Abstract
A set of multiscale simulations has been created to examine the dynamic behavior of the human aortic valve (AV) at the cell, tissue, and organ length scales. Each model is fully three-dimensional and includes appropriate nonlinear, anisotropic material models. The organ-scale model is a dynamic fluid-structure interaction that predicts the motion of the blood, cusps, and aortic root throughout the full cycle of opening and closing. The tissue-scale model simulates the behavior of the AV cusp tissue including the sub-millimeter features of multiple layers and undulated geometry. The cell-scale model predicts cellular deformations of individual cells within the cusps. Each simulation is verified against experimental data. The three simulations are linked: deformations from the organ-scale model are applied as boundary conditions to the tissue-scale model, and the same is done between the tissue and cell scales. This set of simulations is a major advance in the study of the AV as it allows analysis of transient, three-dimensional behavior of the AV over the range of length scales from cell to organ.
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Baumert B, Plass A, Bettex D, Alkadhi H, Desbiolles L, Wildermuth S, Marincek B, Boehm T. Dynamic cine mode imaging of the normal aortic valve using 16-channel multidetector row computed tomography. Invest Radiol 2005;40:637–47.
Billiar K, Sacks MS. Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp-Part I: experimental results. J Biomech Eng 2000a;122:23–30.
Billiar K, Sacks MS. Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp-Part II: a structural constitutive model. J Biomech Eng 2000b;122:327–35.
Boehm T, Husmann L, Leschka S, Desbiolles L, Marincek B, Alkadhi H. Image quality of the aortic and mitral valve with CT: relative versus absolute delay reconstruction. Acad Radiol 2007;14:613–24.
Brewer RJ, Mentzer RM, Deck JD, Ritter RC, Trefil JS, Nolan SP. In vivo study of dimensional changes of aortic-valve leaflets during cardiac cycle. J Thorac Cardiovasc Surg 1977;74:645–50.
Cataloglu A, Clark R, Gould P. Stress analysis of aortic valve leaflets with smoothed geometrical data. J Biomech 1977;10:153.
Cataloglu A, Gould P, Clark R. Refined stress analysis of human aortic heart valves. J Eng Mech Div Proc Am Soc Civil Eng 1976;102:135–50.
Chandran PL, Barocas VH. Deterministic material-based averaging theory model of collagen gel micromechanics. J Biomech Eng-T ASME 2007;129:137–47.
Clark RE, Karara SM, Catalogl A, Gould PL. Determination of diastolic stresses in human aortic-valve through close range stereophotogrammetry. Circulation 1974;50:165–5.
De Hart J, Baaijens FPT, Peters GWM, Schreurs PJG. A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve. J Biomech 2003a;36:699–712.
De Hart J, Peters GWM, Schreurs PJG, Baaijens FPT. A three-dimensional computational analysis of fluid-structure interaction in the aortic valve. J Biomech 2003b;36:103–12.
De Hart J, Peters GWM, Schreurs PJG, Baaijens FPT. Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole. J Biomech 2004;37:303–11.
Deck JD, Thubrikar MJ, Schneider PJ, Nolan SP. Structure, stress, and tissue-repair in aortic-valve leaflets. Cardiovasc Res 1988;22:7–16.
Einstein DR, Kunzelman KS, Reinhall PG, Nicosia MA, Cochran RP. Haemodynamic determinants of the mitral valve closure sound: a finite element study. Med Biol Eng Comput 2004;42:832–46.
Einstein DR, Kunzelman KS, Reinhall PG, Nicosia MA, Cochran RP. Non-linear fluid-coupled computational model of the mitral valve. J Heart Valve Dis 2005;14:376–85.
Fung Y. Biomechanics: mechanical properties of living tissues. New York: Springer; 1993.
Gloeckner D, Billiar K, Sacks M. Effects of mechanical fatigue on the bending properties of the porcine bioprosthetic heart valve. ASAIO J 1999;45:59–63.
Gould P, Cataloglu A, Dhatt G, Cattopadhyay A, Clark R. Stress analysis of the human aortic valve. Comput Struct 1973;3:377.
Grande-Allen K, Cochran R, Reinhall P, Kunzelman K. Finite-element analysis of aortic valve sparing: influence of graft shape and stiffness. IEEE Transa Biomed Eng 2001;48:647–59.
Grande KJ, Cochran RP, Reinhall PG, Kunzelman KS. Stress variations in the human aortic root and valve: the role of anatomic asymmetry. Ann Biomed Eng 1998;26:534–45.
Hallquist J. LS-DYNA theory manual. Livermore; 2006.
Holzapfel GA, Gasser TC, Ogden RW. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 2000;61:1–48.
Huang H-YS. Micromechanical simulations of heart valve tissues: University of Pittsburgh; 2004.
Humphrey JD. Continuum biomechanics of soft biological tissues. Proceedings of the Royal Society of London Series A—Mathematical Physical and Engineering Sciences 2003;459:3–46.
Kim H, Chandran KB, Sacks MS, Lu J. An experimentally derived stress resultant shell model for heart valve dynamic simulations. Ann Biomed Eng 2007;35:30–44.
