Biomechanical Behavior of Bioprosthetic Heart Valve Heterograft Tissues: Characterization, Simulation, and Performance

Abstract

The use of replacement heart valves continues to grow due to the increased prevalence of valvular heart disease resulting from an ageing population. Since bioprosthetic heart valves (BHVs) continue to be the preferred replacement valve, there continues to be a strong need to develop better and more reliable BHVs through and improved the general understanding of BHV failure mechanisms. The major technological hurdle for the lifespan of the BHV implant continues to be the durability of the constituent leaflet biomaterials, which if improved can lead to substantial clinical impact. In order to develop improved solutions for BHV biomaterials, it is critical to have a better understanding of the inherent biomechanical behaviors of the leaflet biomaterials, including chemical treatment technologies, the impact of repetitive mechanical loading, and the inherent failure modes. This review seeks to provide a comprehensive overview of these issues, with a focus on developing insight on the mechanisms of BHV function and failure. Additionally, this review provides a detailed summary of the computational biomechanical simulations that have been used to inform and develop a higher level of understanding of BHV tissues and their failure modes. Collectively, this information should serve as a tool not only to infer reliable and dependable prosthesis function, but also to instigate and facilitate the design of future bioprosthetic valves and clinically impact cardiology.

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Abbreviations

AHA:

American Heart Association

AV:

Aortic valve

BHV:

Bioprosthetic heart valve

BP:

Bovine pericardium

ECM:

Extracellular matrix

FE:

Finite element

GAG:

Glycosaminoglycan

GLBP:

Glutaraldehyde bovine pericardium

GLUT:

Gluraraldehyde treatment

LEHI:

Linear elastic homogeneous incompressible

microCT:

Micro X-ray computed tomography

MRI:

Magnetic resonance images

MV:

Mitral valve

PAV:

Porcine aortic valve

PBS:

Phosphate buffered saline

PD:

Preferred direction

RVE:

Representative volume element

SALS:

Small angle light scattering

TEHV:

Tissue-engineered heart valve

UTS:

Ultimate tensile stregth

VEC:

Valvular endothelial cell

VIC:

Valvular interstitial cell

XD:

Cross-preferred direction

ΔM:

Infinitesimal mass

ΔV:

Infinitesimal volume

ρ:

Mass density

\( \varepsilon \) :

Fiber uniaxial strain (in structural constitutive model)

\( \theta \) :

Fiber orientation angle (in structural constitutive model)

cf :

Volume fraction of fibers (in structural constitutive model)

C :

Left Cauchy-Green stretch tensor

\( D(\varepsilon ) \) :

Fiber recruitment statistical distribution (in structural constitutive model)

E :

Green–Lagrange strain tensor

E ij :

Components of the Green-Lagrange strain tensor

\( I(\theta ) \) :

Angular distribution of scattered light (in SALS analysis)

\( R(\theta ) \) :

Fiber angular distribution (in structural constitutive model)

S :

Second Piola–Kirchhoff stress tensor

Sij :

Components of the second Piola–Kirchhoff stress tensor

\( {\mathbf{S}}^{f} \) :

Second Piola–Kirchhoff stress tensor in the fiber (in structural constitutive model)

\( S_{nn}^{f} \) :

Component of the Piola–Kirchhoff stress tensor in the fiber along fiber direction (in structural constitutive model)

W:

Stored energy function

\( w(\varepsilon ) \) :

Stored energy function of fiber (in structural constitutive model)

Wf :

Stored energy function of the fiber ensemble (in structural constitutive model)

Wm :

Stored energy function of the matrix (in structural constitutive model)

I1, I2, I3 :

Principal invariants of the left Cauchy-Green stretch tensor

References

  1. 1.

    Aggarwal, A., G. Ferrari, E. Joyce, M. J. Daniels, R. Sainger, J. H. Gorman, 3rd, et al. Architectural trends in the human normal and bicuspid aortic valve leaflet and its relevance to valve disease. Ann. Biomed. Eng. 42(5):986–998, 2014. doi:10.1007/s10439-014-0973-0.

    Article  Google Scholar 

  2. 2.

    Aggarwal, A., and M. Sacks. A framework for determination of heart valves’ mechanical properties using inverse-modeling approach. In: Functional Imaging and Modeling of the Heart, edited by H. van Assen, P. Bovendeerd, and T. Delhaas. Lecture Notes in Computer Science: Springer International Publishing, 2015, pp. 285–294.

    Google Scholar 

  3. 3.

    Ali, A., J. C. Halstead, F. Cafferty, L. Sharples, F. Rose, R. Coulden, et al. Are stentless valves superior to modern stented valves? A prospective randomized trial. Circulation. 114(1 Suppl):I535–I540, 2006. doi:10.1161/CIRCULATIONAHA.105.000950.

    Google Scholar 

  4. 4.

    Amini, R., C. E. Eckert, K. Koomalsingh, J. McGarvey, M. Minakawa, J. H. Gorman, et al. On the in vivo deformation of the mitral valve anterior leaflet: effects of annular geometry and referential configuration. Ann. Biomed. Eng. 40(7):1455–1467, 2012. doi:10.1007/s10439-012-0524-5.

    Article  Google Scholar 

  5. 5.

    Astorino, M., J.-F. Gerbeau, O. Pantz, and K.-F. Traoré. Fluid-structure interaction and multi-body contact: application to aortic valves. Comput. Method Appl. Mech. Eng. 198:3603–3612, 2009.

    MathSciNet  MATH  Article  Google Scholar 

  6. 6.

    Baaijens, F. P. T. A fictitious domain/mortar element method for fluid-structure interaction. Int. J. Numer. Methods Fluids 35(7):743–761, 2001.

    MathSciNet  MATH  Article  Google Scholar 

  7. 7.

    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(1):23–30, 2000.

    Article  Google Scholar 

  8. 8.

    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(4):327–335, 2000.

    Article  Google Scholar 

  9. 9.

    Black, M. M., I. C. Howard, X. Huang, and E. A. Patterson. A three-dimensional analysis of a bioprosthetic heart valve. J. Biomech. 24(9):793–801, 1991.

    Article  Google Scholar 

  10. 10.

    Blackstone, E. H. Could it happen again? The Bjork-Shiley convexo-concave heart valve story. Circulation 111(21):2717–2719, 2005.

    Article  Google Scholar 

  11. 11.

    Bogaers, A. E. J., S. Kok, B. D. Reddy, and T. Franz. Quasi-Newton methods for implicit black-box FSI coupling. Comput. Method Appl. Mech. Eng. 279:113–132, 2014.

    MathSciNet  Article  Google Scholar 

  12. 12.

    Borazjani, I. Fluid-structure interaction, immersed boundary-finite element method simulations of bio-prosthetic heart valves. Comput. Method Appl. Mech. Eng. 257:103–116, 2013.

    MathSciNet  MATH  Article  Google Scholar 

  13. 13.

    Borazjani, I., L. Ge, and F. Sotiropoulos. Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. J. Comput. Phys. 227(16):7587–7620, 2008.

    MathSciNet  MATH  Article  Google Scholar 

  14. 14.

    Braunwald, N. S., T. Cooper, and A. G. Morrow. Complete replacement of the mitral valve. Successful clinical application of a flexible polyurethane prosthesis. J. Thorac. Cardiovasc. Surg. 40:1–11, 1960.

    Google Scholar 

  15. 15.

    Buchanan, R. M., and M. S. Sacks. Interlayer micromechanics of the aortic heart valve leaflet. Biomech. Model. Mechanobiol. 2013. doi:10.1007/s10237-013-0536-6.

    Google Scholar 

  16. 16.

    Buehler, M. J. Atomistic and continuum modeling of mechanical properties of collagen: Elasticity, fracture, and self-assembly. J. Mater. Res. 21(08):1947–1961, 2006. doi:10.1557/jmr.2006.0236.

    Article  Google Scholar 

  17. 17.

    Burriesci, G., I. C. Howard, and E. A. Patterson. Influence of anisotropy on the mechanical behaviour of bioprosthetic heart valves. J. Med. Eng. Technol. 23(6):203–215, 1999.

    Article  Google Scholar 

  18. 18.

    Cacciola, G., G. W. Peters, and F. P. Baaijens. A synthetic fiber-reinforced stentless heart valve. J. Biomech. 33(6):653–658, 2000.

    Article  Google Scholar 

  19. 19.

    Cacciola, G., G. W. Peters, and P. J. Schreurs. A three-dimensional mechanical analysis of a stentless fibre-reinforced aortic valve prosthesis. J. Biomech. 33(5):521–530, 2000.

