–134, 2000.

    CAS  Google Scholar 

  18. Boffi, D., L. Gastaldi, L. Heltai, and C. S. Peskin. On the hyper-elastic formulation of the immersed boundary method. Int. J. Numer. Methods Biomed. Eng. 197:2210–2231, 2008.

    Google Scholar 

  19. Boloori_Zadeh, P., S. C. Corbett, and H. Nayeb-Hashemi. Effects of fluid flow shear rate and surface roughness on the calcification of polymeric heart valve leaflet. Mater. Sci. Eng. C. 33:2770–2775, 2013.

    Article  CAS  Google Scholar 

  20. Bonet, J., and R. Wood. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge: Cambridge University Press, 1997.

    Google Scholar 

  21. Brücker, C. Dual-camera DPIV for flow studies past artificial heart valves. Exp. Fluids 22:496–506, 1997.

    Article  Google Scholar 

  22. Brust, M., C. Schaefer, R. Doerr, L. Pan, M. Garcia, P. Arratia, and C. Wagner. Rheology of human blood plasma: viscoelastic versus newtonian behavior. Phys. Rev. Lett. 110:078305, 2013.

    Article  CAS  PubMed  Google Scholar 

  23. Burdon, T. A., D. C. Miller, P. E. Oyer, R. S. Mitchell, E. B. Stinson, V. A. Starnes, and N. E. Shumway. Durability of porcine valves at fifteen years in a representative north american patient population. J Thorac Cardiovasc Surg. 103:238–251, 1992; (discussion 251-232).

    CAS  PubMed  Google Scholar 

  24. Cacciola, G., G. W. M. Peters, and F. P. T. Baaijens. A synthetic fiber-reinforced stentless heart valve. J. Biomech. 33:653–658, 2000.

    Article  CAS  PubMed  Google Scholar 

  25. Campo-Deaño, L., R. P. Dullens, D. G. Aarts, F. T. Pinho, and M. S. Oliveira. Viscoelasticity of blood and viscoelastic blood analogues for use in polydymethylsiloxane in vitro models of the circulatory system. Biomicrofluidics. 7:034102, 2013.

    Article  PubMed Central  CAS  Google Scholar 

  26. Castellini, P., M. Pinotti, and L. Scalise. Particle image velocimetry for flow analysis in longitudinal planes across a mechanical artificial heart valve. Artif. Organs 28:507–513, 2004.

    Article  PubMed  Google Scholar 

  27. Chan, V., A. Kulik, A. Tran, P. Hendry, R. Masters, T. G. Mesana, and M. Ruel. Long-term clinical and hemodynamic performance of the hancock ii versus the perimount aortic bioprostheses. Circulation 122:S10–S16, 2010.

    Article  PubMed  Google Scholar 

  28. Chandra, S., N. M. Rajamannan, and P. Sucosky. Computational assessment of bicuspid aortic valve wall-shear stress: implications for calcific aortic valve disease. Biomech. Model. Mechanobiol. 11:1085–1096, 2012.

    Article  PubMed  Google Scholar 

  29. Chandran, K., R. Fatemi, L. Hiratzka, and C. Harris. Effect of wedging on the flow characteristics past tilting disc aortic valve prosthesis. J. Biomech. 19:181–186, 1986.

    Article  CAS  PubMed  Google Scholar 

  30. Cheng, R., Y. G. Lai, and K. B. Chandran. Three-dimensional fluid-structure interaction simulation of bileaflet mechanical heart valve flow dynamics. Ann. Biomed. Eng. 32:1471–1483, 2004.

    Article  PubMed  PubMed Central  Google Scholar 

  31. Chikwe, J., and F. Filsoufi. Durability of tissue valves. Semin. Thorac. Cardiovasc. Surg. 23:18–23, 2011.

    Article  PubMed  Google Scholar 

  32. Dabagh, M., M. J. Abdekhodaie, and M. T. Khorasani. Effects of polydimethylsiloxane grafting on the calcification, physical properties, and biocompatibility of polyurethane in a heart valve. J. Appl. Polym. Sci. 98:758–766, 2005.

    Article  CAS  Google Scholar 

  33. Daily, B. B., T. W. Pettitt, S. P. Sutera, and W. S. Pierce. Pierce-donachy pediatric vad: progress in development. Ann. Thorac. Surg. 61:437–443, 1996.

    Article  CAS  PubMed  Google Scholar 

  34. Dalmau, M. J., J. M. González-Santos, J. A. Blázquez, J. A. Sastre, J. López-Rodríguez, M. Bueno, M. Castaño, and A. Arribas. Hemodynamic performance of the medtronic mosaic and perimount magna aortic bioprostheses: five-year results of a prospectively randomized study. Eur. J. Cardiothorac. Surg. 39:844–852, 2011.

    Article  PubMed  Google Scholar 

  35. Dasi, L., L. Ge, H. Simon, F. Sotiropoulos, and A. Yoganathan. Vorticity dynamics of a bileaflet mechanical heart valve in an axisymmetric aorta. Phys. Fluids. (1994-present) 19:067105, 2007.

    Article  CAS  Google Scholar 

  36. David, T. E., S. Armstrong, and M. Maganti. Hancock II bioprosthesis for aortic valve replacement: the gold standard of bioprosthetic valves durability? Ann. Thorac. Surg. 90:775–781, 2010.

