Annals of Biomedical Engineering

, Volume 43, Issue 10, pp 2314–2333 | Cite as

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

  • Arash Kheradvar
  • Elliott M. Groves
  • Ahmad Falahatpisheh
  • Mohammad K. Mofrad
  • S. Hamed Alavi
  • Robert Tranquillo
  • Lakshmi P. Dasi
  • Craig A. Simmons
  • K. Jane Grande-Allen
  • Craig J. Goergen
  • Frank Baaijens
  • Stephen H. Little
  • Suncica Canic
  • Boyce Griffith


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.


Computational modeling Heart valves Particle image velocimetry Biaxial testing Multiscale modeling Numerical simulation 



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.


  1. 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.CrossRefGoogle Scholar
  2. 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. 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.PubMedCrossRefGoogle Scholar
  4. 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.PubMedCrossRefGoogle Scholar
  5. 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.PubMedCrossRefGoogle Scholar
  6. 6.
    Amatya, D., D. Troolin, and E. Longmire. 3d3c velocity measurements downstream of artificial heart valves. Methods 7:9, 2009.Google Scholar
  7. 7.
    Antman, S. S. Nonlinear Problems of Elasticity, Volume 107 of Applied Mathematical Sciences. New York: Springer-Verlag, 2005.Google Scholar
  8. 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.PubMedCrossRefGoogle Scholar
  9. 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.PubMedCrossRefGoogle Scholar
  10. 10.
    Bellhouse, B. J., and F. H. Bellhouse. Fluid mechanics of the mitral valve. Nature 224:615–616, 1969.PubMedCrossRefGoogle Scholar
  11. 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. 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.CrossRefGoogle Scholar
  13. 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.CrossRefGoogle Scholar
  14. 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.PubMedCrossRefGoogle Scholar
  15. 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.PubMedCrossRefGoogle Scholar
  16. 16.
    Bischoff, J. E., E. A. Arruda, and K. Grosh. A microstructurally based orthotropic hyperelastic constitutive law. J. Appl. Mech. 69:570–579, 2002.CrossRefGoogle Scholar
  17. 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.Google Scholar
  18. 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. 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.CrossRefGoogle Scholar
  20. 20.
    Bonet, J., and R. Wood. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge: Cambridge University Press, 1997.Google Scholar
  21. 21.
    Brücker, C. Dual-camera DPIV for flow studies past artificial heart valves. Exp. Fluids 22:496–506, 1997.CrossRefGoogle Scholar
  22. 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.PubMedCrossRefGoogle Scholar
  23. 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).PubMedGoogle Scholar
  24. 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.PubMedCrossRefGoogle Scholar
  25. 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.PubMedCentralCrossRefGoogle Scholar
  26. 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.PubMedCrossRefGoogle Scholar
  27. 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.PubMedCrossRefGoogle Scholar
  28. 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.PubMedCrossRefGoogle Scholar
  29. 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.PubMedCrossRefGoogle Scholar
  30. 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.PubMedPubMedCentralCrossRefGoogle Scholar
  31. 31.
    Chikwe, J., and F. Filsoufi. Durability of tissue valves. Semin. Thorac. Cardiovasc. Surg. 23:18–23, 2011.PubMedCrossRefGoogle Scholar
  32. 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.CrossRefGoogle Scholar
  33. 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.PubMedCrossRefGoogle Scholar
  34. 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.PubMedCrossRefGoogle Scholar
  35. 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.CrossRefGoogle Scholar
  36. 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.PubMedCrossRefGoogle Scholar
  37. 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.PubMedCrossRefGoogle Scholar
  38. 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.PubMedCrossRefGoogle Scholar
  39. 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.PubMedCrossRefGoogle Scholar
  40. 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.PubMedCrossRefGoogle Scholar
  41. 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.CrossRefGoogle Scholar
  42. 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.PubMedCrossRefGoogle Scholar
  43. 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.CrossRefGoogle Scholar
  44. 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.CrossRefGoogle Scholar
  45. 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.CrossRefGoogle Scholar
  46. 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.CrossRefGoogle Scholar
  47. 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.PubMedCrossRefGoogle Scholar
  48. 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.PubMedCrossRefGoogle Scholar
  49. 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.Google Scholar
  50. 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.CrossRefGoogle Scholar
  51. 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.CrossRefGoogle Scholar
  52. 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.PubMedCrossRefGoogle Scholar
  53. 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.PubMedCrossRefGoogle Scholar
  54. 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.PubMedPubMedCentralCrossRefGoogle Scholar
  55. 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.PubMedCrossRefGoogle Scholar
  56. 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.Google Scholar
  57. 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.CrossRefGoogle Scholar
  58. 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.CrossRefGoogle Scholar
  59. 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.Google Scholar
  60. 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.CrossRefGoogle Scholar
  61. 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.CrossRefGoogle Scholar
  62. 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.CrossRefGoogle Scholar
  63. 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.PubMedCrossRefGoogle Scholar
  64. 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.CrossRefGoogle Scholar
  65. 65.
    Gross, J. M. Calcification of bioprosthetic heart valves and its assessment. J. Thorac. Cardiovasc. Surg. 121:428–430, 2001.PubMedCrossRefGoogle Scholar
  66. 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.PubMedPubMedCentralCrossRefGoogle Scholar
  67. 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.PubMedGoogle Scholar
  68. 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.PubMedCrossRefGoogle Scholar
  69. 69.
    Holzapfel, G. A. Nonlinear Solid Mechanics. Chichester: Wiley, 2000.Google Scholar
  70. 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.PubMedCrossRefGoogle Scholar
  71. 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.PubMedCrossRefGoogle Scholar
  72. 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.PubMedCrossRefGoogle Scholar
  73. 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.PubMedCrossRefGoogle Scholar
  74. 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.PubMedCrossRefGoogle Scholar
  75. 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.PubMedGoogle Scholar
  76. 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.CrossRefGoogle Scholar
  77. 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.PubMedGoogle Scholar
  78. 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.PubMedCrossRefGoogle Scholar
  79. 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.CrossRefGoogle Scholar
  80. 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.Google Scholar
  81. 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.PubMedGoogle Scholar
  82. 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.PubMedCrossRefGoogle Scholar
  83. 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.PubMedCrossRefGoogle Scholar
  84. 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.PubMedCrossRefGoogle Scholar
  85. 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.PubMedCrossRefGoogle Scholar
