Computational methods for the aortic heart valve and its replacements

References

• Sacks MS, Yoganathan AP. Heart valve function: a biomechanical perspective. Philosophical Trans Royal Soc B: Biol Sci. 2007;362:1369–1391.
   PubMed Web of Science ®Google Scholar
• Otto CM. Timing of aortic valve surgery. Heart. 2000;84:211–218.
   PubMed Web of Science ®Google Scholar
• Benjamin EJ, Blaha MJ, Chiuve SE, et al. Heart disease and stroke statistics—2017 update: a report from the American Heart Association. Circulation. 2017;135:e146–e603.
   PubMed Web of Science ®Google Scholar
• HCUPnet. Healthcare cost and utilization project. Rockville, MD: Agency for Healthcare Research and Quality 1993–2014. cited 2017 May 4. Available from: http://hcupnet.ahrq.gov/
   Google Scholar
• Chambers J. Prosthetic heart valves. Int J Clin Pract. 2014;68:1227–1230.
   PubMed Web of Science ®Google Scholar
• Vesely I. The evolution of bioprosthetic heart valve design and its impact on durability. Cardiovasc Pathol. 2003;12:277–286.
   PubMed Web of Science ®Google Scholar
• Nishimura RA, Otto CM, Bonow RO, et al. AHA/ACC focused update of the 2014 AHA/ACC guideline for the management of patients with valvular heart disease: a report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines. J Am Coll Cardiol. 2017;135:e1159–e1195.
   Google Scholar
• Hoerstrup SP, Weber B. Biological heart valves. Eur Heart J. 2015;36:325–326. Epub 2015/02/11.
   PubMed Web of Science ®Google Scholar
• Siddiqui RF, Abraham JR, Butany J. Bioprosthetic heart valves: modes of failure. Histopathology. 2009;55:135–144.
   PubMed Web of Science ®Google Scholar
• Vesely I. The evolution of bioprosthetic heart valve design and its impact on durability. Cardiovasc Pathol. 2003;12:277–286. Epub 2003/09/26.
   PubMed Web of Science ®Google Scholar
• Sorajja P, Pedersen W. Next-generation transcatheter aortic valve replacement. Evol Revolution. 2014;64:1349–1351.
   Google Scholar
• Jamieson WRLH, Burr LH, Fradet GJ, et al. Carpentier-Edwards supraannular porcine bioprosthesis evaluation over 15 years. Ann Thorac Surg. 1998;66:S49–52.
   PubMed Web of Science ®Google Scholar
• Thiene G, Bortolotti U, Valente M, et al. Mode of failure of the Hancock pericardial valve xenograft. Am J Cardiol. 1989;63:129–133.
   PubMed Web of Science ®Google Scholar
• Flameng W, Rega F, Vercalsteren M, et al. Antimineralization treatment and patient-prosthesis mismatch are major determinants of the onset and incidence of structural valve degeneration in bioprosthetic heart valves. J Thorac Cardiovasc Surg. 2014;147:1219–1224.
   PubMed Web of Science ®Google Scholar
• Flameng W, Meuris B, Yperman J, et al. Factors influencing calcification of cardiac bioprostheses in adolescent sheep. J Thorac Cardiovasc Surg. 2006;132:89–98.
   PubMed Web of Science ®Google Scholar
• Thubrikar MJ, Deck JD, Aouad J, et al. Role of mechanical stress in calcification of aortic bioprosthetic valves. J Thorac Cardiovasc Surg. 1983;86:115–125.
   PubMed Web of Science ®Google Scholar
• Long CC, Marsden AL, Bazilevs Y. Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk. Comput Mech. 2014;54:921–932.
   Web of Science ®Google Scholar
• Fan R, Sacks MS. Simulation of planar soft tissues using a structural constitutive model: finite element implementation and validation. J Biomech. 2014;47:2043–2054.
   PubMed Web of Science ®Google Scholar
• Conti CA, Votta E, Della Corte A, et al. Dynamic finite element analysis of the aortic root from MRI-derived parameters. Med Eng Phys. 2010;32:212–221.
   PubMed Web of Science ®Google Scholar
• Quarteroni A, Manzoni A, Vergara C. The cardiovascular system: mathematical modelling, numerical algorithms and clinical applications. Acta Numerica. 2017;26:365–590.
   Web of Science ®Google Scholar
• Hasan A, Kolahdouz EM, Enquobahrie A, et al. Image-based immersed boundary model of the aortic root. arXiv Preprint. 2017;arXiv:170504279.
