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Articles

Evaluation of a transient, simultaneous, arbitrary Lagrange–Euler based multi-physics method for simulating the mitral heart valve

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Pages 450-458 | Received 18 Nov 2011, Accepted 23 Apr 2012, Published online: 29 May 2012

References

  • Al-AtabiM, EspinoDM, HukinsDWL. 2010. Computer and experimental modelling of blood flow through the mitral valve of the heart. J Biomech Sci Eng. 5(1):78–84.
  • Al-AtabiM, EspinoDM, HukinsDWL, BuchanKG. 2012. Biomechanical assessment of surgical repair of the mitral valve. Proc Inst Mech Eng H.226(4):275–287.
  • AppletonA. 1996. Thermodynamic and mechanical properties of matter. London: Appleton.
  • BarberJE, KasperFR, RatliffNB, CosgroveDM, GriffinBP, VeselyI. 2001. Mechanical properties of myxomatous mitral valves. J Thorac Cardiovasc Surg. 122(5):955–962.
  • BellhouseBJ. 1972. The fluid mechanics of heart valves. In: BergelDH, editor. Cardiovascular fluid dynamics. Vol. 1, London: Academic Press. p. 261–285.
  • CaroCG, PedleyTJ, SchroterRC, SeedWA. 1978. The mechanics of the circulation. Oxford: Oxford University Press.
  • ChenL, McCullochAD, May-NewmanK. 2004. Nonhomogeneous deformation in the anterior leaflet of the mitral valve. Ann Biomed Eng. 32(12):1599–1606.
  • ChengYG, ZhangH. 2010. Immersed boundary method and lattice Boltzmann method coupled FSI simulation of mitral leaflet flow. Comput Fluids. 39(5):871–881.
  • ClarkRE. 1973. Stress–strain characteristics of fresh and frozen human aortic and mitral leaflets and chordae tendineae. J Thorac Cardiovasc Surg. 66(2):202–208.
  • CrossM, CroftTN, McBrideD, SloneAK, WilliamsAJ. 2007. Multiphysics modelling and simulation: progress and challenges. In: NAFEMS World Congress, Vancouver, Canada, 22–25 May 2007, Glasgow: NAFEMS Ltd.
  • Dal PanF, DonzellaG, FucciC, SchreiberM. 2005. Structural effects of an innovative surgical technique to repair heart valve defects. J Biomech. 38(12):2460–2471.
  • De HartJ, BaaijensFP, PetersGW, SchreursPJ. 2003. A computational fluid–structure interaction analysis of a fiber-reinforced stentless aortic valve. J Biomech. 36(5):699–712.
  • De HartJ, PetersGW, SchruersPJ, BaaijensFP. 2000. A two-dimensional fluid–structure interaction model of the aortic valve. J Biomech. 33(9):1079–1088.
  • De HartJ, PetersGW, SchreursPJ, BaaijensFP. 2003. A three-dimensional computational analysis of fluid–structure interaction in the aortic valve. J Biomech. 36(1):103–112.
  • DoneaJ, GiulianiS, HalleuxJP. 1982. An arbitrary Lagrangian–Eulerian finite element method for transient dynamic fluid–structure interactions. Comput Methods Appl Mech Eng. 33(1–3):689–723.
  • DowellEH, HallKC. 2001. Modelling of fluid–structure interaction. Annu Rev Fluid Mech. 33(1):445–490.
  • EinsteinDR, KunzelmanKS, ReinhallPG, NicosiaMA, CochranRP. 2005a. The relationship of normal and abnormal microstructural proliferation to the mitral valve closure sound. J Biomech Eng. 127(1):134–147.
  • EinsteinDR, KunzelmanKS, ReinhallPG, NicosiaMA, CochranRP. 2005b. Non-linear fluid-coupled computational model of the mitral valve. J Heart Valve Dis. 14(3):376–385.
  • EspinoDM, ShepherdDET, BuchanKG. 2007. Effect of mitral valve geometry on valve competence. Heart Vessels. 22(2):109–115.
  • EspinoDM, ShepherdDET, HukinsDWL. 2012a. Development of a transient large strain contact method for biological heart valve simulations. Comput Methods Biomech Biomed Eng, in press. doi: 10.1080/10255842.2011.623676.
  • EspinoDM, ShepherdDET, HukinsDWL. 2012b. Transient large strain contact modelling: a comparison of contact technique for simultaneous fluid–structure interaction. Comput Fluids, in press. DOI: 10.1080/10255842.2011.623676.
  • EspinoDM, ShepherdDET, HukinsDWL, BuchanK. 2005. The role of chordae tendineae in mitral valve competence. J Heart Valve Dis. 14(5):603–609.
  • FormaggiaL, NobileF. 1999. A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements. East-West J Numer Math. 7(2):105–132.
  • GrangerRA. 1985. Fluid mechanics. New York: Holt, Rinehart and Winston.
  • GreenGR, DagumP, GlassonJR, NistalJF, DaughtersGT, IngelsNB, MillerC. 1999. Restricted posterior leaflet motion after mitral ring annuloplasty. Ann Thorac Surg. 68(6):2100–2106.
  • HeathMT. 1997. Scientific computing – an introductory survey. New York: McGraw-Hill.
  • Kaur H. 2007. Determination of material properties of natural heart valves [MEng thesis]. Birmingham: University of Birmingham.
  • KunzelmanKS, CochranRP. 1992. Stress/strain characteristics of porcine mitral valve tissue: parallel versus perpendicular collagen orientation. J Cardiac Surg. 7(1):71–78.
  • KunzelmanKS, CochranRP, ChuongC, RingWS, VerrierED, EberhartRC. 1993. Finite element analysis of the mitral valve. J Heart Valve Dis. 2(3):326–340.