  86. 86.
    Kim Y, Peskin CS. Penalty immersed boundary method for an elastic boundary with mass. Physics of Fluids (1994-present). 19:053103, 2007.Google Scholar
  87. 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.Google Scholar
  88. 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.PubMedCrossRefGoogle Scholar
  89. 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.CrossRefGoogle Scholar
  90. 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.PubMedCrossRefGoogle Scholar
  91. 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.PubMedCrossRefGoogle Scholar
  92. 92.
    Kemp M. Leonardo da vinci: Experience, Experiment and Design. Princeton, NJ: Princeton University Press, 2006.Google Scholar
  93. 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.PubMedPubMedCentralGoogle Scholar
  94. 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.PubMedCrossRefGoogle Scholar
  95. 95.
    Lighthill, S. J. Physiological Fluid Mechanics. Berlin: Springer, 1972.Google Scholar
  96. 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.PubMedCrossRefGoogle Scholar
  97. 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.PubMedCrossRefGoogle Scholar
  98. 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.PubMedCrossRefGoogle Scholar
  99. 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.PubMedGoogle Scholar
  100. 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.PubMedCrossRefGoogle Scholar
  101. 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.CrossRefGoogle Scholar
  102. 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.PubMedGoogle Scholar
  103. 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.PubMedCrossRefGoogle Scholar
  104. 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.CrossRefGoogle Scholar
  105. 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.PubMedCrossRefGoogle Scholar
  106. 106.
    May-Newman, K., C. Lam, and F. C. Yin. A hyperelastic constitutive law for aortic valve tissue. J. Biomech. Eng. 131:081009, 2009.PubMedCrossRefGoogle Scholar
  107. 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. 108.
    May-Newman, K., and F. C. P. Yin. A constitutive law for mitral valve tissue. J. Biomech. Eng. 120:38–47, 1998.PubMedCrossRefGoogle Scholar
  109. 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.PubMedCrossRefGoogle Scholar
  110. 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.Google Scholar
  111. 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.Google Scholar
  112. 112.
    Misfeld, M., and H.-H. Sievers. Heart valve macro- and microstructure. Philos. Trans. R. Soc. B Biol. Sci. 362:1421–1436, 2007.CrossRefGoogle Scholar
  113. 113.
    Mofrad, M. R., and R. D. Kamm. Cellular Mechanotransduction: Diverse Perspectives from Molecules to Tissues. Cambridge, MA: Cambridge University Press, 2009.CrossRefGoogle Scholar
  114. 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.PubMedCrossRefGoogle Scholar
  115. 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.Google Scholar
  116. 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.CrossRefGoogle Scholar
  117. 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.PubMedCrossRefGoogle Scholar
  118. 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.PubMedCrossRefGoogle Scholar
  119. 119.
    Ogden, R. W., and G. A. Holzapfel. Mechanics of Biological Tissue. Berlin: Springer, 2006.Google Scholar
  120. 120.
    Ogden RW. Non-linear Elastic Deformations. New York: Courier Corporation, Ellis Horwood, 1997.Google Scholar
  121. 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. 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.CrossRefGoogle Scholar
  123. 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.CrossRefGoogle Scholar
  124. 124.
    Peskin, C. S. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10:252–271, 1972.CrossRefGoogle Scholar
  125. 125.
    Peskin, C. S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 25:220–252, 1977.CrossRefGoogle Scholar
  126. 126.
    Peskin, C. S. The immersed boundary method. Acta numerica. 11:479–517, 2002.CrossRefGoogle Scholar
  127. 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.CrossRefGoogle Scholar
  128. 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.Google Scholar
  129. 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.PubMedCrossRefGoogle Scholar
  130. 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.CrossRefGoogle Scholar
  131. 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.PubMedCrossRefGoogle Scholar
  132. 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.PubMedGoogle Scholar
  133. 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. 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.PubMedCrossRefGoogle Scholar
  135. 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.PubMedCrossRefGoogle Scholar
  136. 136.
    Sacks, M. S. A method for planar biaxial mechanical testing that includes in-plane shear. J. Biomech. Eng. 121:551–555, 1999.PubMedCrossRefGoogle Scholar
  137. 137.
    Sacks, M., and C. J. Chuong. Orthotropic mechanical properties of chemically treated bovine pericardium. Ann. Biomed. Eng. 26:892–902, 1998.PubMedCrossRefGoogle Scholar
  138. 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.PubMedCrossRefGoogle Scholar
  139. 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.PubMedGoogle Scholar
  140. 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.PubMedGoogle Scholar
  141. 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.PubMedCrossRefGoogle Scholar
  142. 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.PubMedGoogle Scholar
  143. 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.CrossRefGoogle Scholar
  144. 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.PubMedCrossRefGoogle Scholar
  145. 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.CrossRefGoogle Scholar
  146. 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.CrossRefGoogle Scholar
  147. 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.CrossRefGoogle Scholar
  148. 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.PubMedCrossRefGoogle Scholar
  149. 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.PubMedGoogle Scholar
  150. 150.
    Thurston, G. B. Rheological parameters for the viscosity viscoelasticity and thixotropy of blood. Biorheology. 16:149–162, 1978.Google Scholar
  151. 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.CrossRefGoogle Scholar
  152. 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.PubMedPubMedCentralGoogle Scholar
  153. 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.PubMedCrossRefGoogle Scholar
  154. 154.
    Vesely, I., D. Boughner, and T. Song. Tissue buckling as a mechanism of bioprosthetic valve failure. Ann. Thorac. Surg. 46:302–308, 1988.PubMedCrossRefGoogle Scholar
  155. 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.PubMedCrossRefGoogle Scholar
  156. 156.
    Weinberg, E. J., and M. R. Kaazempur-Mofrad. On the constitutive models for heart valve leaflet mechanics. Cardiovasc. Eng. 5:37–43, 2005.CrossRefGoogle Scholar
  157. 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.PubMedCrossRefGoogle Scholar
  158. 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.PubMedPubMedCentralCrossRefGoogle Scholar
  159. 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.PubMedCrossRefGoogle Scholar
  160. 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.PubMedCrossRefGoogle Scholar
  161. 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.PubMedCrossRefGoogle Scholar
  162. 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.PubMedPubMedCentralCrossRefGoogle Scholar
  163. 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.PubMedCrossRefGoogle Scholar
  164. 164.
    Willert, C. E., and M. Gharib. Digital particle image velocimetry. Exp. Fluids 10:181–193, 1991.CrossRefGoogle Scholar
  165. 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.Google Scholar
  166. 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.PubMedCrossRefGoogle Scholar
  167. 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.PubMedGoogle Scholar
  168. 168.
    Yu, Z. A dlm/fd method for fluid/flexible-body interactions. J. Comput. Phys. 207:1–27, 2005.CrossRefGoogle Scholar
  169. 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.CrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2015

