A review of state-of-the-art numerical methods for simulating flow through mechanical heart valves

Medical and Biological Engineering and Computing

Volumn 47, Issue 3, 2009, Pages 245-256

  Sotiropoulos, Fotis ^a   Borazjani, Iman ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Aorta; Immersed boundary; Mechanical heart valve; Numerical method; Simulation

Indexed keywords

AORTA; BILEAFLET; BLOOD CELLS; CELL DAMAGES; COMPUTATIONAL FRAMEWORKS; DECELERATING FLOWS; FLUID-STRUCTURE INTERACTIONS; HEART VALVE REPLACEMENTS; IMMERSED BOUNDARY; LONG LIVES; MECHANICAL HEART VALVE; NUMERICAL SIMULATIONS; PHYSIOLOGIC CONDITIONS; RESEARCH AGENDAS; SIMULATING FLOWS; SIMULATION; VALVE DESIGNS; VALVE LEAFLETS; VIRTUAL SURGERIES;

BLOOD; BLOOD VESSELS; COMPUTATIONAL FLUID DYNAMICS; FLOW PATTERNS; FLUID DYNAMICS; FLUID STRUCTURE INTERACTION; HEART VALVE PROSTHESES; HYDRODYNAMICS; MATHEMATICAL MODELS; NUMBER THEORY; NUMERICAL METHODS; SURGERY; TURBULENCE; VIRTUAL REALITY;

VALVES (MECHANICAL);

HEART VALVE PROSTHESIS; HEART VALVES; HEMODYNAMICS; HEMORHEOLOGY; HUMANS; MODELS, CARDIOVASCULAR; POSTOPERATIVE PERIOD;

EID: 62149095772     PISSN: 01400118     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11517-009-0438-z     Document Type: Review

References (65)

