Computational analysis of an aortic valve jet with Lagrangian coherent structures

Chaos

Volumn 20, Issue 1, 2010, Pages

  Shadden, Shawn C ^a   Astorino, Matteo ^b   Gerbeau, Jean Frédéric ^b  

^a Illinois Institute of Technology   (United States)

^b INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

OXYGEN;

ANIMAL; AORTA VALVE; AORTA VALVE REGURGITATION; AORTA VALVE STENOSIS; ARTICLE; BIOMECHANICS; BIOPHYSICS; COMPUTER PROGRAM; HISTOLOGY; HUMAN; HYDRODYNAMICS; METABOLISM; METHODOLOGY; PATHOLOGY; STATISTICAL MODEL; THREE DIMENSIONAL IMAGING;

ANIMALS; AORTIC VALVE; AORTIC VALVE INSUFFICIENCY; AORTIC VALVE STENOSIS; BIOMECHANICS; BIOPHYSICS; HUMANS; HYDRODYNAMICS; IMAGING, THREE-DIMENSIONAL; MODELS, STATISTICAL; OXYGEN; SOFTWARE;

EID: 77953578906     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3272780     Document Type: Article

References (49)

1. Astorino M, Gerbeau J-F, Pantz O, Traoré K-F. Fluid-structure interaction and multi-body contact: Application to the aortic valves. Comput. Methods Appl. Mech. Eng. 2009, 198:3603-3612. CMMECC, 0045-7825, 10.1016/j.cma.2008.09.012.
2. Astorino M, Gerbeau J-F, Shadden S, Vignon-Clementel IE. Realistic blood flow through the aortic valve: simulation and analysis Nithiarasu, P., Lohner, R., van Loon, R., Conference Proceedings 1st International Conference on Computational and Mathematical Biomedical Engineering (CMBE), Swansea, 2009, edited by,, and.
3. Baaijens F. A fictitious domain/mortar element method for fluid-structure interaction. Int. J. Numer. Methods Fluids 2001, 35:743-761. IJNFDW, 0271-2091, 10.1002/1097-0363(20010415)35:7<743::AID-FLD109>3.0.CO;2-A.
4. Baumgartner H. Hemodynamic assessment of aortic stenosis. J. Am. Coll. Cardiol. 2006, 47:138-140. JACCDI, 0735-1097, 10.1016/j.jacc.2005.10.001.
5. Baumgartner H, Hung J, Bermejo J, Chambers JB, Evangelista A, Griffin BP, Iung B, Otto CM, Pellikka PA, Quinones M. Echocardiographic assessment of valve stenosis: EAE/ASE recommendations for clinical practice. J. Am. Soc. Echocardiogr 2009, 22:1-23. ZZZZZZ, 0894-7317, 10.1016/j.echo.2008.11.029.
6. Carmody CJ, Burriesci G, Howard IC, Patterson EA. An approach to the simulation of fluid-structure interaction in the aortic valve. J. Biomech. 2006, 39:158-169. JBMCB5, 0021-9290, 10.1016/j.jbiomech.2004.10.038.
7. Caro CG, Pedley TJ, Schroter RC, Seed WA. The Mechanics of the Circulation 1978, and, (Oxford University Press, New York).
8. Causin P, Diniz dos Santos N, Gerbeau JF, Guiver C, Metier P. An embedded surface method for valve simulation: Application to stenotic aortic valve estimation. ESAIM: Proceedings 2005, 14:48-62. and,,.
9. Chambers JB, Sprigings DC, Cochrane T, Allen J, Morris R, Black MM, Jackson G. Continuity equation and Gorlin formula compared with directly observed orifice area in native and prosthetic aortic valves. Br. Heart J. 1992, 67:193-199. BHJUAV, 0007-0769, 10.1136/hrt.67.2.193.
10. Chapelle D, Bathe KJ. The Finite Element Analysis of Shells-Fundamentals 2003, and, (Springer-Verlag, Berlin).
11. DeGroff CG, Shandas R, Valdes-Cruz L. Analysis of the effect of flow rate on the Doppler continuity equation for stenotic orifice area calculations: A numerical study. Circulation 1998, 97:1597-1605. CIRCAZ, 0009-7322.
12. De Hart J. Fluid-structure interaction in the aortic heart valve: A three-dimensional computational analysis. 2002, Ph.D. thesis, Technische Universiteit Eindhoven.
13. De Hart J, Baaijens F, Peters GW M, Schreurs PJ G. A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve. J. Biomech. 2003, 36:699-712. JBMCB5, 0021-9290, 10.1016/S0021-9290(02)00448-7.
14. De Hart J, Peters GW M, Schreurs PJ G, Baaijens FP T. A three-dimensional computational analysis of fluid-structure interaction in the aortic valve. J. Biomech. 2003, 36:103-112. JBMCB5, 0021-9290, 10.1016/S0021-9290(02)00244-0.
15. Diniz dos Santos N, Gerbeau J-F, Bourgat J-F. A partitioned fluid-structure algorithm for elastic thin valves with contact. Comput. Methods Appl. Mech. Eng. 2008, 197:1750-1761. CMMECC, 0045-7825, 10.1016/j.cma.2007.03.019.
16. Dumesnil JG, Yoganathan AP. Theoretical and practical differences between the Gorlin formula and the continuity equation for calculating aortic and mitral valve areas. Am. J. Cardiol. 1991, 67:1268-1272. AJCDAG, 0002-9149, 10.1016/0002-9149(91)90939-I.
17. Fernández MA, Gerbeau J-F. Fluid structure interaction problems in haemodynamics. Cardiovascular Mathematics 2009, Formaggia, L., Quarteroni, A., Veneziani, A., in, edited by, (Springer-Verlag, Berlin), Chap. 9.