    Article  Google Scholar 

  20. 20.

    Carew, E. O., A. Garg, J. E. Barber, and I. Vesely. Stress relaxation preconditioning of porcine aortic valves. Ann. Biomed. Eng. 32(4):563–572, 2004.

    Article  Google Scholar 

  21. 21.

    Carmody, C. J., G. Burriesci, I. C. Howard, and E. A. Patterson. An approach to the simulation of fluid-structure interaction in the aortic valve. J. Biomech. 39:158–169, 2006.

    Article  Google Scholar 

  22. 22.

    Cataloglu, A., R. E. Clark, and P. L. Gould. Stress analysis of aortic-valve leaflets with smoothed geometrical data. J. Biomech. 10(3):153–158, 1977. doi:10.1016/0021-9290(77)90053-7.

    Article  Google Scholar 

  23. 23.

    Chandran, K. B. Role of computational simulations in heart valve dynamics and design of valvular prostheses. Cardiovascular engineering and technology. 1(1):18–38, 2010. doi:10.1007/s13239-010-0002-x.

    Article  Google Scholar 

  24. 24.

    Chew, G. G., I. C. Howard, and E. A. Patterson. Simulation of damage in a porcine prosthetic heart valve. J. Med. Eng. Technol. 23(5):178–189, 1999.

    Article  Google Scholar 

  25. 25.

    Chew, P. H., F. C. Yin, and S. L. Zeger. Biaxial stress-strain properties of canine pericardium. J. Mol. Cell. Cardiol. 18(6):567–578, 1986.

    Article  Google Scholar 

  26. 26.

    Choi, H. S., and R. P. Vito. Two-dimensional stress-strain relationship for canine pericardium. J. Biomech. Eng. 112(2):153–159, 1990.

    Article  Google Scholar 

  27. 27.

    Christie, G. W. Anatomy of aortic heart valve leaflets: the influence of glutaraldehyde fixation on function. Eur. J. Cardiothorac. Surg. 6:S25–S33, 1992.

    Article  Google Scholar 

  28. 28.

    Christie, G., and B. Barratt-Boyes, editors Time-dependent changes to the leaflet elasticity of the Medtronic Intact valve in vivo. World Symposium on Heart Valve Disease, London; 1999.

  29. 29.

    Chuong, C. J., and Y. C. Fung. Three-dimensional stress distribution in arteries. J. Biomech. Eng. 105(3):268–274, 1983.

    Article  Google Scholar 

  30. 30.

    Chuong, C. J., and Y. C. Fung. On residual stresses in arteries. J. Biomech. Eng. 108(2):189–192, 1986.

    Article  Google Scholar 

  31. 31.

    Cohn, L. H. Cutler, Elliot, Carr mitral-valve surgery at Peter-Bent-Brigham-Hospital 1923. J. Card. Surg. 9:137–138, 1994.

    Article  Google Scholar 

  32. 32.

    Cohn, L. H., J. J. Collins, Jr, V. J. Disesa, G. S. Couper, P. S. Peigh, W. Kowalker, et al. Fifteen-year experience with 1678 Hancock Porcine bioprosthetic heart vavle replacements. Ann. Surg. 210(4):435–442, 1989.

    Article  Google Scholar 

  33. 33.

    Conti, C. A., E. Votta, A. Della Corte, L. Del Viscovo, C. Bancone, M. Cotrufo, et al. Dynamic finite element analysis of the aortic root from MRI-derived parameters. Med. Eng. Phys. 32(2):212–221, 2010. doi:10.1016/j.medengphy.2009.12.003.

    Article  Google Scholar 

  34. 34.

    Courant, R., K. Friedrichs, and H. Lewy. Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100(1):32–74, 1928.

    MathSciNet  MATH  Article  Google Scholar 

  35. 35.

    Courant, R., K. Friedrichs, and H. Lewy. On the partial difference equations of mathematical physics. IBM J. Res. Develop. 11:215–234, 1967.

    MathSciNet  MATH  Article  Google Scholar 

  36. 36.

    Crofts, C. E., and E. A. Trowbridge. The tensile strength of natural and chemically modified bovine pericardium. J. Biomed. Mater. Res. 22:89–98, 1988.

    Article  Google Scholar 

  37. 37.

    de Hart, J. Fluid-Structure Interaction in the Aortic Heart Valve: a three-dimensional computational analysis (Ph.D. Thesis). Eindhoven: Technische Universiteit Eindhoven, 2002.

    Google Scholar 

  38. 38.

    De Hart, J., F. P. Baaijens, G. W. Peters, and P. J. Schreurs. A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve. J. Biomech. 36(5):699–712, 2003.

    Article  Google Scholar 

  39. 39.

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

    Article  Google Scholar 

  40. 40.

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

    MATH  Article  Google Scholar 

  41. 41.

    Donea, J., A. Huerta, J.-P. Ponthot, and A. Rodriguez-Ferran. Arbitrary Lagrangian-Eulerian Methods. Encyclopedia of Computational Mechanics. New York: Wiley, 2004.

    Google Scholar 

  42. 42.

    Driessen, N. J., C. V. Bouten, and F. P. Baaijens. A structural constitutive model for collagenous cardiovascular tissues incorporating the angular fiber distribution. J. Biomech. Eng. 127(3):494–503, 2005.

    Article  Google Scholar 

  43. 43.

    Eckert, C. E., R. Fan, B. Mikulis, M. Barron, C. A. Carruthers, V. M. Friebe, et al. On the biomechanical role of glycosaminoglycans in the aortic heart valve leaflet. Acta Biomater. 9(1):4653–4660, 2013. doi:10.1016/j.actbio.2012.09.031.

    Article  Google Scholar 

  44. 44.

    Engelmayr, Jr, G. C., D. K. Hildebrand, F. W. Sutherland, J. E. Mayer, Jr, and M. S. Sacks. A novel bioreactor for the dynamic flexural stimulation of tissue engineered heart valve biomaterials. Biomaterials 24(14):2523–2532, 2003.

    Article  Google Scholar 

  45. 45.

    Engelmayr, G. C., and M. S. Sacks. A structural model for the flexural mechanics of nonwoven tissue engineering scaffolds. J. Biomech. Eng. 128:610–622, 2006.

    Article  Google Scholar 

  46. 46.

    Ennker, J., A. Albert, and I. C. Ennker. Stentless aortic valves. Current aspects. HSR Proc. Intens. Care Cardiovasc. Anesthesia. 4(2):77–82, 2012.

    Google Scholar 

  47. 47.

    Fan, R., and M. S. Sacks. Simulation of planar soft tissues using a structural constitutive model: finite element implementation and validation. J. Biomech. 47:2043–2054, 2014.

    Article  Google Scholar 

  48. 48.

    Fata, B., C. A. Carruthers, G. Gibson, S. Watkins, D. Gottlieb, J. E. Mayer, Jr, et al. Regional structural and biomechanical alterations of the ovine main pulmonary artery during postnatal growth. J. Biomech. Eng. 135(2):0210221–02102211, 2013.

    Article  Google Scholar 

  49. 49.

    Fata, B., W. Zhang, R. Amini, and M. Sacks. Insights into regional adaptations in the growing pulmonary artery using a meso-scale structural model: effects of ascending aorta impingement. J. Biomech. Eng. 2014. doi:10.1115/1.4026457.

    Google Scholar 

  50. 50.

    Freed, A. D., and T. C. Doehring. Elastic model for crimped collagen fibrils. J. Biomech. Eng. 127(4):587–593, 2005.

    Article  Google Scholar 

  51. 51.

    Funder JA. Current status on stentless aortic bioprosthesis: a clinical and experimental perspective. Eur. J. Cardiothorac. Surg. 41(4):790–799, 2012. doi:10.1093/ejcts/ezr141.

    Article  Google Scholar 

  52. 52.

    Gabbay, S., U. Bortolotti, F. Wasserman, N. Tindel, S. M. Factor, and R. W. Frater. Long-term follow-up of the Ionescu-Shiley mitral pericardial xenograft. J. Thorac. Cardiovasc. Surg. 88(5 Pt 1):758–763, 1984.

    Google Scholar 

  53. 53.

    Gao, B. Z., S. Pandya, C. Arana, and N. H. C. Hwang. Bioprosthetic heart valve leaflet deformation monitored by double-pulse stereo photogrammetry. Ann. Biomed. Eng. 30(1):11–18, 2002.

    Article  Google Scholar 

  54. 54.