  • KunzelmanKS, EinsteinDR, CochranRP. 2007. Fluid–structure interaction models of the mitral valve: function in normal and pathological states. Phil Trans R Soc B. 362(1484):1393–1406.
  • LauKD, DiazV, ScamblerP, BurriesciG. 2010. Mitral valve dynamics in structural and fluid–structure interaction models. Med Eng Phys. 32(9):1057–1064.
  • LomholtM, NielsenSL, HansenSB, AndersenNT, HasenkamJM. 2002. Differential tension between secondary and primary mitral chordae in an acute in-vivo porcine model. J Heart Valve Dis. 11(3):337–345.
  • MaisanoF, RedaelliA, PennatiG, FumeroR, TorraccaL, AlfieriO. 1999. The hemodynamic effects of double-orifice valve repair for mitral regurgitation: a 3-D computational model. Eur J Cardiothorac Surg. 15(4):419–425.
  • MillardL, EspinoDM, ShepherdDET, HukinsDWL, BuchanKG. 2011. Mechanical properties of chordae tendineae: variation with chordal type and age. J Mech Med Biol. 11(1):221–230.
  • ObadiaJF, CendrineC, ChassignolleJF, JanierM. 1997. Mitral subvalvular apparatus – different functions of primary and secondary chordae. Circulation. 96(9):3124–3128.
  • PeskinCS. 1972. Flow patterns around heart valves: a numerical method. J Comput Phys. 10(2):252–270.
  • PeskinCS. 1977. Numerical analysis of blood flow in the heart. J Comput Phys. 25(3):220–252.
  • ProtV, SkallerudB, SommerG, HolzapfelGA. 2010. On modeling and analysis of healthy and pathological human mitral valves: two case studies. J Mech Behav Biomed Mater. 3(2):167–177.
  • RedaelliA, GuadagniG, FumeroR, MaisanoF, AlfieriO. 2001. A computational study of the hemodynamics after ‘edge to edge’ mitral valve repair. J Biomech Eng. 123(6):565–570.
  • ReulH, TalukderN, MuellerEW. 1981. Fluid mechanics of the natural mitral valve. J Biomech. 14(5):361–372.
  • RodriguezF, LangerF, HarringtonKB, TibayanFA, ZasioMK, LiangD, DaughterGT, IngelsNB, MillerDC. 2005. Effect of cutting second-order chordate on in-vivo anterior mitral leaflet compound curvature. J Heart Valve Dis. 14(5):592–602.
  • SacksMS, EnomotoY, GraybillJR, MerrymanWD, ZeeshanA, YoganathanAJ, LevyRJ, GormanRC, GormanJH, III. 2006. In-vivo dynamic deformation of the mitral valve anterior leaflet. Ann Thorac Surg. 82(4):1369–1378.
  • SalgoIS, GormanJH, III, GormanRC, JacksonBM, BowenFW, PlappertT, St John SuttonMG, EdmundsLH. 2002. Effect of annular shape on leaflet curvature in reducing mitral leaflet stress. Circulation. 106(6):711–717.
  • StijnenJMA, De HartJ, BovendeerdPHM, van de VosseFN. 2004. Evaluation of a fictitious domain method for predicting dynamic response of mechanical heart valves. J Fluid Struct. 19(6):835–850.
  • TibayanFA, RodriguezF, LangerF, ZasioMK, BaileyL, LiangD, DaughtersGT, KarlssonM, IngelsNB, Jr, MillerDC. 2004. Increases in mitral leaflet radii of curvature with chronic ischemic mitral regurgitation. J Heart Valve Dis. 13(5):772–778.
  • van de VosseFN, De HartJ, van OijenCHGA, BessemsD, GuntherTWM, SegalA, WoltersBJBM, StijnenJMA, BaaijensFPT. 2003. Finite-element-based computational methods for cardiovascular fluid–structure interaction. J Eng Math. 47(3–4):335–368.
  • van LoonR, AndersonPD, van de VosseFN. 2006. A fluid–structure interaction method with solid-rigid contact for heart valve dynamics. J Comput Phys. 217(2):806–823.
  • VigmostadSC, UdaykumarHS, LuJ, ChandranKB. 2010. Fluid–structure interaction methods in biological flows with special emphasis on heart valve dynamics. Int J Numer Methods Biomed Eng. 26(3–4):435–470.
  • VottaE, MaisanoF, SonciniM, RedaelliA, MontevecchiFM, AlfieriO. 2002. 3-D computational analysis of the stress distribution on the leaflets after edge-to-edge repair of mitral regurgitation. J Heart Valve Dis. 11(6):810–822.
  • WallW, GerstenbergerA, GamnitzerP, ForsterC, RammE. 2006. Large deformation fluid–structure interaction – advances in ALE methods and new fixed grid approaches, In: BungartzHJ, ShaferM, editors. Fluid–structure interaction. Berlin: Springer. p. 195–232.
  • WattonPN, LuoXY, WangX, BernaccaGM, MolloyP, WheatleyDJ. 2007. Dynamic modelling of prosthetic chorded mitral valves using the immersed boundary method. J Biomech. 40(3):613–626.
  • WenkJF, ZhangZ, ChengG, MalhotraD, Acevedo-BoltonG, BurgerM, SuzukiT, SalonerDA, WallaceAW, GuccioneJM et al., 2010. The first finite element model of the left ventricle with mitral valve: insights into ischemic mitral regurgitation. Ann Thorac Surg. 89(5):1546–1553.
  • WinslowAM. 1966. Numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh. J Comput Phys. 1(2):149–172.
  • YinM, LuoXY, WangTJ, WattonPN. 2010. Effects of flow vortex on a chorded mitral valve in the left ventricle. Int J Numer Methods Biomed Eng. 26(3–4):381–404.

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