   Google Scholar
• Drach A, Khalighi AH, Sacks MS. A comprehensive pipeline for multi‐resolution modeling of the mitral valve: validation, computational efficiency, and predictive capability. Int J Numer Method Biomed Eng. 2017;33:e2921.
   PubMedGoogle Scholar
• Labrosse MR, Beller CJ, Boodhwani M, et al. Subject-specific finite-element modeling of normal aortic valve biomechanics from 3D+t TEE images. Med Image Anal. 2015;20:162–172.
   PubMed Web of Science ®Google Scholar
• Taylor CA, Figueroa CA. Patient-specific modeling of cardiovascular mechanics. Annu Rev Biomed Eng. 2009;11:109–134.
   PubMed Web of Science ®Google Scholar
• Gnyaneshwar R, Kumar RK, Balakrishnan KR. Dynamic analysis of the aortic valve using a finite element model. Ann Thorac Surg. 2002;73:1122–1129. Epub 2002/05/09.
   PubMed Web of Science ®Google Scholar
• Hamid MS, Sabbah HN, Stein PD. Influence of stent height upon stresses on the cusps of closed bioprosthetic valves. J Biomech. 1986;19:759–769.
   PubMed Web of Science ®Google Scholar
• Ghista DN, Reul H. Optimal prosthetic aortic leaflet valve: design parametric and longevity analyses: development of the Avcothane-51 leaflet valve based on the optimum design analysis. J Biomech. 1977;10:313–324. Epub 1977/01/01.
   PubMed Web of Science ®Google Scholar
• Thubrikar M. The aortic valve. Boca Raton, Florida: CRC Press, Inc.; 1990.
   Google Scholar
• Labrosse MR, Beller CJ, Robicsek F, et al. Geometric modeling of functional trileaflet aortic valves: development and clinical applications. J Biomech. 2006;39:2665–2672. Epub 2005/10/04.
   PubMed Web of Science ®Google Scholar
• Haj-Ali R, Marom G, Zekry SB, et al. A general three-dimensional parametric geometry of the native aortic valve and root for biomechanical modeling. J Biomech. 2012;45:2392–2397.
   PubMed Web of Science ®Google Scholar
• Marom G, Halevi R, Haj-Ali R, et al. Numerical model of the aortic root and valve: optimization of graft size and sinotubular junction to annulus ratio. J Thorac Cardiovasc Surg. 2013;146:1227–1231.
   PubMed Web of Science ®Google Scholar
• Rhinoceros. 2015. Available from: http://www.rhino3d.com2013
   Google Scholar
• Hsu M-C, Kamensky D, Xu F, 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. 2015;55:1211–1225.
   PubMed Web of Science ®Google Scholar
• Hsu M-C, Kamensky D, Bazilevs Y, et al. Fluid–structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech. 2014;54:1055–1071.
   PubMed Web of Science ®Google Scholar
• Auricchio F, Conti M, Morganti S, et al. A computational tool to support pre-operative planning of stentless aortic valve implant. Med Eng Phys. 2011;33:1183–1192. Epub 2011/06/11.
   PubMed Web of Science ®Google Scholar
• Kouhi E, Morsi YS. A parametric study on mathematical formulation and geometrical construction of a stentless aortic heart valve. J Artif Organs. 2013;16:425–442.
   PubMed Web of Science ®Google Scholar
• Li K, Sun W. Simulated transcatheter aortic valve deformation: a parametric study on the impact of leaflet geometry on valve peak stress. Int J Numer Method Biomed Eng. 2016;33:e02814.
   Web of Science ®Google Scholar
• Fan R, Bayoumi AS, Chen P, et al. Optimal elastomeric scaffold leaflet shape for pulmonary heart valve leaflet replacement. J Biomech. 2013;46:662–669. Epub 2013/01/09.
   PubMed Web of Science ®Google Scholar
• Thubrikar M. The aortic valve. Boca Raton: CRC; 1990.
   Google Scholar
• Chandran KB, Kim SH, Han G. Stress distribution on the cusps of a polyurethane trileaflet heart valve prosthesis in the closed position. J Biomech. 1991;24:385–395.
   PubMed Web of Science ®Google Scholar
• Bapat VN, Attia R, Thomas M. Effect of valve design on the stent internal diameter of a bioprosthetic valve: a concept of true internal diameter and its implications for the valve-in-valve procedure. JACC: Cardiovasc Int. 2014;7:115–127.
   PubMed Web of Science ®Google Scholar
• Flameng W, Herregods M-C, Vercalsteren M, et al. Prosthesis-patient mismatch predicts structural valve degeneration in bioprosthetic heart valves. Circulation. 2010;121:2123–2129.