    Gao, Z. B., S. Pandya, N. Hosein, M. S. Sacks, and N. H. C. Hwang. Bioprosthetic heart valve leaflet motion monitored by dual camera stereo photogrammetry. J. Biomech. 33(2):199–207, 2000. doi:10.1016/S0021-9290(99)00165-7.

    Article  Google Scholar 

  55. 55.

    Garikipati, K., S. Göktepe, and C. Miehe. Elastica-based strain energy functions for soft biological tissue. J. Mech. Phys. Solids 56(4):1693–1713, 2008. doi:10.1016/j.jmps.2007.07.005.

    MathSciNet  MATH  Article  Google Scholar 

  56. 56.

    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(2):1782–1809, 2007.

    MathSciNet  MATH  Article  Google Scholar 

  57. 57.

    Gilmanov, A., T. B. Le, and F. Sotiropoulos. A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains. J. Comput. Phys. 300:814–843, 2015. doi:10.1016/j.jcp.2015.08.008.

    MathSciNet  Article  Google Scholar 

  58. 58.

    Gilmanov, A., and F. Sotiropoulos. Comparative hemodynamics in an aorta with bicuspid and trileaflet valves. Theoret. Comput. Fluid Dyn. 30(1):67–85, 2015. doi:10.1007/s00162-015-0364-7.

    Google Scholar 

  59. 59.

    Gingold, R. A., and J. J. Monaghan. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181(3):375–389, 1977. doi:10.1093/mnras/181.3.375.

    MATH  Article  Google Scholar 

  60. 60.

    Girardot, M. N., M. Torrianni, and J. M. Girardot. Effect of AOA on glutaraldehyde-fixed bioprosthetic heart vavlve cusps and walls: binding and calcification studies. Int. J. Artif. Organs 17:76–82, 1994.

    Google Scholar 

  61. 61.

    Gloeckner, D. C., K. L. Billiar, and M. S. Sacks. Effects of mechanical fatigue on the bending properties of the porcine bioprosthetic heart valve. ASAIO J. 45(1):59–63, 1999. doi:10.1097/00002480-199901000-00014.

    Article  Google Scholar 

  62. 62.

    Gnyaneshwar, R., R. K. Kumar, and K. R. Balakrishnan. Dynamic analysis of the aortic valve using a finite element model. Ann. Thorac. Surg. 73(4):1122–1129, 2002.

    Article  Google Scholar 

  63. 63.

    Go, A. S., D. Mozaffarian, V. L. Roger, E. J. Benjamin, J. D. Berry, M. J. Blaha, et al. Heart disease and stroke statistics—2014 update: a report from the American Heart Association. Circulation 129(3):e28–e292, 2014. doi:10.1161/01.cir.0000441139.02102.80.

    Article  Google Scholar 

  64. 64.

    Go, A., D. Mozaffarian, V. Roger, E. Benjamin, J. Berry, W. Borden, et al. Heart disease and stroke statistics—2013 update: a report from the American Heart Association. Circulation 127(1):e6–e245, 2013.

    Article  Google Scholar 

  65. 65.

    Gorman, 3rd, J. H., R. C. Gorman, B. M. Jackson, Y. Enomoto, M. G. St John-Sutton, and L. H. Edmunds, Jr. Annuloplasty ring selection for chronic ischemic mitral regurgitation: lessons from the ovine model. Ann. Thorac. Surg. 76(5):1556–1563, 2003.

    Article  Google Scholar 

  66. 66.

    Gorman, 3rd, J. H., K. B. Gupta, J. T. Streicher, R. C. Gorman, B. M. Jackson, M. B. Ratcliffe, et al. Dynamic three-dimensional imaging of the mitral valve and left ventricle by rapid sonomicrometry array localization. J. Thorac. Cardiovasc. Surg. 112(3):712–726, 1996.

    Article  Google Scholar 

  67. 67.

    Gould, P. L., A. Cataloglu, G. Dhatt, A. Chattopadhyay, and R. E. Clark. Stress analysis of the human aortic valve. Comput. Struct. 3(2):377–384, 1973.

    Article  Google Scholar 

  68. 68.

    Grande, K. J., R. P. Cochran, P. G. Reinhall, and K. S. Kunzelman. Stress variations in the human aortic root and valve: The role of anatomic asymmetry. Ann. Biomed. Eng. 26(4):534–545, 1998. doi:10.1114/1.122.

    Article  Google Scholar 

  69. 69.

    Grande, K. J., R. P. Cochran, P. G. Reinhall, and K. S. Kunzelman. Mechanisms of aortic valve incompetence in aging: a finite element model. J. Heart Valve Dis. 8(2):149–156, 1999.

    Google Scholar 

  70. 70.

    Grande, K. J., R. P. Cochran, P. G. Reinhall, and K. S. Kunzelman. Mechanisms of aortic valve incompetence: finite element modeling of aortic root dilatation. Ann. Thorac. Surg. 69(6):1851–1857, 2000.

    Article  Google Scholar 

  71. 71.

    Grande-Allen, K. J., R. P. Cochran, P. G. Reinhall, and K. S. Kunzelman. Re-creation of sinuses is important for sparing the aortic valve: a finite element study. J. Thorac. Cardiovasc. Surg. 119(4 Pt 1):753–763, 2000.

    Article  Google Scholar 

  72. 72.

    Grande-Allen, K. J., R. P. Cochran, P. G. Reinhall, and K. S. Kunzelman. Mechanisms of aortic valve incompetence: finite-element modeling of Marfan syndrome. J. Thorac. Cardiovasc. Surg. 122(5):946–954, 2001. doi:10.1067/mtc.2001.116314.

    Article  Google Scholar 

  73. 73.

    Grande-Allen, K. J., R. P. Cochran, P. G. Reinhall, and K. S. Kunzelman. Finite-element analysis of aortic valve-sparing: influence of graft shape and stiffness. IEEE Trans Biomed. Eng. 48(6):647–659, 2001. doi:10.1109/10.923783.

    Article  Google Scholar 

  74. 74.

    Grant, C. W., and B. G. Barrat-Boyes. Mechanical properties of porcine pulmonary valve leaflets: how do they differ from aortic leaflets. Ann. Thorac. Surg. 60(Supplement 2):S195–S199, 1995.

    Google Scholar 

  75. 75.

    Grashow, J. S., M. S. Sacks, J. Liao, and A. P. Yoganathan. Planar biaxial creep and stress relaxation of the mitral valve anterior leaflet. Ann. Biomed. Eng. 34(10):1509–1518, 2006.

    Article  Google Scholar 

  76. 76.

    Grashow, J. S., A. P. Yoganathan, and M. S. Sacks. Biaixal stress-stretch behavior of the mitral valve anterior leaflet at physiologic strain rates. Ann. Biomed. Eng. 34(2):315–325, 2006. doi:10.1007/s10439-005-9027-y.

    Article  Google Scholar 

  77. 77.

    Griffith, B. E. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions. Int. J. Numer. Methods Biomed. Eng. 28(3):317–345, 2012.

    MathSciNet  MATH  Article  Google Scholar 

  78. 78.

    Hamid, M. S., H. N. Sabbah, and P. D. Stein. Comparison of finite-element stress-analysis of aortic-valve leaflet using either membrane elements or solid elements. Comput. Struct. 20(6):955–961, 1985. doi:10.1016/0045-7949(85)90015-X.

    MATH  Article  Google Scholar 

  79. 79.

    Hamid, M. S., H. N. Sabbah, and P. D. Stein. Influence of stent height upon stresses on the cusps of closed bioprosthetic valves. J. Biomech. 19:759–769, 1986.

    Article  Google Scholar 

  80. 80.

    Hamid, M. S., H. N. Sabbah, and P. D. Stein. Influence of stent height upon stresses on the cusps of closed bioprosthetic valves. J. Biomech. 19(9):759–769, 1986. doi:10.1016/0021-9290(86)90199-5.

    Article  Google Scholar 

  81. 81.

    Harada, Y., M. Kawada, K. Ishihara, M. Higashidate, H. Kurosawa, and Y. Imai. A new valved conduit with commissures using a glutaraldehyde preserved equine pericardium. Kyobu Geka. 42(6):457–459, 1989.

    Google Scholar 

  82. 82.

    Harken, D. E., H. S. Soroff, W. J. Taylor, A. A. Lefemine, S. K. Gupta, and S. Lunzer. Partial and complete prostheses in aortic insufficiency. J. Thorac. Cardiovasc. Surg. 40:744–762, 1960.

    Google Scholar 

  83. 83.