    Article  PubMed  Google Scholar 

  37. De Hart, J., F. P. T. Baaijens, G. W. M. Peters, and P. J. G. Schreurs. A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve. J. Biomech. 36:699–712, 2003.

    Article  PubMed  Google Scholar 

  38. De Hart, J., G. W. Peters, P. J. Schreurs, and F. P. Baaijens. A two-dimensional fluid–structure interaction model of the aortic value. J. Biomech. 33:1079–1088, 2000.

    Article  PubMed  Google Scholar 

  39. De Hart, J., G. Peters, P. Schreurs, and F. Baaijens. A three-dimensional computational analysis of fluid–structure interaction in the aortic valve. J. Biomech. 36:103–112, 2003.

    Article  PubMed  Google Scholar 

  40. De Hart, J., G. Peters, P. Schreurs, and F. Baaijens. Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole. J. Biomech. 37:303–311, 2004.

    Article  PubMed  Google Scholar 

  41. Donea, J., S. Giuliani, and J. Halleux. An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions. Comput. Methods Appl. Mech. Eng. 33:689–723, 1982.

    Article  Google Scholar 

  42. Driessen, N. J. B., R. A. Boerboom, J. M. Huyghe, C. V. C. Bouten, and F. P. T. Baaijens. Computational analyses of mechanically induced collagen fiber remodeling in the aortic heart valve. J. Biomech. Eng. 125:549–557, 2003.

    Article  PubMed  Google Scholar 

  43. Fai, T. G., B. E. Griffith, Y. Mori, and C. S. Peskin. Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers I: numerical method and results. SIAM J. Sci. Comput. 35:B1132–B1161, 2013.

    Article  Google Scholar 

  44. Fai, T. G., B. E. Griffith, Y. Mori, and C. S. Peskin. Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers II: theory. SIAM J. Sci. Comput. 36:B589–B621, 2014.

    Article  Google Scholar 

  45. Falahatpisheh, A., and A. Kheradvar. High-speed particle image velocimetry to assess cardiac fluid dynamics in vitro: from performance to validation. Eur. J. Mech. B. Fluids 35:2–8, 2012.

    Article  Google Scholar 

  46. Falahatpisheh, A., G. Pedrizzetti, and A. Kheradvar. Three-dimensional reconstruction of cardiac flows based on multi-planar velocity fields. Exp. Fluids 55:1–15, 2014.

    Article  CAS  Google Scholar 

  47. Faludi, R., M. Szulik, J. D’hooge, P. Herijgers, F. Rademakers, G. Pedrizzetti, and J.-U. Voigt. Left ventricular flow patterns in healthy subjects and patients with prosthetic mitral valves: an in vivo study using echocardiographic particle image velocimetry. J Thorac Cardiovasc Surg. 139:1501–1510, 2010.

    Article  PubMed  Google Scholar 

  48. Fann, J. I., D. C. Miller, K. A. Moore, R. S. Mitchell, P. E. Oyer, E. B. Stinson, R. C. Robbins, B. A. Reitz, and N. E. Shumway. Twenty-year clinical experience with porcine bioprostheses. Ann. Thorac. Surg. 62:1301–1312, 1996.

    Article  CAS  PubMed  Google Scholar 

  49. Flamini V, DeAnda A, Griffith BE. Immersed boundary-finite element model of fluid-structure interaction in the aortic root. arXiv preprint arXiv:1501.02287. 2015.

  50. Gao, H., X. Ma, N. Qi, C. Berry, B. E. Griffith, and X. Luo. A finite strain nonlinear human mitral valve model with fluid-structure interaction. Int. J. Numer. Methods Biomed. Eng. 30:1597–1613, 2014.

    Article  Google Scholar 

  51. Gao, H., H. Wang, C. Berry, X. Luo, and B. E. Griffith. Quasi-static image-based immersed boundary-finite element model of left ventricle under diastolic loading. Int. J. Numer. Methods Biomed. Eng. 30:1199–1222, 2014.

    Article  Google Scholar 

  52. Ge, L., L. P. Dasi, F. Sotiropoulos, and A. P. Yoganathan. Characterization of hemodynamic forces induced by mechanical heart valves: reynolds vs. viscous stresses. Ann. Biomed. Eng. 36:276–297, 2008.

    Article  PubMed  Google Scholar 

  53. Ge, L., H.-L. Leo, F. Sotiropoulos, and A. P. Yoganathan. Flow in a mechanical bileaflet heart valve at laminar and near-peak systole flow rates: Cfd simulations and experiments. J. Biomech. Eng. 127:782–797, 2005.

    Article  PubMed  Google Scholar 

  54. Ge, L., and F. Sotiropoulos. A numerical method for solving the 3d unsteady incompressible navier–stokes equations in curvilinear domains with complex immersed boundaries. J. Comput. Phys. 225:1782–1809, 2007.

    Article  PubMed  PubMed Central  Google Scholar 

  55. Ghista, D., and A. Rao. Mitral-valve mechanics—stress/strain characteristics of excised leaflets, analysis of its functional mechanics and its medical application. Med. Biol. Eng. 11:691–702, 1973.