   PubMed Web of Science ®Google Scholar
• Xiong FL, Goetz WA, Chong CK, et al. Finite element investigation of stentless pericardial aortic valves: relevance of leaflet geometry. Ann Biomed Eng. 2010;38:1908–1918. Epub 2010/03/10.
   PubMed Web of Science ®Google Scholar
• Nestola MG, Faggiano E, Vergara C, et al. Computational comparison of aortic root stresses in presence of stentless and stented aortic valve bio-prostheses. Comput Methods Biomech Biomed Eng. 2017;20:171–181. Epub 2016/07/28.
   PubMed Web of Science ®Google Scholar
• Xu F, Morganti S, Zakerzadeh R, et al. A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid–structure interaction analysis. ICES REPORT 17-11, The Institute for Computational Engineering and Sciences, The University of Texas at Austin, 2017. ICES REPORT 17-11.
   Google Scholar
• Morganti S, Auricchio F, Benson DJ, et al. Patient-specific isogeometric structural analysis of aortic valve closure. Comput Method Appl M. 2015;284:508–520.
   Web of Science ®Google Scholar
• Grbic S, Ionasec R, Vitanovski D, et al. Complete valvular heart apparatus model from 4D cardiac CT. Med Image Anal. 2012;16:1003–1014.
   PubMed Web of Science ®Google Scholar
• Sacks MS, Chuong CJ. Orthotropic mechanical properties of chemically treated bovine pericardium. Ann Biomed Eng. 1998;26:892–902.
   PubMed Web of Science ®Google Scholar
• Sun W, Sacks MS, Sellaro TL, et al. Biaxial mechanical response of bioprosthetic heart valve biomaterials to high in-plane shear. J Biomech Eng-T Asme. 2003;125:372–380.
   PubMed Web of Science ®Google Scholar
• Sacks MS, Smith DB, Hiester ED. A small angle light scattering device for planar connective tissue microstructural analysis. Ann Biomed Eng. 1997;25:678–689.
   PubMed Web of Science ®Google Scholar
• Kalyana Sundaram GB, Balakrishnan KR, Kumar RK. Aortic valve dynamics using a fluid structure interaction model–The physiology of opening and closing. J Biomech. 2015;48:1737–1744. Epub 2015/06/11.
   PubMed Web of Science ®Google Scholar
• Flameng W, Jashari R, De Visscher G, et al. Calcification of allograft and stentless xenograft valves for right ventricular outflow tract reconstruction: an experimental study in adolescent sheep. J Thorac Cardiovasc Surg. 2011;141:1513–1521.
   PubMed Web of Science ®Google Scholar
• Sugimoto H, Sacks MS. Effects of leaflet stiffness on dynamic bioprosthetic heart valve leaflet shape. Cardiovasc Eng Technol. 2013;4:2–15.
   PubMedGoogle Scholar
• Avanzini A, Battini D. Structural analysis of a stented pericardial heart valve with leaflets mounted externally. Proc Instit Mech Eng, H: J Eng Med. 2014;228:985–995.
   PubMed Web of Science ®Google Scholar
• Chew GG, Howard IC, Patterson EA. Simulation of damage in a porcine prosthetic heart valve. J Med Eng Technol. 1999;23:178–189.
   PubMed Web of Science ®Google Scholar
• Cataloglu A, Clark RE, Gould PL. Stress analysis of aortic-valve leaflets with smoothed geometrical data. J Biomech. 1977;10:153–158.
   PubMed Web of Science ®Google Scholar
• Hamid MS, Sabbah HN, Stein PD. Comparison of finite-element stress-analysis of aortic-valve leaflet using either membrane elements or solid elements. Comput Struct. 1985;20:955–961.
   Web of Science ®Google Scholar
• Rousseau EPM, Vansteenhoven AA, Janssen JD, et al. A mechanical analysis of the closed Hancock heart-valve prosthesis. J Biomech. 1988;21:545–562.
   PubMed Web of Science ®Google Scholar
• Black MM, Howard IC, Huang X, et al. A three-dimensional analysis of a bioprosthetic heart valve. J Biomech. 1991;24:793–801.
   PubMed Web of Science ®Google Scholar
• Huang X, Black MM, Howard IC, et al. A two-dimensional finite element analysis of a bioprosthetic heart valve. J Biomech. 1990;23:753–762.
   PubMed Web of Science ®Google Scholar
• Sun W, Sacks MS. Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues. Biomech Model Mechanobiol. 2005;4:190–199.