    Hiester, E. D., and M. S. Sacks. Optimal bovine pericardial tissue selection sites. I. Fiber architecture and tissue thickness measurements. J. Biomed. Mater. Res. 39(2):207–214, 1998.

    Article  Google Scholar 

  84. 84.

    Hiester, E. D., and M. S. Sacks. Optimal bovine pericardial tissue selection sites. II. Cartographic analysis. J. Biomed. Mater. Res. 39(2):215–221, 1998.

    Article  Google Scholar 

  85. 85.

    Hilbert, S. L., V. J. Ferrans, and W. M. Swanson. Optical methods for the nondestructive evaluation of collagen morphology in bioprosthetic heart valves. J. Biomed. Mater. Res. 20(9):1411–1421, 1986. doi:10.1002/jbm.820200914.

    Article  Google Scholar 

  86. 86.

    Holzapfel, G. A., T. C. Gasser, and R. W. Ogden. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elasticity. 61(1–3):1–48, 2000. doi:10.1023/A:1010835316564.

    MathSciNet  MATH  Article  Google Scholar 

  87. 87.

    Howard, I. C., E. A. Patterson, and A. Yoxall. On the opening mechanism of the aortic valve: some observations from simulations. J. Med. Eng. Technol. 27(6):259–266, 2003. doi:10.1080/0309190031000096621.

    Article  Google Scholar 

  88. 88.

    Hsu, M.-C., D. Kamensky, Y. Bazilevs, M. S. Sacks, and T. J. R. Hughes. Fluid-structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput. Mech. 54:1055–1071, 2014.

    MathSciNet  MATH  Article  Google Scholar 

  89. 89.

    Hsu, M.-C., D. Kamensky, F. Xu, J. Kiendl, C. Wang, M. C. H. Wu, et al. Dynamic and fluid-structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models. Comput. Mech. 55:1211–1225, 2015.

    MATH  Article  Google Scholar 

  90. 90.

    Huang, X., M. M. Black, I. C. Howard, and E. A. Patterson. A two-dimensional finite element analysis of a bioprosthetic heart valve. J. Biomech. 23(8):753–762, 1990.

    Article  Google Scholar 

  91. 91.

    Huang, H. Y., J. Liao, and M. S. Sacks. In-situ deformation of the aortic valve interstitial cell nucleus under diastolic loading. J. Biomech. Eng. 129(6):880–889, 2007. doi:10.1115/1.2801670.

    Article  Google Scholar 

  92. 92.

    Hughes, T. J. R., J. A. Cottrell, and Y. Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput. Methods Appl. Mech. Eng. 194:4135–4195, 2005.

    MathSciNet  MATH  Article  Google Scholar 

  93. 93.

    Hughes, T. J. R., W. K. Liu, and T. K. Zimmermann. Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput. Method Appl. Mech. Eng. 29:329–349, 1981.

    MathSciNet  MATH  Article  Google Scholar 

  94. 94.

    Humphrey, J. D. Cardiovascular solid mechanics: cells, tissues, and organs. Lightning Source: UKltd, 2002.

    Google Scholar 

  95. 95.

    Humphrey, J. D., R. K. Strumpf, and F. C. Yin. Determination of a constitutive relation for passive myocardium: I. A new functional form. J. Biomech. Eng. 112(3):333–339, 1990.

    Article  Google Scholar 

  96. 96.

    Humphrey, J. D., R. K. Strumpf, and F. C. Yin. Determination of a constitutive relation for passive myocardium: II. Parameter estimation. J Biomech Eng. 112(3):340–346, 1990.

    Article  Google Scholar 

  97. 97.

    Humphrey, J. D., R. K. Strumpf, and F. C. Yin. A constitutive theory for biomembranes: application to epicardial mechanics. J. Biomech. Eng. 114(4):461–466, 1992.

    Article  Google Scholar 

  98. 98.

    Humphrey, J. D., D. L. Vawter, and R. P. Vito. Mechanical behavior of excised canine visceral pleura. Ann. Biomed. Eng. 14(5):451–466, 1986.

    Article  Google Scholar 

  99. 99.

    Iyengar, A. K. S., H. Sugimoto, D. B. Smith, and M. S. Sacks. Dynamic in vitro quantification of bioprosthetic heart valve leaflet motion using structured light projection. Ann. Biomed. Eng. 29(11):963–973, 2001.

    Article  Google Scholar 

  100. 100.

    Jamieson, W. R. L. H., L. H. Burr, G. J. Fradet, R. T. Miyagishima, M. T. Janusz, and S. V. Lichtenstein. Carpentier-Edwards supraannular porcine bioprosthesis evaluation over 15 years. Ann. Thorac. Surg. 66(6 Suppl):S49–S52, 1998.

    Article  Google Scholar 

  101. 101.

    Jennings, L. M., M. Butterfield, C. Booth, K. G. Watterson, and J. Fisher. The pulmonary bioprosthetic heart valve: its unsuitability for use as an aortic valve replacement. J. Heart Valve Dis. 11(5):668–678, 2002.

    Google Scholar 

  102. 102.

    Johnson, A. A., and T. E. Tezduyar. Parallel Computation of Incompressible Flows with Complex Geometries. Int J Numer Meth Fl. 24:1321–1340, 1997.

    MATH  Article  Google Scholar 

  103. 103.

    Johnson, A. A., and T. E. Tezduyar. 3d simulation of fluid-particle interactions with the number of particles reaching 100. Comput. Method Appl. Mech. Eng. 145:301–321, 1997.

    MATH  Article  Google Scholar 

  104. 104.

    Johnson, A. A., and T. E. Tezduyar. Advanced mesh generation and update methods for 3D flow simulations. Comput. Mech. 23:130–143, 1999.

    MATH  Article  Google Scholar 

  105. 105.

    Jones, M., E. E. Eidbo, S. L. Hilbert, V. J. Ferrans, and R. E. Clark. Anticalcification treatments of bioprosthetic heart valves: in vivo studies in sheep. J. Card. Surg. 4(1):69–73, 1989.

    Article  Google Scholar 

  106. 106.

    Jouan, J. Mitral valve repair over five decades. Ann. Cardiothorac. Surg. 4(4):322–334, 2015. doi:10.3978/j.issn.2225-319X.2015.01.07.

    Google Scholar 

  107. 107.

    Kamensky, D., M.-C. Hsu, D. Schillinger, J. A. Evans, A. Aggarwal, Y. Bazilevs, et al. An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves. Comput. Method Appl. Mech. Eng. 284:1005–1053, 2015.

    MathSciNet  Article  Google Scholar 

  108. 108.

    Kiendl, J. Isogeometric Analysis and Shape Optimal Design of Shell Structures. Lehrstuhl für Statik: Technische Universität München, München, 2011.

    Google Scholar 

  109. 109.

    Kiendl, J., K.-U. Bletzinger, J. Linhard, and R. Wüchner. Isogeometric shell analysis with Kirchhoff-Love elements. Comput. Method Appl. Mech. Eng. 198:3902–3914, 2009.

    MathSciNet  MATH  Article  Google Scholar 

  110. 110.

    Kiendl, J., M.-C. Hsu, M. C. H. Wu, and A. Reali. Isogeometric Kirchhoff-Love shell formulations for general hyperelastic materials. Comput. Method Appl. Mech. Eng. 291:280–303, 2015.

    MathSciNet  Article  Google Scholar 

  111. 111.

    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(1):30–44, 2007. doi:10.1007/s10439-006-9203-8.

    Article  Google Scholar 

  112. 112.

    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(2):262–275, 2008. doi:10.1007/s10439-007-9409-4.

    Article  Google Scholar 

  113. 113.

    Kronick, P. L., and M. S. Sacks. Matrix macromolecules that affect the viscoelasticity of calfskin. J Biomech Eng-T ASME. 116(2):140–145, 1994. doi:10.1115/1.2895712.

    Article  Google Scholar 

  114. 114.

    Krucinski, S., I. Vesely, M. A. Dokainish, and G. Campbell. Numerical simulation of leaflet flexure in bioprosthetic valves mounted on rigid and expansile stents. J. Biomech. 26(8):929–943, 1993.

    Article  Google Scholar 

  115. 115.

    Kunzelman, K. S., D. R. Einstein, and R. P. Cochran. Fluid-structure interaction models of the mitral valve: function in normal and pathological states. Philos. Trans. R. Soc. Lond. B Biol. Sci. 362(1484):1393–1406, 2007. doi:10.1098/rstb.2007.2123.

    Article  Google Scholar 

  116. 116.