Kim H, Lu J, Sacks MS, Chandran KB. Dynamic simulation pericardial bioprosthetic heart valve function. J Biomech Eng-T ASME 2006;128:717–24.
Lansac E, Lim HS, Shomura Y, Lim KH, Rice NT, Goetz W, Acar C, Duran CMG. A four-dimensional study of the aortic root dynamics. Eur J Cardiothorac Surg 2002;22:497–503.
Lim C, Zhou E, Quek S. Mechanical models for living cells—a review. J Biomech 2006;39:195–216.
Merryman WD, Huang H-YS, Schoen FJ, Sacks MS. The effects of cellular contraction on aortic valve leaflet flexural stiffness. J Biomech 2006a;39:88–96.
Merryman WD, Youn I, Lukoff HD, Krueger PM, Guilak F, Hopkins RA, Sacks MS. Correlation between heart valve instertitial cell stiffness and transvalvular pressure: implications for collagen biosynthesis. Heart Circ Physiol 2006b;290:H224–31.
Migliavacca F, Balossino R, Pennati G, Dubini G, Hsia TY, de Leval MR, Bove EL. Multiscale modelling in biofluidynamics: Application to reconstructive paediatric cardiac surgery. J Biomech 2006;39:1010–20.
Mofrad MRK, Kamm RD, editors. Cytoskeletal mechanics: models and measurements. Cambridge University Press; 2006.
Nichols W, O’Rourke M. McDonald’s blood flow in arteries. 5th ed. London: Arnold; 1998.
Nicosia MA, Cochran RP, Einstein DR, Rutland CJ, Kunzelman KS. A coupled fluid-structure finite element modle of the aortic valve and root. J Heart Valve Dis 2003;12:781–9.
Otto CM. Calcification of bicuspid aortic valves. Heart 2002;88:321–2.
Rousseau EPM, Sauren A, Vanhout MC, Vansteenhoven AA. Elastic and viscoelastic material behavior of fresh and glutaraldehyde-treated porcine aortic-valve tissue. J Biomech 1983;16:339–48.
Sacks MS. The biomechanical effects of fatigue on the porcine bioprosthetic heart valves. J Long Term Effects Med Implants 2001;11(3–4):231–47.
Sacks MS, Smith DB, Hiester ED. The aortic valve microstructure: effects of transvalvular pressure. J Biomed Mater Res 1998;41:131–41.
Sacks MS, Yoganathan AP. Heart valve function: a biomechanical perspective. Phil Trans R Soc B 2007;362:1369–91.
Stella JA, Sacks MS. On the biaxial mechanical properties of the layers of the aortic valve leaflet. J Biomech Eng 2007; in press.
Sun W, Abad A, Sacks MS. Simulated bioprosthetic heart valve deformation under quasi-static loading. J Biomech Eng-T ASME 2005;127:905–14.
Sun W, Sacks MS. Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues. Biomech Model Mechanobiol 2005;4:190–9.
Sung H-W, Chang Y, Chui C-T, Chen C-N, Liang H-C. Mechanical properties of a porcine aortic valve fixed with a naturally occurring croslinking agent. Biomaterials 1999;20:1759–72.
Taylor P, Batten P, Brand N, Thomas P, Yacoub M. The cardiac valve interstitial cell. Int J Biochem Cell Biol 2003;35:113–8.
Thubrikar M. The aortic valve. Boca Raton: CRC Press; 1990.
Thubrikar M, Piepgrass WC, Deck JD, Nolan SP. Stresses of natural versus prosthetic aortic-valve leaflets invivo. Ann Thorac Surg 1980;30:230–9.
Thubrikar MJ, Nolan SP, Aouad J, Deck JD. Stress sharing between the sinus and leaflets of canine aortic valve. Ann Thorac Surg 1986;42:434–40.
Vesely I. Reconstruction of loads in the fibrosa and ventricularis of porcine aortic valves. ASAIO J 1996;42:M739–46.
Vesely I, Lozon A. Natural preload of aortic valve leaflet components during glutaraldehyde fixation: effects on tissue mechanics. J Biomech 1993;26:121–31.
Vesely I, Noseworthy R. Micromechanics of the fibrosa and the ventricularis in aortic valve leaflets. J Biomech 1991;25:101–13.
Weinberg EJ, Kaazempur-Mofrad MR. A large-strain finite element formulation for biological tissues with application to mitral valve leaflet tissue mechanics. J Biomech 2005;39:1557–61.
Weinberg EJ, Kaazempur-Mofrad MR. A finite shell element for heart mitral valve leaflet mechanics, with large deformations and 3D constitutive model. J Biomech 2006;40:705–11.
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Weinberg, E.J., Kaazempur Mofrad, M.R. Transient, Three-dimensional, Multiscale Simulations of the Human Aortic Valve. Cardiovasc Eng 7, 140–155 (2007). https://doi.org/10.1007/s10558-007-9038-4
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DOI: https://doi.org/10.1007/s10558-007-9038-4