    Article  CAS  PubMed  Google Scholar 

  56. Glasmacher B, Reul H, Rau G, Erckes C, Weiland J. In vitro investigation of the calcification behaviour of polyurethane biomaterials. Polyurethanes Biomed. Eng. II:151–168, 1986.

  57. Glowinski, R., T.-W. Pan, T. I. Hesla, and D. D. Joseph. A distributed lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiph. Flow 25:755–794, 1999.

    Article  CAS  Google Scholar 

  58. Griffith, B. E. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions. Int. J. Numer. Methods Biomed. Eng. 28:317–345, 2012.

    Article  Google Scholar 

  59. Griffith, B. E., R. D. Hornung, D. M. McQueen, and C. S. Peskin. Parallel and adaptive simulation of cardiac fluid dynamics. In: Advanced computational infrastructures for parallel and distributed applications, edited by M. Parashar, X. Li. pp. 105–130. 2010.

  60. Griffith, B. E., V. Flamini, A. DeAnda, and L. Scotten. Simulating the dynamics of an aortic valve prosthesis in a pulse duplicator: numerical methods and initial experience. J. Med. Devices 7:040912, 2013.

    Article  Google Scholar 

  61. Griffith, B. E., R. D. Hornung, D. M. McQueen, and C. S. Peskin. An adaptive, formally second order accurate version of the immersed boundary method. J. Comput. Phys. 223:10–49, 2007.

    Article  Google Scholar 

  62. Griffith, B. E., X. Luo, D. M. McQueen, and C. S. Peskin. Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method. Int. J. Appl. Mech. 1:137–177, 2009.

    Article  Google Scholar 

  63. Grigioni, M., C. Daniele, G. D’Avenio, U. Morbiducci, C. Del Gaudio, M. Abbate, and D. Di Meo. Innovative technologies for the assessment of cardiovascular medical devices: state-of-the-art techniques for artificial heart valve testing. Expert Rev. Med. Devices 1:81–93, 2004.

    Article  PubMed  Google Scholar 

  64. Grigioni, M., C. Daniele, C. Del Gaudio, A. Balducci, U. Morbiducci, G. D’Avenio, and V. Barbaro. Critical aspects for a CFD simulation compared with PIV analysis of the flow field downstream of a prosthetic heart valve. Simulations in biomedicine 6:271, 2003.

    Article  Google Scholar 

  65. Gross, J. M. Calcification of bioprosthetic heart valves and its assessment. J. Thorac. Cardiovasc. Surg. 121:428–430, 2001.

    Article  CAS  PubMed  Google Scholar 

  66. Groves, E. M., A. Falahatpisheh, J. L. Su, and A. Kheradvar. The effects of positioning of transcatheter aortic valves on fluid dynamics of the aortic root. ASAIO J. 60:545–552, 2014.

    Article  PubMed  PubMed Central  Google Scholar 

  67. Haziza, F., G. Papouin, B. Barratt-Boyes, G. Christie, and R. Whitlock. Tears in bioprosthetic heart valve leaflets without calcific degeneration. J. Heart Valve Dis. 5:35–39, 1996.

    CAS  PubMed  Google Scholar 

  68. Hochareon, P., K. B. Manning, A. A. Fontaine, J. M. Tarbell, and S. Deutsch. Wall shear-rate estimation within the 50 cc penn state artificial heart using particle image velocimetry. J. Biomech. Eng. 126:430–437, 2004.

    Article  PubMed  Google Scholar 

  69. Holzapfel, G. A. Nonlinear Solid Mechanics. Chichester: Wiley, 2000.

    Google Scholar 

  70. Humphrey, J. D., and F. C. P. Yin. On constitutive relations and finite deformations of passive cardiac tissue: I. A pseudostrain-energy function. J. Biomech. Eng. 109:298–304, 1987.

    Article  CAS  PubMed  Google Scholar 

  71. Jahed, Z., H. Shams, M. Mehrbod, and M. R. Mofrad. Mechanotransduction pathways linking the extracellular matrix to the nucleus. Int. Rev. Cell Mol. Biol. 310:171–220, 2014.

    Article  CAS  PubMed  Google Scholar 

  72. Jamieson, W. R. E., L. H. Burr, A. I. Munro, and R. T. Miyagishima. Carpentier-edwards standard porcine bioprosthesis: a 21-year experience. Ann. Thorac. Surg. 66:S40–S43, 1998.

    Article  CAS  PubMed  Google Scholar 

  73. Jamieson, W. R. E., R. Koerfer, C. A. Yankah, A. Zittermann, R. I. Hayden, H. Ling, R. Hetzer, and W. B. Dolman. Mitroflow aortic pericardial bioprosthesis—clinical performance. Eur. J. Cardiothorac. Surg. 36:818–824, 2009.

    Article  PubMed  Google Scholar 

  74. Jamieson, W. R. E., L. J. Rosado, A. I. Munro, A. N. Gerein, L. H. Burr, R. T. Miyagishima, M. T. Janusz, and G. F. O. Tyers. Carpentier-edwards standard porcine bioprosthesis: primary tissue failure (structural valve deterioration) by age groups. Ann. Thorac. Surg. 46:155–162, 1988.