Authors and Affiliations

  • Arash Kheradvar
    • 1
    • 2
  • Elliott M. Groves
    • 1
    • 2
  • Ahmad Falahatpisheh
    • 1
  • Mohammad K. Mofrad
    • 3
  • S. Hamed Alavi
    • 1
  • Robert Tranquillo
    • 4
  • Lakshmi P. Dasi
    • 5
  • Craig A. Simmons
    • 6
    • 7
  • K. Jane Grande-Allen
    • 8
  • Craig J. Goergen
    • 9
  • Frank Baaijens
    • 10
  • Stephen H. Little
    • 11
  • Suncica Canic
    • 12
  • Boyce Griffith
    • 13
    • 14
  1. 1.Department of Biomedical Engineering, The Edwards Lifesciences Center for Advanced Cardiovascular TechnologyUniversity of California, IrvineIrvineUSA
  2. 2.Department of Medicine, Division of CardiologyUniversity of California, Irvine School of MedicineIrvineUSA
  3. 3.Department of Bioengineering and Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA
  4. 4.Department of Biomedical EngineeringUniversity of MinnesotaMinneapolisUSA
  5. 5.Department of Mechanical Engineering, School of Biomedical EngineeringColorado State UniversityFort CollinsUSA
  6. 6.Department of Mechanical & Industrial EngineeringUniversity of TorontoTorontoCanada
  7. 7.Institute of Biomaterials & Biomedical EngineeringUniversity of TorontoTorontoCanada
  8. 8.Department of BioengineeringRice UniversityHoustonUSA
  9. 9.Weldon School of Biomedical EngineeringPurdue UniversityWest LafayetteUSA
  10. 10.Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  11. 11.Houston Methodist DeBakey Heart & Vascular CenterHoustonUSA
  12. 12.Department of MathematicsUniversity of HoustonHoustonUSA
  13. 13.Department of Mathematics, Center for Interdisciplinary Applied MathematicsUniversity of North Carolina at Chapel HillChapel HillUSA
  14. 14.McAllister Heart InstituteUniversity of North Carolina at Chapel Hill School of MedicineChapel HillUSA

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