   PubMed Web of Science ®Google Scholar
• Iyengar AKS, Sugimoto H, Smith DB, et al. Dynamic in vitro quantification of bioprosthetic heart valve leaflet motion using structured light projection. Ann Biomed Eng. 2001;29:963–973.
   PubMed Web of Science ®Google Scholar
• Soares JS, Feaver KR, Zhang W, et al. Biomechanical behavior of bioprosthetic heart valve heterograft tissues: characterization, simulation, and performance. Cardiovasc Eng Technol. 2016;7:309–351.
   PubMed Web of Science ®Google Scholar
• Gould PL, Cataloglu A, Clark RE. Mathematical modelling of human aortic valve leaflets. Appl Math Model. 1976;1:33–36.
   Google Scholar
• Sun W, Abad A, Sacks MS. Simulated bioprosthetic heart valve deformation under quasi-static loading. J Biomech Eng. 2005;127:905–914.
   PubMed Web of Science ®Google Scholar
• Chuong CJ, Fung YC. Three-dimensional stress distribution in arteries. J Biomech Eng. 1983;105:268–274.
   PubMed Web of Science ®Google Scholar
• Tong P, Fung YC. The stress-strain relationship for the skin. J Biomech. 1976;9:649–657.
   PubMed Web of Science ®Google Scholar
• Chew PH, Yin FC, Zeger SL. Biaxial stress-strain properties of canine pericardium. J Mol Cell Cardiol. 1986;18:567–578.
   PubMed Web of Science ®Google Scholar
• Humphrey JD, Strumpf RK, Yin FC. A constitutive theory for biomembranes: application to epicardial mechanics. J Biomech Eng. 1992;114:461–466.
   PubMed Web of Science ®Google Scholar
• Patterson EA, Howard IC, Thornton MA. A comparative study of linear and nonlinear simulations of the leaflets in a bioprosthetic heart valve during the cardiac cycle. J Med Eng Technol. 1996;20:95–108.
   PubMed Web of Science ®Google Scholar
• Howard IC, Patterson EA, Yoxall A. On the opening mechanism of the aortic valve: some observations from simulations. J Med Eng Technol. 2003;27:259–266.
   PubMedGoogle Scholar
• Li J, Luo XY, Kuang ZB. A nonlinear anisotropic model for porcine aortic heart valves. J Biomech. 2001;34:1279–1289.
   PubMed Web of Science ®Google Scholar
• Driessen NJ, Mol A, Bouten CV, et al. Modeling the mechanics of tissue-engineered human heart valve leaflets. J Biomech. 2007;40:325–334. Epub 2006/03/15.
   PubMed Web of Science ®Google Scholar
• De Hart J, Peters GWM, Schreurs PJG, et al. A three-dimensional computational analysis of fluid-structure interaction in the aortic valve. J Biomech. 2003;36:103–112.
   PubMed Web of Science ®Google Scholar
• Sun W, Sacks MS, Sellaro TL, et al. Biaxial mechanical response of bioprosthetic heart valve biomaterials to high in-plane shear. J Biomechanical Eng. 2003;125:372–380.
   PubMed Web of Science ®Google Scholar
• Kim H, Lu J, Sacks MS, et al. Dynamic simulation pericardial bioprosthetic heart valve function. J Biomech Eng. 2006;128:717–724.
   PubMed Web of Science ®Google Scholar
• Saleeb AF, Kumar A, Thomas VS. The important roles of tissue anisotropy and tissue-to-tissue contact on the dynamical behavior of a symmetric tri-leaflet valve during multiple cardiac pressure cycles. Med Eng Phys. 2013;35:23–35.
   PubMed Web of Science ®Google Scholar
• De Hart J, Baaijens FPT, Peters GWM, et al. A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve. J Biomech. 2003;36:699–712.
   PubMed Web of Science ®Google Scholar
• Burriesci G, Howard IC, Patterson EA. Influence of anisotropy on the mechanical behaviour of bioprosthetic heart valves. J Med Eng Technol. 1999;23:203–215.
   PubMed Web of Science ®Google Scholar
• Martin C, Sun W. Bio-prosthetic heart valve stress analysis: impacts of leaflet properties and stent tip deflection. In: Proulx T, editor. Mechanics of biological systems and materials, volume 2: proceedings of the 2011 annual conference on experimental and applied mechanics. New York, NY: Springer New York; 2011. p. 73–78.
   Google Scholar
• Koch TM, Reddy BD, Zilla P, et al. Aortic valve leaflet mechanical properties facilitate diastolic valve function. Comput Methods Biomech Biomed Eng. 2010;13:225–234. Epub 2009/08/07.