1. American Heart Association (2007) Heart disease and stroke statistics, 2007 update. Technical report
2. Bluestein D, Rambod E, Gharib M (2000) Vortex shedding as a mechanism for free emboli formation in mechanical heart valves. J Biomech Eng Trans ASME 122(2):125-134
3. Borazjani I (2008) Numerical simulations of fluid/structure interaction problems in biological flows. Ph.D thesis, University of Minnesota
4. Borazjani I, Ge L, Sotiropoulos F (2008) Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3d rigid bodies. J Computat Phys 227(16):7587-7620
5. Borazjani I, Ge L, Sotiropoulos F (2008) High resolution fluid-structure interaction simulations of flow through a bi-leaflet mechanical heart valve in an anatomic aorta. Ann Biomed Eng (submitted)
6. Browne P, Ramuzat A, Saxena R, Yoganathan AP (2000) Experimental investigation of the steady flow downstream of the St. Jude bileaflet heart valve: A comparison between laser Doppler velocimetry and particle image velocimetry techniques. Ann Biomed Eng 28(1):39-47
7. Cheng R, Lai YG, Chandran KB (2003) Two-dimensional fluid-structure interaction simulation of bileaflet mechanical heart valve flow dynamics. J Heart Valve Dis 12(6):772-80
8. Cheng R, Lai YG, Chandran KB (2004) Three-dimensional fluid-structure interaction simulation of bileaflet mechanical heart valve flow dynamics. Ann Biomed Eng 32(11):1471-1483
9. Choi JI, Oberoi RC, Edwards JR, Rosati JA (2007) An immersed boundary method for complex incompressible flows. J Computat Phys 224(2):757-784
10. Dasi LP, Ge L, Simon HA, Sotiropoulos F, Yoganathan AP (2007) Vorticity dynamics of a bileaflet mechanical heart valve in an axisymmetric aorta. Phys Fluids 19:067105 (AIP)
11. De Hart J, Baaijens FPT, Peters GWM, Schreurs PJG (2003) A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve. J Biomech 36(5):699-712
12. De Hart J, Peters GWM, Schreurs PJG, Baaijens FPT (2000) A two-dimensional fluid-structure interaction model of the aortic value. J Biomech 33(9):1079-1088
13. De Hart J, Peters GWM, Schreurs PJG, Baaijens FPT (2003) A three-dimensional computational analysis of fluid-structure interaction in the aortic valve. J Biomech 36(1):103-112
14. De Hart J, Peters GWM, Schreurs PJG, Baaijens FPT (2004) Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole. J Biomech 37(3):303-311
15. Donea J, Giuliani S, Halleux JP (1982) An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comp Methods Appl Mech Eng 33(1-3):689-723
16. Dumont K, Vierendeels J, Kaminsky R, van Nooten G, Verdonck P, Bluestein D (2007) Comparison of the hemodynamic and thrombogenic performance of two bileaflet mechanical heart valves Using a CFD/FSI model. J Biomech Eng 129:558
17. Ellis JT, Healy TM, Fontaine AA, Saxena R, Yoganathan AP (1996) Velocity measurements and flow patterns within the hinge region of a medtronic parallel bileaflet mechanical valve with clear housing. J Heart Valve Dis 5(6):591-599
18. Fadlun EA, Verzicco R, Orlandi P, Mohd-Yusof J (2000) Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations. J Comput Phys 161(1):35-60
19. Felippa CA, Park KC, Farhat C (2001) Partitioned analysis of coupled mechanical systems. Comp Methods Appl Mech Eng 190(24-25):3247
20. Feng Z, Umezu M, Fujimoto T, Tsukahara T, Nurishi M, Kawaguchi D (2000) In vitro hydrodynamic characteristics among three bileaflet valves in the mitral position. Artif Organs 24(5):346-354
21. Ge L, Dasi LP, Sotiropoulos F, Yoganathan AP (2008) Characterization of hemodynamic forces induced by mechanical heart valves: Reynolds vs. viscous stresses. Ann Biomed Eng 36(2):276-297
22. Ge L, Fellow P, Leo HL, Student PD, Sotiropoulos F, Yoganathan AP (2005) Flow in a mechanical bileaflet heart valve at laminar and near-peak systole flow rates: Cfd simulations and experiments. J Biomech Eng 127:782
23. Ge L, Jones SC, Sotiropoulos F, Healy TM, Yoganathan AP (2003) Numerical simulation of flow in mechanical heart valves: Grid resolution and the assumption of flow symmetry. J Biomech Eng Trans ASME 125(5):709-718
24. Ge L, Sotiropoulos F (2007) A numerical method for solving the 3d unsteady incompressible navierstokes equations in curvilinear domains with complex immersed boundaries. J Comput Phys 225(2):1782-1809
25. Gilmanov A, Sotiropoulos F (2005) A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies. J Comput Phys 207:457-492
26. Gilmanov A, Sotiropoulos F, Balaras E (2003) A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids. J Comput Phys 191(2):660-669
27. Glowinski R, Pan TW, Hesla TI, Joseph DD (1999) A distributed Lagrange multiplier/fictitious domain method for particulate flows. Int J Multiphase Flow 25(5):755-794
28. Griffith BE, Hornung RD, McQueen DM, Peskin CS (2007) An adaptive, formally second order accurate version of the immersed boundary method. J Comput Phys 223(1):10-49
29. Grigioni M, Daniele C, D'Avenio G, Barbaro V (2002) Evaluation of the surface-averaged load exerted on a blood element by the reynolds shear stress field provided by artificial cardiovascular devices. J Biomech 35(12):1613-1622
30. Hellums JD (1994) 1993 Whitaker lecture: Biorheology in thrombosis research. Ann Biomed Eng 22(5):445-455
31. Kim J, Kim D, Choi H (2001) An immersed-bounday finite-volume method for simulations of flow in complex geometries. J Comput Phys 171:132-150