    Labrosse, M. R., C. J. Beller, M. Boodhwani, C. Hudson, and B. Sohmer. Subject-specific finite-element modeling of normal aortic valve biomechanics from 3D + t TEE images. Med. Image Anal. 20(1):162–172, 2015. doi:10.1016/j.media.2014.11.003.

    Article  Google Scholar 

  117. 117.

    Lanir, Y. A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues. J. Biomech. 12(6):423–436, 1979.

    Article  Google Scholar 

  118. 118.

    Lanir, Y. Plausibility of structural constitutive equations for swelling tissues–implications of the C-N and S-E conditions. J. Biomech. Eng. 118(1):10–16, 1996.

    Article  Google Scholar 

  119. 119.

    Leat, M. E., and J. Fisher. Comparative-study of the function of the abiomed polyurethane heart-valve for use in left-ventricular assist devices. J. Biomed. Eng. 15(6):516–520, 1993. doi:10.1016/0141-5425(93)90068-A.

    Article  Google Scholar 

  120. 120.

    Lee, J. M., and D. R. Boughner. Tissue mechanics of canine pericardium in different test environments. Circ. Res. 49:533–544, 1981.

    Article  Google Scholar 

  121. 121.

    Lee, J. M., D. R. Boughner, and D. W. Courtman. The glutaraldehyde-stabilized porcine aortic valve xenograft. II. Effect of fixation with or without pressure on the tensile viscoelastic properties of the leaflet material. J. Biomed. Mater. Res. 18:79–98, 1984.

    Article  Google Scholar 

  122. 122.

    Lee, J. M., S. A. Haberer, and D. R. Boughner. The bovine pericardial xenograft: I. Effect of fixation in aldehydes without constraint on the tensile properties of bovine pericardium. J. Biomed. Mater. Res. 23:457–475, 1989.

    Article  Google Scholar 

  123. 123.

    Lee, C.-H., W. Zhang, J. Liao, C. A. Carruthers, J. I. Sacks, and M. S. Sacks. On the presence of affine fibril and fiber kinematics in the mitral valve anterior leaflet. Biophys. J. 108(8):2074–2087, 2015. doi:10.1016/j.bpj.2015.03.019.

    Article  Google Scholar 

  124. 124.

    Leeson-Dietrich, J., D. Boughner, and I. Vesely. Porcine pulmonary and aortic valves: a comparison of their tensile viscoelastic properties at physiological strain rates. J. Heart Valve Dis. 4:88–94, 1995.

    Google Scholar 

  125. 125.

    Leon, M. B., C. R. Smith, M. J. Mack, R. R. Makkar, L. G. Svensson, S. K. Kodali, et al. Transcatheter or surgical aortic-valve replacement in intermediate-risk patients. New Engl. J. Med. 2016. doi:10.1056/NEJMoa1514616.

    Google Scholar 

  126. 126.

    Li, J., X. Y. Luo, and Z. B. Kuang. A nonlinear anisotropic model for porcine aortic heart valves. J. Biomech. 34(10):1279–1289, 2001. doi:10.1016/S0021-9290(01)00092-6.

    Article  Google Scholar 

  127. 127.

    Li, K., and W. Sun. Simulated thin pericardial bioprosthetic valve leaflet deformation under static pressure-only loading conditions: implications for percutaneous valves. Ann. Biomed. Eng. 38(8):2690–2701, 2010. doi:10.1007/s10439-010-0009-3.

    Article  Google Scholar 

  128. 128.

    Liao, J., E. M. Joyce, and M. S. Sacks. Effects of decellularization on the mechanical and structural properties of the porcine aortic valve leaflet. Biomaterials 29(8):1065–1074, 2008. doi:10.1016/j.biomaterials.2007.11.007.

    Article  Google Scholar 

  129. 129.

    Liao, J., L. Yang, J. Grashow, and M. S. Sacks, editors. Collagen fibril kinematics in mitral valve leaflet under biaxial elongation, creep, and stress relaxation. Society for Heart Valve Disease Third Biennial Meeting, 2005; Vancouver: SHVD.

  130. 130.

    Liao, J., L. Yang, J. Grashow, and M. S. Sacks. The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet. J. Biomech. Eng. 129(1):78–87, 2007. doi:10.1115/1.2401186.

    Article  Google Scholar 

  131. 131.

    Lo, D., and I. Vesely. Biaxial strain analysis of the porcine aortic valve. Ann. Thorac. Surg. 60(2 Suppl):S374–S378, 1995.

    Article  Google Scholar 

  132. 132.

    Lovekamp, J. J., D. T. Simionescu, J. J. Mercuri, B. Zubiate, M. S. Sacks, and N. R. Vyavahare. Stability and function of glycosaminoglycans in porcine bioprosthetic heart valves. Biomaterials 27(8):1507–1518, 2006. doi:10.1016/j.biomaterials.2005.08.003.

    Article  Google Scholar 

  133. 133.

    Maestro, M. M., J. Turnay, N. Olmo, P. Fernández, D. Suárez, J. M. García Páez, et al. Biochemical and mechanical behavior of ostrich pericardium as a new biomaterial. Acta Biomater. 2(2):213–219, 2006.

    Article  Google Scholar 

  134. 134.

    Makhijani, V. B., H. Q. Yang, P. J. Dionne, and M. J. Thubrikar. Three-dimensional coupled fluid-structure simulation of pericardial bioprosthetic aortic valve function. ASAIO J. 43(5):M387–M392, 1997.

    Article  Google Scholar 

  135. 135.

    Mako, W. J., and I. Vesely. In vivo and in vitro models of calcification in porcine aortic valve cusps. J. Heart Valve Dis. 6(3):316–323, 1997.

    Google Scholar 

  136. 136.

    Martin, C., and W. Sun. Biomechanical characterization of aortic valve tissue in humans and common animal models. J. Biomed. Mater. Res. A 100(6):1591–1599, 2012.

    Article  Google Scholar 

  137. 137.

    Mercuri, J. J., J. J. Lovekamp, D. T. Simionescu, and N. R. Vyavahare. Glycosaminoglycan-targeted fixation for improved bioprosthetic heart valve stabilization. Biomaterials 28(3):496–503, 2007. doi:10.1016/j.biomaterials.2006.09.005.

    Article  Google Scholar 

  138. 138.

    Merryman, W. D., H. Y. Huang, F. J. Schoen, and M. S. Sacks. The effects of cellular contraction on aortic valve leaflet flexural stiffness. J. Biomech. 39(1):88–96, 2006.

    Article  Google Scholar 

  139. 139.

    Michler, C., H. van Brummelen, and R. de Borst. An investigation of Interface-GMRES(R) for fluid-structure interaction problems with flutter and divergence. Comput. Mech. 47(1):17–29, 2011.

    MathSciNet  MATH  Article  Google Scholar 

  140. 140.

    Mirnajafi, A., J. M. Raymer, L. R. McClure, and M. S. Sacks. The flexural rigidity of the aortic valve leaflet in the commissural region. J. Biomech. 39(16):2966–2973, 2006. doi:10.1016/j.jbiomech.2005.10.026.

    Article  Google Scholar 

  141. 141.

    Mirnajafi, A., J. Raymer, M. J. Scott, and M. S. Sacks. The effects of collagen fiber orientation on the flexural properties of pericardial heterograft biomaterials. Biomaterials 26(7):795–804, 2005. doi:10.1016/j.biomaterials.2004.03.004.

    Article  Google Scholar 

  142. 142.

    Mirnajafi, A., B. Zubiate, and M. S. Sacks. Effects of cyclic flexural fatigue on porcine bioprosthetic heart valve heterograft biomaterials. J. Biomed. Mater. Res. A. 94(1):205–213, 2010. doi:10.1002/jbm.a.32659.

    Article  Google Scholar 

  143. 143.

    Mittal, R., and G. Iaccarino. Immersed boundary methods. Annu. Rev. Fluid Mech. 37:239–261, 2005.

    MathSciNet  MATH  Article  Google Scholar 

  144. 144.

    Moore, M. A., R. E. Phillips, Jr, B. K. McIlroy, V. M. Walley, and P. J. Hendry. Evaluation of porcine valves prepared by dye-mediated photooxidation. Ann. Thorac. Surg. 66(6 Suppl):S245–S248, 1998.

    Article  Google Scholar 

  145. 145.

    Morganti, S., F. Auricchio, D. J. Benson, F. I. Gambarin, S. Hartmann, T. J. R. Hughes, et al. Patient-specific isogeometric structural analysis of aortic valve closure. Comput. Method Appl. M. 284:508–520, 2015.

    MathSciNet  Article  Google Scholar 

  146. 146.