   PubMed Web of Science ®Google Scholar
• Gilmanov A, Stolarski H, Sotiropoulos F. Non-linear rotation-free shell finite-element models for aortic heart valves. J Biomech. 2017;50:56–62.
   PubMed Web of Science ®Google Scholar
• Joda A, Jin Z, Haverich A, et al. Multiphysics simulation of the effect of leaflet thickness inhomogeneity and material anisotropy on the stress–strain distribution on the aortic valve. J Biomech. 2016;49:2502–2512.
   PubMed Web of Science ®Google Scholar
• Billiar KL, Sacks MS. Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp–part I: experimental results. J Biomech Eng. 2000;122:23–30. Epub 2000/05/03.
   PubMed Web of Science ®Google Scholar
• Sun W, Sacks MS, Scott MJ. Effects of boundary conditions on the estimation of the planar biaxial mechanical properties of soft tissues. J Biomech Eng-T Asme. 2005;127:709–715.
   PubMed Web of Science ®Google Scholar
• Aggarwal A, Ferrari G, Joyce E, et al. Architectural trends in the human normal and bicuspid aortic valve leaflet and its relevance to valve disease. Ann Biomed Eng. 2014;42:986–998.
   PubMed Web of Science ®Google Scholar
• Aggarwal A, Sacks MS. An inverse modeling approach for semilunar heart valve leaflet mechanics: exploitation of tissue structure. Biomech Model Mechanobiol. 2016;15:909–932.
   PubMed Web of Science ®Google Scholar
• Aggarwal A, Sacks M. A framework for determination of heart valves’ mechanical properties using inverse-modeling approach. In: Van Assen H, Bovendeerd P, Delhaas T, editors. Functional imaging and modeling of the heart. lecture notes in computer science. Vol. 9126. Heidelberg: Springer International Publishing; 2015. p. 285–294.
   Google Scholar
• Aggarwal A. An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function. Biomech Model Mechanobiol. 2017;16:1309–1327.
   PubMed Web of Science ®Google Scholar
• Sacks MS. Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. J Biomech Eng. 2003;125:280–287.
   PubMed Web of Science ®Google Scholar
• Sun W, Sacks MS. Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues. Biomech Model Mechanobiol. 2005;4:190–199.
   PubMed Web of Science ®Google Scholar
• Mirnajafi A, Zubiate B, Sacks MS. Effects of cyclic flexural fatigue on porcine bioprosthetic heart valve heterograft biomaterials. J Biomed Mat Res Part. 2010;94:205–213. Epub 2010/02/19.
   PubMed Web of Science ®Google Scholar
• Martin C, Sun W. Simulation of long-term fatigue damage in bioprosthetic heart valves: effects of leaflet and stent elastic properties. Biomech Model Mechanobiol. 2014;13:759–770.
   PubMed Web of Science ®Google Scholar
• Sacks MS, Zhang W, Wognum S. A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues. Interface Focus. 2016;6:20150090.
   PubMed Web of Science ®Google Scholar
• Zhang W, Sacks MS. Modeling the response of exogenously crosslinked tissue to cyclic loading: the effects of permanent set. J Mech Behav Biomed Mater. 2017;75:336–350.
   PubMedGoogle Scholar
• Prosthetic Devices Branch DoC, Respiratory and Neurological Devices. Replacement heart valve guidance. Rockfied, Maryland: Center for Devices and Radiological Health (FDA). cited 1993 Dec 7. (no. Version 4.0).
   Google Scholar
• Sun W, Abad A, Sacks MS. Simulated bioprosthetic heart valve deformation under quasi-static loading. J Biomechanical Eng. 2005;127:905–914.
   PubMed Web of Science ®Google Scholar
• Saleeb AF, Kumar A, Thomas VS. The important roles of tissue anisotropy and tissue-to-tissue contact on the dynamical behavior of a symmetric tri-leaflet valve during multiple cardiac pressure cycles. Med Eng Phys. 2013;35:23–35. Epub 2012/04/10.
   PubMed Web of Science ®Google Scholar
• Auricchio F, Conti M, Ferrara A, et al. Patient-specific simulation of a stentless aortic valve implant: the impact of fibres on leaflet performance. Comput Methods Biomech Biomed Engin. 2014;17:277–285.
   PubMed Web of Science ®Google Scholar
• Kim H, Lu J, Sacks MS, et al. Dynamic simulation of bioprosthetic heart valves using a stress resultant shell model. Ann Biomed Eng. 2008;36:262–275.