    Article  CAS  PubMed  Google Scholar 

  75. Jorge-Herrero, E., J. M. Garcia Paez, and J. L. Del Castillo-Olivares Ramos. Tissue heart valve mineralization: review of calcification mechanisms and strategies for prevention. J. Appl.Biomater. Biomech. 3:67–82, 2005.

    CAS  PubMed  Google Scholar 

  76. Kaminsky, R., S. Kallweit, M. Rossi, U. Morbiducci, L. Scalise, P. Verdonck, and E. Tomasini. Piv measurements of flows in artificial heart valves. Particle image velocimetry. Berlin, Heidelberg: Springer, pp. 55–72, 2008.

    Book  Google Scholar 

  77. Kaminsky, R., U. Morbiducci, M. Rossi, L. Scalise, P. Verdonck, and M. Grigioni. Time-resolved PIV technique for high temporal resolution measurement of mechanical prosthetic aortic valve fluid dynamics. Int. J. Artif. Organs 30:153–162, 2007.

    CAS  PubMed  Google Scholar 

  78. Kapolos, J., D. Mavrilas, Y. Missirlis, and P. G. Koutsoukos. Model experimental system for investigation of heart valve calcification in vitro. J. Biomed. Mater. Res. 38:183–190, 1997.

    Article  CAS  PubMed  Google Scholar 

  79. Kelley, T., S. Marquez, and C. Popelar. In vitro testing of heart valve substitutes. In: Heart Valves, edited by P. A. Iaizzo, R. W. Bianco, A. J. Hill, and J. D. St Louis. US: Springer, 2013, pp. 283–320.

    Chapter  Google Scholar 

  80. Kheradvar A, Groves EL, Tseng E. Foldavalve: a novel 14fr totally repositionable and retrievable transcatheter aortic valve: proof of concept in sheep. EuroIntervention. 10(pii):20141002–20141001, 2015.

  81. Kheradvar, A., and A. Falahatpisheh. The effects of dynamic saddle annulus and leaflet length on transmitral flow pattern and leaflet stress of a bileaflet bioprosthetic mitral valve. J. Heart Valve Dis. 21:225–233, 2012.

    PubMed  Google Scholar 

  82. Kheradvar, A., J. Kasalko, D. Johnson, and M. Gharib. An in vitro study of changing profile heights in mitral bioprostheses and their influence on flow. ASAIO J. 52:34–38, 2006.

    Article  PubMed  Google Scholar 

  83. Kheradvar, A., M. Milano, and M. Gharib. Correlation between vortex ring formation and mitral annulus dynamics during ventricular rapid filling. ASAIO J. 53:8–16, 2007.

    Article  PubMed  Google Scholar 

  84. Kim, H., K. B. Chandran, M. S. Sacks, and J. Lu. An experimentally derived stress resultant shell model for heart valve dynamic simulations. Ann. Biomed. Eng. 35:30–44, 2007.

    Article  PubMed  Google Scholar 

  85. Kim, H., J. Lu, M. S. Sacks, and K. B. Chandran. Dynamic simulation of bioprosthetic heart valves using a stress resultant shell model. Ann. Biomed. Eng. 36:262–275, 2008.

    Article  PubMed  Google Scholar 

  86. Kim Y, Peskin CS. Penalty immersed boundary method for an elastic boundary with mass. Physics of Fluids (1994-present). 19:053103, 2007.

  87. Kim Y, Zhu L, Wang X, Peskin C. On various techniques for computer simulation of boundaries with mass. In: Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, 2003, pp. 1746–1750.

  88. Kini, V., C. Bachmann, A. Fontaine, S. Deutsch, and J. M. Tarbell. Integrating particle image velocimetry and laser doppler velocimetry measurements of the regurgitant flow field past mechanical heart valves. Artif. Organs 25:136–145, 2001.

    Article  CAS  PubMed  Google Scholar 

  89. Krings, M., D. Kanellopoulou, D. Mavrilas, and B. Glasmacher. In vitro ph-controlled calcification of biological heart valve prostheses. Materialwiss. Werkstofftech. 37:432–435, 2006.

    Article  CAS  Google Scholar 

  90. Kunzelman, K. S., and R. Cochran. Stress/strain characteristics of porcine mitral valve tissue: parallel versus perpendicular collagen orientation. J. Card. Surg. 7:71–78, 1992.

    Article  CAS  PubMed  Google Scholar 

  91. Leo, H., L. P. Dasi, J. Carberry, H. A. Simon, and A. Yoganathan. Fluid dynamic assessment of three polymeric heart valves using particle image velocimetry. Ann. Biomed. Eng. 34:936–952, 2006.

    Article  PubMed  Google Scholar 

  92. Kemp M. Leonardo da vinci: Experience, Experiment and Design. Princeton, NJ: Princeton University Press, 2006.

    Google Scholar 

  93. Levy, R. J., F. J. Schoen, J. T. Levy, A. C. Nelson, S. L. Howard, and L. J. Oshry. Biologic determinants of dystrophic calcification and osteocalcin deposition in glutaraldehyde-preserved porcine aortic valve leaflets implanted subcutaneously in rats. Am. J. Pathol. 113:143–145, 1983.

    CAS  PubMed  PubMed Central  Google Scholar 

  94. Li, J., X. Y. Luo, and Z. B. Kuang. A nonlinear anisotropic model for porcine aortic heart valves. J. Biomech. 34:1279–1289, 2001.