    Mozaffarian, D., E. J. Benjamin, A. S. Go, D. K. Arnett, M. J. Blaha, M. Cushman, et al. Heart disease and stroke statistics—2015 update: a report from the American Heart Association. Circulation 131(4):e29–e322, 2015. doi:10.1161/CIR.0000000000000152.

    Article  Google Scholar 

  147. 147.

    Neethling, W. M., S. Cooper, J. J. Van Den Heever, J. Hough, and A. J. Hodge. Evaluation of kangaroo pericardium as an alternative substitute for reconstructive cardiac surgery. J. Cardiovasc. Surg. 43(3):301–306, 2002.

    Google Scholar 

  148. 148.

    Parry, D. A. The molecular and fibrillar structure of collagen and its relationship to the mechanical properties of connective tissue. Biophys. Chem. 29(1–2):195–209, 1988.

    Article  Google Scholar 

  149. 149.

    Patterson, E. A., I. C. Howard, and M. A. Thornton. A comparative study of linear and nonlinear simulations of the leaflets in a bioprosthetic heart valve during the cardiac cycle. J. Med. Eng. Technol. 20(3):95–108, 1996. doi:10.3109/03091909609008387.

    Article  Google Scholar 

  150. 150.

    Payne, D. M., H. P. Koka, P. J. Karanicolas, M. W. Chu, A. D. Nagpal, M. Briel, et al. Hemodynamic performance of stentless versus stented valves: a systematic review and meta-analysis. J. Card. Surg. 23(5):556–564, 2008. doi:10.1111/j.1540-8191.2008.00705.x.

    Article  Google Scholar 

  151. 151.

    Pereira, C. A., J. M. Lee, and S. A. Haberer. Effect of alternative crosslinking methods on the low strain rate viscoelastic properties of bovine pericardial bioprosthetic material. J. Biomed. Mater. Res. 24:345–361, 1990.

    Article  Google Scholar 

  152. 152.

    Perez de Arenaza, D., B. Lees, M. Flather, F. Nugara, T. Husebye, M. Jasinski, et al. Randomized comparison of stentless versus stented valves for aortic stenosis: effects on left ventricular mass. Circulation 112(17):2696–2702, 2005. doi:10.1161/CIRCULATIONAHA.104.521161.

    Article  Google Scholar 

  153. 153.

    Peskin, C. S. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10(2):252–271, 1972.

    MATH  Article  Google Scholar 

  154. 154.

    Pibarot, P., and J. G. Dumesnil. Valvular heart disease: changing concepts in disease management. Circulation 119:1034–1048, 2009.

    Article  Google Scholar 

  155. 155.

    Pouch, A., S. Tian, M. Takabe, H. Wang, J. Yuan, A. Cheung, et al. Segmentation of the aortic valve apparatus in 3D echocardiographic images: deformable modeling of a branching medial structure. In: Statistical Atlases and Computational Models of the Heart—Imaging and Modelling Challenges, edited by O. Camara, T. Mansi, M. Pop, K. Rhode, M. Sermesant, and A. Young. Lecture Notes in Computer Science: Springer International Publishing, 2015, pp. 196–203.

    Google Scholar 

  156. 156.

    Quinonez, L. G., R. Breitbart, W. Tworetsky, J. E. Lock, A. C. Marshall, and S. M. Emani. Stented bovine jugular vein graft (Melody valve) for surgical mitral valve replacement in infants and children. J. Thorac. Cardiovasc. Surg. 148(4):1443–1449, 2014. doi:10.1016/j.jtcvs.2013.10.059.

    Article  Google Scholar 

  157. 157.

    Rabkin, E., S. P. Hoerstrup, M. Aikawa, J. E. Mayer, Jr, and F. J. Schoen. Evolution of cell phenotype and extracellular matrix in tissue-engineered heart valves during in vitro maturation and in vivo remodeling. J. Heart Valve Dis. 11(3):308–314, 2002.

    Google Scholar 

  158. 158.

    Roger, V. L., A. S. Go, D. M. Lloyd-Jones, E. J. Benjamin, J. D. Berry, W. B. Borden, et al. Heart disease and stroke statistics—2012 update: a report from the American Heart Association. Circulation 125(1):e2–e220, 2012. doi:10.1161/CIR.0b013e31823ac046.

    Article  Google Scholar 

  159. 159.

    Ross, D. N. Replacement of aortic and mitral valves with a pulmonary autograft. Lancet 2(7523):956–958, 1967.

    Article  Google Scholar 

  160. 160.

    Rousseau, E. P. M., A. A. Vansteenhoven, J. D. Janssen, and H. A. Huysmans. A mechanical analysis of the closed hancock heart-valve prosthesis. J. Biomech. 21(7):545–562, 1988. doi:10.1016/0021-9290(88)90218-7.

    Article  Google Scholar 

  161. 161.

    Sacks, M. S. A structural constitutive model for chemically treated planar tissues under biaxial loading. Comput. Mech. 26(3):243–249, 2000. doi:10.1007/S004660000175.

    MATH  Article  Google Scholar 

  162. 162.

    Sacks, M. S. Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar-collagenous tissues. J. Biomech. Eng. T ASME 125(2):280–287, 2003. doi:10.1115/1.1544508.

    Article  Google Scholar 

  163. 163.

    Sacks, M. S., and C. J. Chuong. Orthotropic mechanical properties of chemically treated bovine pericardium. Ann. Biomed. Eng. 26(5):892–902, 1998. doi:10.1114/1.135.

    Article  Google Scholar 

  164. 164.

    Sacks, M. S., Y. Enomoto, J. R. Graybill, W. D. Merryman, A. Zeeshan, A. P. Yoganathan, et al. In-vivo dynamic deformation of the mitral valve anterior leaflet. Ann. Thorac. Surg. 82(4):1369–1377, 2006. doi:10.1016/j.athoracsur.2006.03.117.

    Article  Google Scholar 

  165. 165.

    Sacks, M. S., A. Mirnajafi, W. Sun, and P. Schmidt. Bioprosthetic heart valve heterograft biomaterials: structure, mechanical behavior and computational simulation. Expert Rev. Med. Devic. 3(6):817–834, 2006. doi:10.1586/17434440.3.6.817.

    Article  Google Scholar 

  166. 166.

    Sacks, M. S., and F. J. Schoen. Collagen fiber disruption occurs independent of calcification in clinically explanted bioprosthetic heart valves. J. Biomed. Mater. Res. 62(3):359–371, 2002.

    Article  Google Scholar 

  167. 167.

    Sacks, M. S., F. J. Schoen, and J. E. Mayer. Bioengineering challenges for heart valve tissue engineering. Annu. Rev. Biomed. Eng. 11:289–313, 2009. doi:10.1146/annurev-bioeng-061008-124903.

    Article  Google Scholar 

  168. 168.

    Sacks, M. S., D. B. Smith, and E. D. Hiester. A small angle light scattering device for planar connective tissue microstructural analysis. Ann. Biomed. Eng. 25(4):678–689, 1997.

    Article  Google Scholar 

  169. 169.

    Sacks, M. S., and W. Sun. Multiaxial mechanical behavior of biological materials. Annu. Rev. Biomed. Eng. 5:251–284, 2003. doi:10.1146/Annurev.Bioeng.5.011303.120714.

    Article  Google Scholar 

  170. 170.

    Sacks, M. S., W. Zhang, and S. Wognum. A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues. Interface Focus. 6(1):20150090, 2016. doi:10.1098/rsfs.2015.0090.

    Article  Google Scholar 

  171. 171.

    Salgo, I. S., J. H. Gorman, R. C. Gorman, B. M. Jackson, F. W. Bowen, T. Plappert, et al. Effect of annular shape on leaflet curvature in reducing mitral leaflet stress. Circulation 106(6):711–717, 2002. doi:10.1161/01.Cir.0000025426.39426.83.

    Article  Google Scholar 

  172. 172.

    Salmasi, M. Y., M. Acharya, N. Humayun, D. Baskaran, S. Hubbard, and H. Vohra. Is valve repair preferable to valve replacement in ischaemic mitral regurgitation? A systematic review and meta-analysis. Eur. J. Cardiothorac. Surg. 2016. doi:10.1093/ejcts/ezw053.

    Google Scholar 

  173. 173.

    Sasaki, N., and S. Odajima. Elongation mechanism of collagen fibrils and force-strain relations of tendon at each level of structural hierarchy. J. Biomech. 29(9):1131–1136, 1996.

    Article  Google Scholar 

  174. 174.