   PubMed Web of Science ®Google Scholar
• Vignon-Clementel IE, Figueroa CA, Jansen KE, et al. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Method Appl M. 2006;195:3776–3796.
   Web of Science ®Google Scholar
• Zakerzadeh R, Zunino P Fluid-structure interaction in arteries with a poroelastic wall model. 21st Iranian Conference of Biomedical Engineering (ICBME) IEEE,35–9
   Google Scholar
• Vignon-Clementel IE, Figueroa C, Jansen K, et al. Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries. Comput Methods Biomech Biomed Eng. 2010;13:625–640.
   PubMed Web of Science ®Google Scholar
• Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc. 1977;181:375–389.
   Web of Science ®Google Scholar
• Mao W, Li K, Caballero A, et al. Fully-coupled FSI simulation of bioprosthetic heart valve using smoothed particle hydrodynamics. Cardiology. 2016;134:178.
   Web of Science ®Google Scholar
• Toma M, Jensen MO, Einstein DR, et al. Fluid-structure interaction analysis of papillary muscle forces using a comprehensive mitral valve model with 3D chordal structure. Ann Biomed Eng. 2016;44:942–953.
   Web of Science ®Google Scholar
• Lai YG, Chandran KB, Lemmon J. A numerical simulation of mechanical heart valve closure fluid dynamics. J Biomech. 2002;35:881–892.
   PubMed Web of Science ®Google Scholar
• Cheng R, Lai YG, Chandran KB. Three-dimensional fluid-structure interaction simulation of bileaflet mechanical heart valve flow dynamics. Ann Biomed Eng. 2004;32:1471–1483.
   PubMed Web of Science ®Google Scholar
• Makhijani VB, Yang HQ, Dionne PJ, et al. Three-dimensional coupled fluid-structure simulation of pericardial bioprosthetic aortic valve function. Asaio J. 1997;43:M387–M92.
   PubMed Web of Science ®Google Scholar
• Johnson AA, Tezduyar TE. Parallel computation of incompressible flows with complex geometries. Int J Numer Methods Fluids. 1997;24:1321–1340.
   Web of Science ®Google Scholar
• Tezduyar T, Aliabadi S, Behr M, et al. Massively parallel finite element computation of 3D flows - mesh update strategies in computation of moving boundaries and interfaces. Parallel Comput Fluid Dyn New Trends Advanc. 1995:21–30.
   Google Scholar
• Johnson AA, Tezduyar TE. 3D simulation of fluid-particle interactions with the number of particles reaching 100. Comput Method Appl M. 1997;145:301–321.
   Web of Science ®Google Scholar
• Johnson AA, Tezduyar TE. Advanced mesh generation and update methods for 3D flow Simulations. Comput Mech. 1999;23:130–143.
   Web of Science ®Google Scholar
• Hughes TJR, Liu WK, Zimmermann TK. Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Method Appl M. 1981;29:329–349.
   Web of Science ®Google Scholar
• Donea J, Giuliani S, Halleux JP. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comput Method Appl M. 1982;33:689–723.
   Web of Science ®Google Scholar
• Donea J, Huerta A, Ponthot J-P, et al. Arbitrary Lagrangian-Eulerian methods. Encyclopedia Comput Mech. 2004;1.
   Google Scholar
• Tezduyar TE, Behr M, Liou J. 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 M. 1992;94:339–351.
   Web of Science ®Google Scholar
• Tezduyar TE, Behr M, Mittal S, et al. 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 M. 1992;94:353–371.
   Web of Science ®Google Scholar
• Takizawa K, Tezduyar TE, Buscher A, et al. Space-time interface-tracking with topology change (ST-TC). Comput Mech. 2014;54:955–971.
   Web of Science ®Google Scholar
• Takizawa K, Tezduyar T, Buscher A, et al. Space-time fluid mechanics computation of heart valve models. Comput Mech. 2014;1–14.
   Web of Science ®Google Scholar
• Peskin CS. Flow patterns around heart valves: a numerical method. J Comput Phys. 1972;10:252–271.
   Web of Science ®Google Scholar
• Mittal R, Iaccarino G. Immersed boundary methods. Annu Rev Fluid Mech. 2005;37:239–261.
   Web of Science ®Google Scholar
• Sotiropoulos F, Yang X. Immersed boundary methods for simulating fluid-structure interaction. Prog Aerosp Sci. 2014;65:1–21.
   Web of Science ®Google Scholar
• Tezduyar TE. Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Meth Fl. 2003;43:555–575.
   Web of Science ®Google Scholar
• Takizawa K, Moorman C, Wright S, et al. Wall shear stress calculations in space-time finite element computation of arterial fluid-structure interactions. Comput Mech. 2010;46:31–41.