    Article  CAS  PubMed  Google Scholar 

  95. Lighthill, S. J. Physiological Fluid Mechanics. Berlin: Springer, 1972.

    Google Scholar 

  96. Lim, W. L., Y. T. Chew, T. C. Chew, and H. T. Low. Particle image velocimetry in the investigation of flow past artificial heart valves. Ann. Biomed. Eng. 22:307–318, 1994.

    Article  CAS  PubMed  Google Scholar 

  97. Lim, W., Y. Chew, T. Chew, and H. Low. Steady flow dynamics of prosthetic aortic heart valves: a comparative evaluation with piv techniques. J. Biomech. 31:411–421, 1998.

    Article  CAS  PubMed  Google Scholar 

  98. Lim, W., Y. Chew, T. Chew, and H. Low. Pulsatile flow studies of a porcine bioprosthetic aortic valve in vitro: Piv measurements and shear-induced blood damage. J. Biomech. 34:1417–1427, 2001.

    Article  CAS  PubMed  Google Scholar 

  99. Linde, T., K. F. Hamilton, D. L. Timms, T. Schmitz-Rode, and U. Steinseifer. A low-volume tester for the thrombogenic potential of mechanical heart valve prostheses. J. Heart Valve Dis. 20:510–517, 2011.

    PubMed  Google Scholar 

  100. Luo, X., B. Griffith, X. Ma, M. Yin, T. Wang, C. Liang, P. Watton, and G. Bernacca. Effect of bending rigidity in a dynamic model of a polyurethane prosthetic mitral valve. Biomech. Model. Mechanobiol. 11:815–827, 2012.

    Article  CAS  PubMed  Google Scholar 

  101. Ma, X., H. Gao, B. E. Griffith, C. Berry, and X. Luo. Image-based fluid–structure interaction model of the human mitral valve. Comput. Fluids 71:417–425, 2013.

    Article  Google Scholar 

  102. Mako, W. J., and I. Vesely. In vivo and in vitro models of calcification in porcine aortic valve cusps. J. Heart Valve Dis. 6:316–323, 1997.

    CAS  PubMed  Google Scholar 

  103. Manning, K. B., V. Kini, A. A. Fontaine, S. Deutsch, and J. M. Tarbell. Regurgitant flow field characteristics of the st. Jude bileaflet mechanical heart valve under physiologic pulsatile flow using particle image velocimetry. Artif. Organs 27:840–846, 2003.

    Article  PubMed  Google Scholar 

  104. Mavrilas, D., A. Apostolaki, J. Kapolos, P. G. Koutsoukos, M. Melachrinou, V. Zolota, and D. Dougenis. Development of bioprosthetic heart valve calcification in vitro and in animal models: morphology and composition. J. Cryst. Growth 205:554–562, 1999.

    Article  CAS  Google Scholar 

  105. Mavrilas, D., J. Kapolos, P. G. Koutsoukos, and D. Dougenis. Screening biomaterials with a new in vitro method for potential calcification: porcine aortic valves and bovine pericardium. J. Mater. Sci. Mater. Med. 15:699–704, 2004.

    Article  CAS  PubMed  Google Scholar 

  106. May-Newman, K., C. Lam, and F. C. Yin. A hyperelastic constitutive law for aortic valve tissue. J. Biomech. Eng. 131:081009, 2009.

    Article  PubMed  Google Scholar 

  107. May-Newman, K., and F. C. Yin. Biaxial mechanical behavior of excised porcine mitral valve leaflets. Am. J. Physiol. Heart Circ. Physiol. 38:H1319, 1995.

    Google Scholar 

  108. May-Newman, K., and F. C. P. Yin. A constitutive law for mitral valve tissue. J. Biomech. Eng. 120:38–47, 1998.

    Article  CAS  PubMed  Google Scholar 

  109. McClure, R. S., N. Narayanasamy, E. Wiegerinck, S. Lipsitz, A. Maloney, J. G. Byrne, S. F. Aranki, G. S. Couper, and L. H. Cohn. Late outcomes for aortic valve replacement with the carpentier-edwards pericardial bioprosthesis: up to 17-year follow-up in 1,000 patients. Ann. Thorac. Surg. 89:1410–1416, 2010.

    Article  PubMed  Google Scholar 

  110. McQueen, D. M., and C. S. Peskin. Computer-assisted design of butterfly bileaflet valves for the mitral position. Scand. Cardiovasc. J. 19:139–148, 1985.

    CAS  Google Scholar 

  111. McQUEEN, D. M., C. S. Peskin, and E. L. Yellin. Fluid dynamics of the mitral valve: physiological aspects of a mathematical model. Am. J. Physiol. Heart Circ. Physiol. 242:H1095–H1110, 1982.

    CAS  Google Scholar 

  112. Misfeld, M., and H.-H. Sievers. Heart valve macro- and microstructure. Philos. Trans. R. Soc. B Biol. Sci. 362:1421–1436, 2007.

    Article  Google Scholar 

  113. Mofrad, M. R., and R. D. Kamm. Cellular Mechanotransduction: Diverse Perspectives from Molecules to Tissues. Cambridge, MA: Cambridge University Press, 2009.