    Sasaki, N., and S. Odajima. Stress-strain curve and Young’s modulus of a collagen molecule as determined by the X-ray diffraction technique. J. Biomech. 29:655–658, 1996.

    Article  Google Scholar 

  175. 175.

    Sauren, A. A., M. C. van Hout, A. A. van Steenhoven, F. E. Veldpaus, and J. D. Janssen. The mechanical properties of porcine aortic valve tissues. J. Biomech. 16(5):327–337, 1983.

    Article  Google Scholar 

  176. 176.

    Schoen, F. Aortic valve structure-function correlations: Role of elastic fibers no longer a stretch of the imagination. J. Heart Valve Dis. 6:1–6, 1997.

    MathSciNet  Google Scholar 

  177. 177.

    Schoen, F. J. Pathologic findings in explanted clinical bioprosthetic valves fabricated from photooxidized bovine pericardium. J. Heart Valve Dis. 7(2):174–179, 1998.

    MathSciNet  Google Scholar 

  178. 178.

    Schoen, F. J., J. Fernandez, L. Gonzalezlavin, and A. Cernaianu. Causes of failure and pathological findings in surgically removed ionescu-shiley standard bovine pericardial heart-valve bioprostheses—emphasis on progressive structural deterioration. Circulation 76(3):618–627, 1987.

    Article  Google Scholar 

  179. 179.

    Siddiqui, R. F., J. R. Abraham, and J. Butany. Bioprosthetic heart valves: modes of failure. Histopathology 55(2):135–144, 2009.

    Article  Google Scholar 

  180. 180.

    Simo, J. C., and D. D. Fox. On a stress resultant geometrically exact shell-model. 1. Formulation and optimal parametrization. Comput. Method Appl. Mech. Eng. 72(3):267–304, 1989. doi:10.1016/0045-7825(89)90002-9.

    MathSciNet  MATH  Article  Google Scholar 

  181. 181.

    Simo, J. C., D. D. Fox, and M. S. Rifai. On a stress resultant geometrically exact shell-model. 3. computational aspects of the nonlinear-theory. Comput. Method Appl. Mech. Eng. 79(1):21–70, 1990. doi:10.1016/0045-7825(90)90094-3.

    MathSciNet  MATH  Article  Google Scholar 

  182. 182.

    Smith, D. B., M. S. Sacks, P. M. Pattany, and R. Schroeder. High-resolution magnetic resonance imaging to characterize the geometry of fatigued porcine bioprosthetic heart valves. J. Heart Valve Dis. 6(4):424–432, 1997.

    Google Scholar 

  183. 183.

    Smith, D. B., M. S. Sacks, P. M. Pattany, and R. Schroeder. Fatigue-induced changes in bioprosthetic heart valve three-dimensional geometry and the relation to tissue damage. J. Heart Valve Dis. 8(1):25–33, 1999.

    Google Scholar 

  184. 184.

    Sotiropoulos, F., and I. Borazjani. A review of state-of-the-art numerical methods for simulating flow through mechanical heart valves. Med. Biol. Eng. Compu. 47(3):245–256, 2009. doi:10.1007/s11517-009-0438-z.

    Article  Google Scholar 

  185. 185.

    Sotiropoulos, F., and X. Yang. Immersed boundary methods for simulating fluid-structure interaction. Prog. Aerosp. Sci. 65:1–21, 2014.

    Article  Google Scholar 

  186. 186.

    Sripathi, V. C., R. K. Kumar, and K. R. Balakrishnan. Further insights into normal aortic valve function: Role of a compliant aortic root on leaflet opening and valve orifice area. Ann. Thorac. Surg. 77(3):844–851, 2004. doi:10.1016/S0003-4975(03)01518-2.

    Article  Google Scholar 

  187. 187.

    Starr, A. The artificial heart valve. Nat. Med. 13:1160–1164, 2007.

    Article  Google Scholar 

  188. 188.

    Stella, J. A., J. Liao, and M. S. Sacks. Time-dependent biaxial mechanical behavior of the aortic heart valve leaflet. J. Biomech. 40(14):3169–3177, 2007. doi:10.1016/j.jbiomech.2007.04.001.

    Article  Google Scholar 

  189. 189.

    Stock, U. A., T. Sakamoto, S. Hatsuoka, D. P. Martin, M. Nagashima, A. M. Moran, et al. Patch augmentation of the pulmonary artery with bioabsorbable polymers and autologous cell seeding. J Thorac Cardiovasc Surg. 120(6):1158–1167, 2000; (discussion 68).

    Article  Google Scholar 

  190. 190.

    Stradins, P., R. Lacis, I. Ozolanta, B. Purina, V. Ose, L. Feldmane, et al. Comparison of biomechanical and structural properties between human aortic and pulmonary valve. Eur. J. Cardiothorac. Surg. 26(3):634–639, 2004.

    Article  Google Scholar 

  191. 191.

    Sturla, F., E. Votta, M. Stevanella, C. A. Conti, and A. Redaelli. Impact of modeling fluid-structure interaction in the computational analysis of aortic root biomechanics. MedEngPhys. 35:1721–1730, 2013.

    Google Scholar 

  192. 192.

    Sugimoto, H., and M. S. Sacks. Effects of leaflet stiffness on in vitro dynamic bioprosthetic heart valve leaflet shape. Cardiovasc. Eng. Technol. 4(1):2–15, 2013.

    Article  Google Scholar 

  193. 193.

    Sun, W., A. Abad, and M. S. Sacks. Simulated bioprosthetic heart valve deformation under quasi-static loading. J. Biomech. Eng. 127(6):905–914, 2005.

    Article  Google Scholar 

  194. 194.

    Sun, W., and M. S. Sacks. Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues. Biomech. Model Mechan. 4(2–3):190–199, 2005. doi:10.1007/S10237-005-0075-X.

    Article  Google Scholar 

  195. 195.

    Sun, W., M. S. Sacks, and M. J. Scott. Effects of boundary conditions on the estimation of the planar biaxial mechanical properties of soft tissues. J. Biomech. Eng. T ASME 127(4):709–715, 2005. doi:10.1115/1.1933931.

    Article  Google Scholar 

  196. 196.

    Sun, W., M. S. Sacks, T. L. Sellaro, W. S. Slaughter, and M. J. Scott. Biaxial mechanical response of bioprosthetic heart valve biomaterials to high in-plane shear. J. Biomech. Eng. 125:372–380, 2003.

    Article  Google Scholar 

  197. 197.

    Sung, H. W., Y. Chang, C. T. Chiu, C. N. Chen, and H. C. Liang. Crosslinking characteristics and mechanical properties of a bovine pericardium fixed with a naturally occurring crosslinking agent. J. Biomed. Mater. Res. 47(2):116–126, 1999.

    Article  Google Scholar 

  198. 198.

    Sung, H. W., Y. Chang, C. T. Chiu, C. N. Chen, and H. C. Liang. Mechanical properties of a porcine aortic valve fixed with a naturally occurring crosslinking agent. Biomaterials 20(19):1759–1772, 1999.

    Article  Google Scholar 

  199. 199.

    Sung, H. W., W. H. Chang, C. Y. Ma, and M. H. Lee. Crosslinking of biological tissues using genipin and/or carbodiimide. J. Biomed. Mater. Res. 63(3):427–438, 2003.

    Article  Google Scholar 

  200. 200.

    Sutherland, F. W., T. E. Perry, Y. Yu, M. C. Sherwood, E. Rabkin, Y. Masuda, et al. From stem cells to viable autologous semilunar heart valve. Circulation 111(21):2783–2791, 2005.

    Article  Google Scholar 

  201. 201.

    Takizawa, K., C. Moorman, S. Wright, J. Christopher, and T. E. Tezduyar. Wall shear stress calculations in space-time finite element computation of arterial fluid-structure interactions. Comput. Mech. 46:31–41, 2010.

    MathSciNet  MATH  Article  Google Scholar 

  202. 202.

    Takizawa, K., T. E. Tezduyar, A. Buscher, and S. Asada. Space-time interface-tracking with topology change (ST-TC). Comput. Mech. 54(4):955–971, 2013.

    MathSciNet  MATH  Article  Google Scholar 

  203. 203.

    Takizawa, K., T. Tezduyar, A. Buscher, and S. Asada. Space-time fluid mechanics computation of heart valve models. Comput. Mech. 54(4):973–986, 2014.

    MathSciNet  MATH  Article  Google Scholar 

  204. 204.

    Tepole, A. B., H. Kabaria, K.-U. Bletzinger, and E. Kuhl. Isogeometric Kirchhoff-Love shell formulations for biological membranes. Comput. Method Appl. Mech. Eng. 293:328–347, 2015.