   Web of Science ®Google Scholar
• Ge L, Sotiropoulos F. A numerical method for solving the 3D unsteady incompressible Navier-Stokes equations in curvilinear domains with complex immersed boundaries. J Comput Phys. 2007;225:1782–1809.
   PubMed Web of Science ®Google Scholar
• Borazjani I, Ge L, Sotiropoulos F. Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. J Comput Phys. 2008;227:7587–7620.
   PubMed Web of Science ®Google Scholar
• Borazjani I. Fluid-structure interaction, immersed boundary-finite element method simulations of bio-prosthetic heart valves. Comput Method Appl M. 2013;257:103–116.
   Web of Science ®Google Scholar
• Gilmanov A, Le TB, Sotiropoulos F. A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains. J Comput Phys. 2015;300:814–843.
   Web of Science ®Google Scholar
• Gilmanov A, Sotiropoulos F. Comparative hemodynamics in an aorta with bicuspid and trileaflet valves. Theor Computational Fluid Dyn. 2015;30:67–85.
   Web of Science ®Google Scholar
• Griffith BE, Luo X, McQueen DM, et al. Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method. Int J Appl Mech. 2009;1:137–177.
   Web of Science ®Google Scholar
• Flamini V, DeAnda A, Griffith BE. Immersed boundary-finite element model of fluid-structure interaction in the aortic root. Theor Computational Fluid Dyn. 2016;30:139–164.
   PubMed Web of Science ®Google Scholar
• Baaijens FPT. A fictitious domain/mortar element method for fluid-structure interaction. Int J Numer Methods Fluids. 2001;35:743–761.
   Web of Science ®Google Scholar
• De Hart J Fluid-structure interaction in the aortic heart valve: a three-dimensional computational analysis [ Ph.D. Thesis]. Eindhoven, Netherlands: Technische Universiteit Eindhoven; 2002
   Google Scholar
• Van Loon R A 3D method for modelling the fluid-structure interaction of heart valves [ Ph.D. Thesis]. Eindhoven, Netherlands: Technische Universiteit Eindhoven; 2005
   Google Scholar
• Van Loon R, Anderson PD, van de Vosse FN. A fluid-structure interaction method with solid-rigid contact for heart valve dynamics. J Comput Phys. 2006;217:806–823.
   Web of Science ®Google Scholar
• Van Loon R. Towards computational modelling of aortic stenosis. Int J Numer Method Biomed Eng. 2010;26:405–420.
   Web of Science ®Google Scholar
• Kamensky D, Hsu M-C, Schillinger D, et al. An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves. Comput Method Appl M. 2015;284:1005–1053.
   PubMed Web of Science ®Google Scholar
• Bazilevs Y, Calo VM, Cottrell JA, et al. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng. 2007;197:173–201.
   Web of Science ®Google Scholar
• Hughes TJR, Cottrell JA, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Method Appl M. 2005;194:4135–4195.
   Web of Science ®Google Scholar
• Cottrell JA, Hughes TJR, Bazilevs Y. Isogeometric analysis: towards integration of CAD and FEA. UK: John Wiley & Sons; 2009.
   Google Scholar
• Bavo AM, Rocatello G, Iannaccone F, et al. Fluid-structure interaction simulation of prosthetic aortic valves: comparison between immersed boundary and arbitrary Lagrangian-Eulerian techniques for the mesh representation. PloS One. 2016;11:e0154517.
   PubMed Web of Science ®Google Scholar
• Corp. L-DFESLST. Available from: http://www.lstc.com/products/ls-dyna
   Google Scholar
• Carmody CJ, Burriesci G, Howard IC, et al. An approach to the simulation of fluid-structure interaction in the aortic valve. J Biomech. 2006;39:158–169.
   PubMed Web of Science ®Google Scholar
• Sturla F, Votta E, Stevanella M, et al. Impact of modeling fluid-structure interaction in the computational analysis of aortic root biomechanics. Med Eng Phys. 2013;35:1721–1730.
   PubMed Web of Science ®Google Scholar
• Wu W, Pott D, Mazza B, 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. 2016;44:590–603.
   PubMed Web of Science ®Google Scholar
• Courant R, Friedrichs K, Lewy H. On the partial difference equations of mathematical physics. IBM J Res Develop. 1967;11:215–234.
   Web of Science ®Google Scholar
• Courant R, Friedrichs K, Lewy H. Uber die partiellen Differenzengleichungen der mathematischen Physik. Mathematische Annalen. 1928;100:32–74.