    Book  Google Scholar 

  114. Mol, A., N. B. Driessen, M. M. Rutten, S. Hoerstrup, C. C. Bouten, and F. T. Baaijens. Tissue engineering of human heart valve leaflets: a novel bioreactor for a strain-based conditioning approach. Ann. Biomed. Eng. 33:1778–1788, 2005.

    Article  PubMed  Google Scholar 

  115. Morbiducci U, D Avenio G, Del Gaudio C, Grigioni M. Testing requirements for steroscopic particle image velocimetry measurements of mechanical heart valves fluid dynamics. RAPPORTI ISTISAN. 46:21, 2005.

  116. Mori, Y., and C. S. Peskin. Implicit second-order immersed boundary methods with boundary mass. Comput. Methods Appl. Mech. Eng. 197:2049–2067, 2008.

    Article  Google Scholar 

  117. Morsi, Y. S., W. W. Yang, C. S. Wong, and S. Das. Transient fluid–structure coupling for simulation of a trileaflet heart valve using weak coupling. J. Artif. Organs. 10:96–103, 2007.

    Article  PubMed  Google Scholar 

  118. Nobili, M., U. Morbiducci, R. Ponzini, C. Del Gaudio, A. Balducci, M. Grigioni, F. M. Montevecchi, and A. Redaelli. Numerical simulation of the dynamics of a bileaflet prosthetic heart valve using a fluid–structure interaction approach. J. Biomech. 41:2539–2550, 2008.

    Article  PubMed  Google Scholar 

  119. Ogden, R. W., and G. A. Holzapfel. Mechanics of Biological Tissue. Berlin: Springer, 2006.

    Google Scholar 

  120. Ogden RW. Non-linear Elastic Deformations. New York: Courier Corporation, Ellis Horwood, 1997.

    Google Scholar 

  121. Othmer, H. G., F. R. Adler, M. A. Lewis, and J. C. Dallon. Case Studies in Mathematical Modeling–Ecology, Physiology, and Cell Biology. Englewood Cliffs, NJ: Prentice Hall, 1997.

    Google Scholar 

  122. Patankar, N. A., P. Singh, D. D. Joseph, R. Glowinski, and T.-W. Pan. A new formulation of the distributed lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiph. Flow 26:1509–1524, 2000.

    Article  CAS  Google Scholar 

  123. Pereira, F., M. Gharib, D. Dabiri, and D. Modarress. Defocusing digital particle image velocimetry: a 3-component 3-dimensional dpiv measurement technique. Application to bubbly flows. Exp Fluids. 29:S078–S084, 2000.

    Article  Google Scholar 

  124. Peskin, C. S. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10:252–271, 1972.

    Article  Google Scholar 

  125. Peskin, C. S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 25:220–252, 1977.

    Article  Google Scholar 

  126. Peskin, C. S. The immersed boundary method. Acta numerica. 11:479–517, 2002.

    Article  Google Scholar 

  127. Peskin, C. S., and D. M. McQueen. Modeling prosthetic heart valves for numerical analysis of blood flow in the heart. J. Comput. Phys. 37:113–132, 1980.

    Article  Google Scholar 

  128. Peskin, C. S., and D. M. McQueen. Mechanical equilibrium determines the fractal fiber architecture of aortic heart valve leaflets. Am. J. Physiol. Heart Circ. Physiol. 266:H319–H328, 1994.

    CAS  Google Scholar 

  129. Pettenazzo, E., M. Deiwick, G. Thiene, G. Molin, B. Glasmacher, F. Martignago, T. Bottio, H. Reul, and M. Valente. Dynamic in vitro calcification of bioprosthetic porcine valves: evidence of apatite crystallization. J. Thorac. Cardiovasc. Surg. 121:500–509, 2001.

    Article  CAS  PubMed  Google Scholar 

  130. Pierrakos, O., P. P. Vlachos, and D. P. Telionis. Time-resolved dpiv analysis of vortex dynamics in a left ventricular model through bileaflet mechanical and porcine heart valve prostheses. J. Biomech. Eng. 126:714–726, 2005.

    Article  Google Scholar 

  131. Quaini, A., S. Canic, R. Glowinski, S. Igo, C. J. Hartley, W. Zoghbi, and S. Little. Validation of a 3d computational fluid–structure interaction model simulating flow through an elastic aperture. J. Biomech. 45:310–318, 2012.

    Article  CAS  PubMed  Google Scholar 

  132. Redaelli, A., H. Bothorel, E. Votta, M. Soncini, U. Morbiducci, Gaudio C. Del, A. Balducci, and M. Grigioni. 3-d simulation of the st. Jude medical bileaflet valve opening process: fluid-structure interaction study and experimental validation. J. Heart Valve Dis. 13:804–813, 2004.

    PubMed  Google Scholar 

  133. Rieß, F.-C., R. Bader, E. Cramer, L. Hansen, S. Schiffelers, J. Wallrath, and G. Wahl. The mosaic porcine bioprosthesis: role of age on clinical performance in aortic position. J. Thorac. Cardiovasc. Surg. 141(1440–1448):e1441, 2011.