32. King MJ, Corden J, David T, Fisher J (1996) A three-dimensional, time-dependent analysis of flow through a bileaflet mechanical heart valve: Comparison of experimental and numerical results. J Biomech 29(5):609-618
33. Kiris C, Kwak D, Rogers S, Chang ID (1997) Computational approach for probing the flow through artificial heart devices. J Biomech Eng 119:452-460
34. Krishnan S, Udaykumar HS, Marshall JS, Chandran KB (2006) Two-dimensional dynamic simulation of platelet activation during mechanical heart valve closure. Ann Biomed Eng 34(10):1519-1534
35. Le DV, Khoo BC, Peraire J (2006) An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries. J Comput Phys 220(1):109-138
36. Leveque RJ, Li Z (1994) The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J Numer Anal 31(4):1019-1044
37. Leverett LB, Hellums JD, Alfrey CP, Lynch EC (1972) Red blood cell damage by shear stress. Biophys J 12(3):257
38. Lim WL, Chew YT, Chew TC, Low HT (1998) Steady flow dynamics of prosthetic aortic heart valves a comparative evaluation with PIV techniques. J Biomech 31(5):411-421
39. Manning KB, Kini V, Fontaine AA, Deutsch S, Tarbell JM (2003) Regurgitant flow field characteristics of the st. jude bileaflet mechanical heart valve under physiologic pulsatile flow using particle image velocimetry. Artif Org 27(9):840-846
40. Marella S, Krishnan S, Liu H, Udaykumar HS (2005) Sharp interface Cartesian grid method I: An easily implemented technique for 3D moving boundary computations. J Comput Phys 210(1):1-31
41. Mittal R, Iaccarino G (2005). Immersed boundary methods. Ann Rev Fluid Mech 37:239-261
42. Mok DP, Wall WA, Ramm E (2001) Accelerated iterative substructuring schemes for instationary fluid-structure interaction. First MIT conference on computational fluid and solid mechanics, pp 1325-1328
43. Nobili M, Morbiducci U, Ponzini R, Del Gaudio C, Balducci A, Grigioni M, Maria Montevecchi F, Redaelli A (2008) Numerical simulation of the dynamics of a bileaflet prosthetic heart valve using a fluid-structure interaction approach. J Biomech 41(11):2539-2550
44. Nyboe C, Funder JA, Smerup MH, Nygaard H, Hasenkam JM (2006) Turbulent stress measurements downstream of three bileaflet heart valve designs in pigs. Eur J Cardio-Thoracic Surg 29(6):1008-1013
45. Nygaard H, Paulsen PK, Hasenkam JM, Pedersen EM, Rovsing PE (1994) Turbulent stresses downstream of three mechanical aortic valve prostheses in human beings
46. Pedrizzetti G, Domenichini F (2006) Flow-driven opening of a valvular leaflet. J Fluid Mech 569:321-330
47. Pedrizzetti G, Domenichini F (2007) Asymmetric opening of a simple bileaflet valve. Phys Rev Lett 98(21):214503
48. Peskin CS (1972) Flow patterns around heart valves: A numerical method. J Comput Phys 10:252-271
49. Peskin CS, McQueen DM (1989) A three-dimensional computational method for blood flow in the heart. 1. Immersed elastic fibers in a viscous incompressible fluid. J Comput Phy 81(2):372-405
50. Rosenfeld M, Avrahami I, Einav S (2002) Unsteady effects on the flow across tilting disk valves. J Biomech Eng 124(1):21-29
51. Shim E, Chang K (1994) Three-dimensional vortex flow past a tilting disc valve using a segregated finite element scheme. Comput Dyn J 3:205
52. Shim EB, Chang KS (1997) Numerical analysis of three-dimensional Björk-Shiley valvular flow in an aorta. J Biomech Eng 119:45
53. Stijnen JMA, de Hart J, Bovendeerd PHM, van de Vosse FN (2004) Evaluation of a fictitious domain method for predicting dynamic response of mechanical heart valves. J Fluids Struct 19(6):835-850
54. Tai CH, Liew KM, Zhao Y (2007) Numerical simulation of 3D fluid-structure interaction flow using an immersed object method with overlapping grids. Comput Struct 85(11-14):749-762
55. Travis BR, Leo HL, Shah PA, Frakes DH, Yoganathan AP (2002) An analysis of turbulent shear stresses in leakage flow through a bileaflet mechanical prostheses. J Biomech Eng 124(2):155-165
56. Tseng YH, Ferziger JH (2003) A ghost-cell immersed boundary method for flow in complex geometry. J Comput Phys 192(2):593-623
57. Udaykumar HS, Mittal R, Shyy W (1999) Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids. J Comput Phys 153(2):535-574
58. van Loon R, Anderson PD, Baaijens FPT, van de Vosse FN (2005) A three-dimensional fluid-structure interaction method for heart valve modelling. Comptes rendus-Mécanique 333(12):856-866
59. van Loon R, Anderson PD, de Hart J, Baaijens FPT (2004) A combined ÿctitious domain = adaptive meshing method for uid-structure interaction in heart valves. Int J Numer Meth Fluids 46:533-544
60. van Loon R, Anderson PD, van de Vosse FN (2006) A fluid-structure interaction method with solid-rigid contact for heart valve dynamics. J Comput Phys 217(2):806-823
61. Vierendeels J, Dumont K, Dick E, Verdonck P (2005) Analysis and stabilization of fluid-structure interaction algorithm for rigid-body motion. AIAA J 43(12):2549
62. Xu S, Wang ZJ (2006) An immersed interface method for simulating the interaction of a fluid with moving boundaries. J Comput Phy 216(2):454-493
63. Yin W, Alemu Y, Affeld K, Jesty J, Bluestein D (2004) Flow-induced platelet activation in bileaflet and monoleaflet mechanical heart valves. Ann Biomed Eng 32(8):1058-1066
64. Yoganathan AP, He Z, Jones SC (2004) Fluid mechanics of heart valves. Ann Rev Biomed Eng 6:331-362
65. Yoganathan AP, Woo YR, Sung HW (1986) Turbulent shear stress measurements in the vicinity of aortic heart valve prostheses. J Biomech 19(6):433-42