   Web of Science ®Google Scholar
• Bogaers AEJ, Kok S, Reddy BD, et al. Quasi-Newton methods for implicit black-box FSI coupling. Comput Method Appl M. 2014;279:113–132.
   Web of Science ®Google Scholar
• Van Brummelen EH. Added mass effects of compressible and incompressible flows in fluid-structure interaction. J Appl Mechanics. 2009;76:021206.
   Web of Science ®Google Scholar
• Michler C, Van Brummelen H, de Borst R. An investigation of interface-GMRES(R) for fluid-structure interaction problems with flutter and divergence. Comput Mech. 2011;47:17–29.
   Web of Science ®Google Scholar
• Astorino M, Gerbeau J-F, Pantz O, et al. Fluid-structure interaction and multi-body contact: application to aortic valves. Comput Method Appl M. 2009;198:3603–3612.
   Web of Science ®Google Scholar
• Gaetano FD, Bagnoli P, Zaffora A, et al. A newly developed tri-leaflet polymeric heart valve prosthesis. J Mech Med Biol. 2015;15:1540009.
   PubMed Web of Science ®Google Scholar
• Yoganathan AP, Chandran KB, Sotiropoulos F. Flow in prosthetic heart valves: state-of-the-art and future directions. Ann Biomed Eng. 2005;33:1689–1694. Epub 2006/01/04.
   PubMed Web of Science ®Google Scholar
• Amini R, Eckert CE, Koomalsingh K, et al. On the in vivo deformation of the mitral valve anterior leaflet: effects of annular geometry and referential configuration. Ann Biomed Eng. 2012;40:1455–1467.
   PubMed Web of Science ®Google Scholar
• Pouch A, Tian S, Takabe M, et al. Segmentation of the aortic valve apparatus in 3D echocardiographic images: deformable modeling of a branching medial structure. In: Camara O, Mansi T, Pop M, et al., editors. Statistical atlases and computational models of the heart - imaging and modelling challenges. Lecture Notes in Computer Science. Switzerland: Springer International Publishing; 2015. p. 196–203.
   Google Scholar
• Aggarwal A, Pouch AM, Lai E, et al. In-vivo heterogeneous functional and residual strains in human aortic valve leaflets. J Biomech. 2016;49:2481–2490.
   PubMed Web of Science ®Google Scholar
• Murphy SV, Atala A. 3D bioprinting of tissues and organs. Nat Biotech. 2014;32:773–785.
   PubMed Web of Science ®Google Scholar
• Duan B, Hockaday LA, Kang KH, et al. 3D bioprinting of heterogeneous aortic valve conduits with alginate/gelatin hydrogels. J Biomed Mat Res Part. 2013;101:1255–1264.
   PubMed Web of Science ®Google Scholar
• Gould PL, Cataloglu A, Dhatt G, et al. Stress analysis of the human aortic valve. Comput Struct. 1973;3:377–384.
   Google Scholar
• Krucinski S, Vesely I, Dokainish MA, et al. Numerical simulation of leaflet flexure in bioprosthetic valves mounted on rigid and expansile stents. J Biomech. 1993;26:929–943.
   PubMed Web of Science ®Google Scholar
• Leat ME, Fisher J. Comparative-study of the function of the abiomed polyurethane heart-valve for use in left-ventricular assist devices. J Biomed Eng. 1993;15:516–520.
   PubMedGoogle Scholar
• Hamid MS, Sabbah HN, Stein PD. Influence of stent height upon stresses on the cusps of closed bioprosthetic valves. J Biomech. 1986;19:759–769.
   PubMed Web of Science ®Google Scholar
• Cacciola G, Peters GW, Baaijens FP. A synthetic fiber-reinforced stentless heart valve. J Biomech. 2000;33:653–658.
   PubMed Web of Science ®Google Scholar
• Cacciola G, Peters GW, Schreurs PJ. A three-dimensional mechanical analysis of a stentless fibre-reinforced aortic valve prosthesis. J Biomech. 2000;33:521–530.
   PubMed Web of Science ®Google Scholar
• Einav S, Stolero D, Avidor JM, et al. Wall shear stress distribution along the cusp of a tri-leaflet prosthetic valve. J Biomed Eng. 1990;12:13–18. Epub 1990/01/01.
   PubMedGoogle Scholar
• Back M, Gasser TC, Michel JB, et al. Biomechanical factors in the biology of aortic wall and aortic valve diseases. Cardiovasc Res. 2013;99:232–241. Epub 2013/03/06.
   PubMed Web of Science ®Google Scholar