    Google Scholar 

  134. Riess, F.-C., E. Cramer, L. Hansen, S. Schiffelers, G. Wahl, J. Wallrath, S. Winkel, and P. Kremer. Clinical results of the medtronic mosaic porcine bioprosthesis up to 13 years. Eur. J. Cardiothorac. Surg. 37:145–153, 2010.

    Article  PubMed  Google Scholar 

  135. Rousseau, E. P. M., A. A. van Steenhoven, J. D. Janssen, and H. A. Huysmans. A mechanical analysis of the closed hancock heart valve prosthesis. J. Biomech. 21:545–562, 1988.

    Article  CAS  PubMed  Google Scholar 

  136. Sacks, M. S. A method for planar biaxial mechanical testing that includes in-plane shear. J. Biomech. Eng. 121:551–555, 1999.

    Article  CAS  PubMed  Google Scholar 

  137. Sacks, M., and C. J. Chuong. Orthotropic mechanical properties of chemically treated bovine pericardium. Ann. Biomed. Eng. 26:892–902, 1998.

    Article  CAS  PubMed  Google Scholar 

  138. Saikrishnan, N., C.-H. Yap, N. Milligan, N. Vasilyev, and A. Yoganathan. In vitro characterization of bicuspid aortic valve hemodynamics using particle image velocimetry. Ann. Biomed. Eng. 40:1760–1775, 2012.

    Article  PubMed  Google Scholar 

  139. Schoen, F. J., G. Golomb, and R. J. Levy. Calcification of bioprosthetic heart valves: a perspective on models. J. Heart Valve Dis. 1:110–114, 1992.

    CAS  PubMed  Google Scholar 

  140. Schoen, F. J., H. Harasaki, K. M. Kim, H. C. Anderson, and R. J. Levy. Biomaterial-associated calcification: pathology, mechanisms, and strategies for prevention. J. Biomed. Mater. Res. 22:11–36, 1988.

    CAS  PubMed  Google Scholar 

  141. Schoen, F. J., and R. J. Levy. Calcification of tissue heart valve substitutes: progress toward understanding and prevention. Ann. Thorac. Surg. 79:1072–1080, 2005.

    Article  PubMed  Google Scholar 

  142. Shandas, R., and J. Kwon. Digital particle image velocimetry (dpiv) measurements of the velocity profiles through bileaflet mechanical valves: In vitro steady. Biomed. Sci. Instrum. 32:161–167, 1996.

    CAS  PubMed  Google Scholar 

  143. Shirgaonkar, A. A., M. A. MacIver, and N. A. Patankar. A new mathematical formulation and fast algorithm for fully resolved simulation of self-propulsion. J. Comput. Phys. 228:2366–2390, 2009.

    Article  Google Scholar 

  144. Stella, J. A., and M. S. Sacks. On the biaxial mechanical properties of the layers of the aortic valve leaflet. J. Biomech. Eng. 129:757–766, 2007.

    Article  PubMed  Google Scholar 

  145. Stewart, S. F., P. Hariharan, E. G. Paterson, G. W. Burgreen, V. Reddy, S. W. Day, M. Giarra, K. B. Manning, S. Deutsch, and M. R. Berman. Results of fda’s first interlaboratory computational study of a nozzle with a sudden contraction and conical diffuser. Cardiovasc. Eng. Technol. 4:374–391, 2013.

    Article  Google Scholar 

  146. Stewart, S. F., E. G. Paterson, G. W. Burgreen, P. Hariharan, M. Giarra, V. Reddy, S. W. Day, K. B. Manning, S. Deutsch, and M. R. Berman. Assessment of cfd performance in simulations of an idealized medical device: results of fda’s first computational interlaboratory study. Cardiovasc. Eng. Technol. 3:139–160, 2012.

    Article  Google Scholar 

  147. Stijnen, J., J. De Hart, P. Bovendeerd, and F. Van de Vosse. Evaluation of a fictitious domain method for predicting dynamic response of mechanical heart valves. J. Fluids Struct. 19:835–850, 2004.

    Article  Google Scholar 

  148. Sun, W., A. Abad, and M. S. Sacks. Simulated bioprosthetic heart valve deformation under quasi-static loading. J. Biomech. Eng. 127:905–914, 2005.

    Article  PubMed  Google Scholar 

  149. Thubrikar, M. J., J. D. Deck, J. Aouad, and S. P. Nolan. Role of mechanical stress in calcification of aortic bioprosthetic valves. J. Thorac. Cardiovasc. Surg. 86:115–125, 1983.

    CAS  PubMed  Google Scholar 

  150. Thurston, G. B. Rheological parameters for the viscosity viscoelasticity and thixotropy of blood. Biorheology. 16:149–162, 1978.

    Google Scholar 

  151. Valant, A. Z., L. Žiberna, Y. Papaharilaou, A. Anayiotos, and G. C. Georgiou. The influence of temperature on rheological properties of blood mixtures with different volume expanders—implications in numerical arterial hemodynamics simulations. Rheol. Acta 50:389–402, 2011.

    Article  CAS  Google Scholar 

  152. Valente, M., U. Bortolotti, and G. Thiene. Ultrastructural substrates of dystrophic calcification in porcine bioprosthetic valve failure. Am. J. Pathol. 119:12–21, 1985.