    MathSciNet  Article  Google Scholar 

  205. 205.

    Tezduyar, T. E. Computation of moving boundaries and interfaces and stabilization parameters. Int. J. Numer. Methods F. 43:555–575, 2003.

    MathSciNet  MATH  Article  Google Scholar 

  206. 206.

    Tezduyar, T., S. Aliabadi, M. Behr, A. Johnson, and S. Mittal. Massively parallel finite element computation of 3D flows—mesh update strategies in computation of moving boundaries and interfaces. Parallel Computational Fluid Dynamics. New Trends and Advances. 1995; pp. 21–30.

  207. 207.

    Tezduyar, T. E., M. Behr, and J. Liou. A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: I1 The concept and the preliminary numerical tests. Comput. Method Appl. Mech. Eng. 94(3):339–351, 1992.

    MathSciNet  MATH  Article  Google Scholar 

  208. 208.

    Tezduyar, T. E., M. Behr, S. Mittal, and J. Liou. A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: II1 Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput. Method Appl. Mech. Eng. 94(3):353–371, 1992.

    MathSciNet  MATH  Article  Google Scholar 

  209. 209.

    Thornton, M. A., L. C. Howard, and E. A. Patterson. Three-dimensional stress analysis of polypropylene leaflets for prosthetic heart valves. Med. Eng. Phys. 19(6):588–597, 1997. doi:10.1016/S1350-4533(96)00042-2.

    Article  Google Scholar 

  210. 210.

    Thubrikar, M. The Aortic Valve. Boca Raton: CRC, 1990.

    Google Scholar 

  211. 211.

    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(1):115–125, 1983.

    Google Scholar 

  212. 212.

    Thubrikar, M. J., J. L. Heckman, and S. P. Nolan. High speed cine-radiographic study of aortic valve leaflet motion. J. Heart Valve Dis. 2(6):653–661, 1993.

    Google Scholar 

  213. 213.

    Thubrikar, M. J., J. R. Skinner, R. T. Eppink, and S. P. Nolan. Stress analysis of porcine bioprosthetic heart valves in vivo. J. Biomed. Mater. Res. 16(6):811–826, 1982. doi:10.1002/jbm.820160607.

    Article  Google Scholar 

  214. 214.

    Toma, M., M. O. Jensen, D. R. Einstein, A. P. Yoganathan, R. P. Cochran, and K. S. Kunzelman. Fluid-structure interaction analysis of papillary muscle forces using a comprehensive mitral valve model with 3D chordal structure. Ann. Biomed. Eng. 2015. doi:10.1007/s10439-015-1385-5.

    Google Scholar 

  215. 215.

    Tong, P., and Y. C. Fung. The stress-strain relationship for the skin. J. Biomech. 9(10):649–657, 1976.

    Article  Google Scholar 

  216. 216.

    Trowbridge, E. A., and C. E. Crofts. Pericardial heterograft valves: an assessment of leaflet stresses and their implications for heart valve design. J. Biomed. Eng. 9(4):345–355, 1987.

    Article  Google Scholar 

  217. 217.

    Trowbridge, E. A., P. V. Lawford, and C. E. Crofts. Pericardial heterografts: a comparative study of suture pull-out and tissue strength. J. Biomed. Eng. 11(4):311–314, 1989.

    Article  Google Scholar 

  218. 218.

    van Brummelen, E. H. Added mass effects of compressible and incompressible flows in fluid-structure interaction. J. Appl. Mech. 76:021206, 2009.

    Article  Google Scholar 

  219. 219.

    van Loon, R. A 3D method for modelling the fluid-structure interaction of heart valves (Ph.D. thesis). Eindhoven: Technische Universiteit Eindhoven, 2005.

    Google Scholar 

  220. 220.

    van Loon, R. Towards computational modelling of aortic stenosis. Int. J. Numer. Methods Biomed. Eng. 26:405–420, 2010.

    MathSciNet  MATH  Article  Google Scholar 

  221. 221.

    van Loon, R., P. D. Anderson, and F. N. van de Vosse. A fluid-structure interaction method with solid-rigid contact for heart valve dynamics. J. Comput. Phys. 217:806–823, 2006.

    MathSciNet  MATH  Article  Google Scholar 

  222. 222.

    Vesely, I. The role of elastin in aortic valve mechanics. J. Biomech. 31(2):115–123, 1998.

    Article  Google Scholar 

  223. 223.

    Vesely, I., J. E. Barber, and N. B. Ratliff. Tissue damage and calcification may be independent mechanisms of bioprosthetic heart valve failure. J. Heart Valve Dis. 10(4):471–477, 2001.

    Google Scholar 

  224. 224.

    Vesely, I., and D. Boughner. Analysis of the bending behaviour of porcine xenograft leaflets and of neutral aortic valve material: bending stiffness, neutral axis and shear measurements. J. Biomech. 22(6–7):655–671, 1989.

    Article  Google Scholar 

  225. 225.

    Vesely, I., and R. Noseworthy. Micromechanics of the fibrosa and the ventricularis in aortic valve leaflets. J. Biomech. 25(1):101–113, 1992.

    Article  Google Scholar 

  226. 226.

    Vyavahare, N., M. Ogle, F. J. Schoen, R. Zand, D. C. Gloeckner, M. S. Sacks, et al. Mechanisms of bioprosthetic heart valve failure: Fatigue causes collagen denaturation and glycosaminoglycan loss. J. Biomed. Mater. Res. 46:44–50, 1999.

    Article  Google Scholar 

  227. 227.

    Wells, S. M., and M. S. Sacks. Effects of fixation pressure on the biaxial mechanical behavior of porcine bioprosthetic heart valves with long-term cyclic loading. Biomaterials 23(11):2389–2399, 2002.

    Article  Google Scholar 

  228. 228.

    Wiegner, A. W., O. H. Bing, T. K. Borg, and J. B. Caulfield. Mechanical and structural correlates of canine pericardium. Circ. Res. 49(3):807–814, 1981.

    Article  Google Scholar 

  229. 229.

    Wilber, J. P., and J. R. Walton. The convexity properties of a class of constitutive models for biological soft issues. Math. Mech. Solids 7(3):217–235, 2002. doi:10.1177/108128602027726.

    MathSciNet  MATH  Article  Google Scholar 

  230. 230.

    Wu, W., D. Pott, B. Mazza, T. Sironi, E. Dordoni, C. Chiastra, et al. Fluid-structure interaction model of a percutaneous aortic valve: comparison with an in vitro test and feasibility study in a patient-specific case. Ann. Biomed. Eng. 44(2):590–603, 2016. doi:10.1007/s10439-015-1429-x.

    Article  Google Scholar 

  231. 231.

    Yahia, L. H., and G. Drouin. Microscopical investigation of canine anterior cruciate ligament and patellar tendon: collagen fascicle morphology and architecture. J. Orthop. Res. 7(2):243–251, 1989. doi:10.1002/jor.1100070212.

    Article  Google Scholar 

  232. 232.

    Ye, Q., G. Zund, S. Jockenhoevel, S. P. Hoerstrup, A. Schoeberlein, J. Grunenfelder, et al. Tissue engineering in cardiovascular surgery: new approach to develop completely human autologous tissue. Eur. J. Cardiothorac. Surg. 17(4):449–454, 2000.

    Article  Google Scholar 

  233. 233.

    Zhang, W., S. Ayoub, J. Liao, and M. S. Sacks. On the mechanical role of collagen and elastin fibers in the layers of the mitral heart valve leaflet. J. Mech. Behav. Biomed. Mater., in press.

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Acknowledgments

National Institute of Health, Award Number R01 HL119297 and R01 HL63954 to MSS. National Institute of Health, Award T32 to KRF. American Heart Association, Post Doctoral Fellowship 14POST18720037 to AA.

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Correspondence to Michael S. Sacks.

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Associate Editor Ajit P. Yoganathan oversaw the review of this article.

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Soares, J.S., Feaver, K.R., Zhang, W. et al. Biomechanical Behavior of Bioprosthetic Heart Valve Heterograft Tissues: Characterization, Simulation, and Performance. Cardiovasc Eng Tech 7, 309–351 (2016). https://doi.org/10.1007/s13239-016-0276-8

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Keywords

  • Bioprosthetic heart valve
  • Heterograft
  • Valve mechanics
  • Constitutive modeling
  • Mechanical testing
  • Exogenous crosslinking
  • Fluid structure interaction
  • Modeling and simulation