    CAS  PubMed  PubMed Central  Google Scholar 

  153. Vesely, I., and D. Boughner. Analysis of the bending behaviour of porcine xenograft leaflets and of natural aortic valve material: bending stiffness, neutral axis and shear measurements. J. Biomech. 22:655–671, 1989.

    Article  CAS  PubMed  Google Scholar 

  154. Vesely, I., D. Boughner, and T. Song. Tissue buckling as a mechanism of bioprosthetic valve failure. Ann. Thorac. Surg. 46:302–308, 1988.

    Article  CAS  PubMed  Google Scholar 

  155. Webb, C. L., J. J. Benedict, F. J. Schoen, J. A. Linden, and R. J. Levy. Inhibition of bioprosthetic heart valve calcification with aminodiphosphonate covalently bound to residual aldehyde groups. Ann. Thorac. Surg. 46:309–316, 1988.

    Article  CAS  PubMed  Google Scholar 

  156. Weinberg, E. J., and M. R. Kaazempur-Mofrad. On the constitutive models for heart valve leaflet mechanics. Cardiovasc. Eng. 5:37–43, 2005.

    Article  Google Scholar 

  157. Weinberg, E. J., and M. R. Kaazempur-Mofrad. A large-strain finite element formulation for biological tissues with application to mitral valve leaflet tissue mechanics. J. Biomech. 39:1557–1561, 2006.

    Article  PubMed  Google Scholar 

  158. Weinberg, E. J., P. J. Mack, F. J. Schoen, G. García-Cardeña, and M. R. K. Mofrad. Hemodynamic environments from opposing sides of human aortic valve leaflets evoke distinct endothelial phenotypes in vitro. Cardiovasc. Eng. 10:5–11, 2010.

    Article  PubMed  PubMed Central  Google Scholar 

  159. Weinberg, E. J., and M. R. K. Mofrad. A finite shell element for heart mitral valve leaflet mechanics, with large deformations and 3d constitutive material model. J. Biomech. 40:705–711, 2007.

    Article  PubMed  Google Scholar 

  160. Weinberg, E. J., and M. R. K. Mofrad. Transient, three-dimensional, multiscale simulations of the human aortic valve. Cardiovasc. Eng. 7:140–155, 2007.

    Article  PubMed  Google Scholar 

  161. Weinberg, E. J., and M. R. K. Mofrad. A multiscale computational comparison of the bicuspid and tricuspid aortic valves in relation to calcific aortic stenosis. J. Biomech. 41:3482–3487, 2008.

    Article  PubMed  Google Scholar 

  162. Weinberg, E. J., F. J. Schoen, and M. R. Mofrad. A computational model of aging and calcification in the aortic heart valve. PLoS ONE 4:e5960, 2009.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  163. Weska, R. F., C. G. Aimoli, G. M. Nogueira, A. A. Leirner, M. J. S. Maizato, O. Z. Higa, B. Polakievicz, R. N. M. Pitombo, and M. M. Beppu. Natural and prosthetic heart valve calcification: morphology and chemical composition characterization. Artif. Organs 34:311–318, 2010.

    Article  CAS  PubMed  Google Scholar 

  164. Willert, C. E., and M. Gharib. Digital particle image velocimetry. Exp. Fluids 10:181–193, 1991.

    Article  Google Scholar 

  165. Wouters L, Rousseau E, Steenhoven vA, German A. An experimental set-up for the in vitro analysis of polyurethane calcification. In: Polyurethanes in biomedical engineering: II: Proceedings of the 2nd International Conference on Polyurethanes in Biomedical Engineering, Fellbach/Stuttgart, edited by H. Planck, June 18–19. vol. 3, p. 169, 1986/1987.

  166. Yin, W., Y. Alemu, K. Affeld, J. Jesty, and D. Bluestein. Flow-induced platelet activation in bileaflet and monoleaflet mechanical heart valves. Ann. Biomed. Eng. 32:1058–1066, 2004.

    Article  PubMed  Google Scholar 

  167. Yotsumoto, G., Y. Moriyama, H. Toyohira, S. Shimokawa, Y. Iguro, S. Watanabe, H. Masuda, K. Hisatomi, and A. Taira. Congenital bicuspid aortic valve: analysis of 63 surgical cases. J. Heart Valve Dis. 7:500–503, 1998.

    CAS  PubMed  Google Scholar 

  168. Yu, Z. A dlm/fd method for fluid/flexible-body interactions. J. Comput. Phys. 207:1–27, 2005.

    Article  Google Scholar 

  169. Zhu, L., and C. S. Peskin. Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J. Comput. Phys. 179:452–468, 2002.

    Article  CAS  Google Scholar 

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Acknowledgments

This review article was prepared after the Mathematics Guiding Bioartificial Heart Valve Design meeting held at the Ohio State University, October 28 to 31, 2013. The authors would like to acknowledge the Mathematical Biosciences Institute and its grant from National Science Foundation (DMS 0931642) that facilitated the meeting.

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Associate Editor K. A. Athanasiou oversaw the review of this article.

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Kheradvar, A., Groves, E.M., Falahatpisheh, A. et al. Emerging Trends in Heart Valve Engineering: Part IV. Computational Modeling and Experimental Studies. Ann Biomed Eng 43, 2314–2333 (2015). https://doi.org/10.1007/s10439-015-1394-4

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