18. Garcia D, Barenbrug P, Pibarot P, Dekker A, van der Veen FH, Maessen JG, Dumesnil JG, Durand LG. A ventricular-vascular coupling model in presence of aortic stenosis. Am. J. Physiol. 2005, 288:H1874-H1884. AJPHAP, 0002-9513.
19. Garcia D, Durand LG. Aortic Stenosis and Systemic Hypertension, Modeling of 2006, Wiley Encyclopedia of Biomedical Engineering (Wiley, New York).
20. Garcia D, Kadem L. What do you mean by aortic valve area: Geometric orifice area, effective orifice area or Gorlin area?. J. Heart Valve Dis. 2006, 15:601-608. ZZZZZZ, 0966-8519, and.
21. Garcia D, Pibarot P, Dumesnil JG, Sakr F, Durand LG. Assessment of aortic valve stenosis severity: A new index based on the energy loss concept. Circulation 2000, 101:765-771. CIRCAZ, 0009-7322.
22. Gorlin R, Gorlin SC. Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts. Am. Heart J. 1951, 41:1-29. AHJOA2, 0002-8703, 10.1016/0002-8703(51)90002-6.
23. Guivier C, Deplano V, Pibarot P. New insights into the assessment of the prosthetic valve performance in the presence of subaortic stenosis through a fluid-structure interaction model. J. Biomech. 2007, 40:2283-2290. JBMCB5, 0021-9290, 10.1016/j.jbiomech.2006.10.010.
24. Haller G. Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 2001, 149:248-277. PDNPDT, 0167-2789, 10.1016/S0167-2789(00)00199-8.
25. Kenwright DN, Lane DA. Interactive time-dependent particle tracing using tetrahedral decomposition. IEEE Trans. Vis. Comput. Graph. 1996, 2:120-129. ITVGEA, 1077-2626, 10.1109/2945.506224.
26. Ku DN, Giddens DP, Zarins CK, Glagov S. Pulsatile flow and atherosclerosis in the human carotid bifurcation: positive correlation between plaque location and low and oscillating shear-stress. Arterioscler. 1985, 5:293-302. .
27. Lekien F, Shadden SC, Marsden JE. Lagrangian coherent structures in n-dimensional systems. J. Math. Phys. 2007, 48:065404. JMAPAQ, 0022-2488, 10.1063/1.2740025.
28. McQueen DM, Peskin CS. Heart simulation by an immersed boundary method with formal second-order accuracy and reduced numerical viscosity. Mechanics for a New Millennium 2001, Aref, H., Phillips, J. W., in, edited by and (Springer, Netherlands).
29. Mok DP, Wall WA, Ramm E. Accelerated iterative substructuring schemes for instationary fluid-structure interaction. Computational Fluid and Solid Mechanics 2001, 1325-1328. Bathe, K. J., 10.1016/B978-008043944-0/50907-0, in, edited by (Elsevier, New York), pp.
30. Müller J-D. Heart valve fluid-structure interaction using weak coupling. CMBE09 2009, Nithiarasu, P., Löhner, R., van Loon, R., in, edited by, (Wiley, New York).
31. Pantz O. A Frictionless Contact Algorithm for Deformable Bodies 2008, preprint CMAP (cole Polytechnique, R.I. 647).
32. Ranga A, Bouchot O, Mongrain R, Ugolini P, Raymond C. Computational simulations of the aortic valve validated by imaging data: Evaluation of valve-sparing techniques. Interact. Cardiovasc. Thorac. Surg. 2006, 5:373-378. 10.1510/icvts.2005.121483, 1569-9293.
33. Richards KL, Cannon SR, Miller JF, Creawford MH. Calculation of aortic valve area by Doppler echocardiography: A direct application of the continuity equation. Circulation 1986, 73:964-969. CIRCAZ, 0009-7322.
34. Shadden SC. A dynamical systems approach to unsteady systems. 2006, Ph.D. thesis, California Institute of Technology.
35. Shadden SC, Dabiri JO, Marsden JE. Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 2006, 18:047105. PHFLE6, 1070-6631, 10.1063/1.2189885.
36. Shadden SC, Lekien F, Marsden JE. Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 2005, 212:271-304. PDNPDT, 0167-2789, 10.1016/j.physd.2005.10.007.
37. Shadden SC, Taylor CA. Characterization of coherent structures in the cardiovascular system. Ann. Biomed. Eng. 2008, 36:1152-1162. ABMECF, 0090-6964, 10.1007/s10439-008-9502-3.
38. Sotiropoulos F, Borazjani I. A review of the state-of-the-art numerical methods for simulating flow through mechanical heart valves. Med. Biol. Eng. Comput. 2009, 47:245-256. MBECDY, 0140-0118, 10.1007/s11517-009-0438-z.
39. Tran T-D. Construction d'un modéle 3d comprenant les sinus de valsalva, la valve aortique et l'arche aortique. 2006, M.S. thesis, cole Polytechnique Montreal.
40. van Loon R. Towards computational modelling of aortic stenosis. Communications in Numerical Methods in Engineering 2009, (Wiley).
41. van Loon R, Anderson PD, De Hart J, Baaijens FP T. A combined fictitious domain/adaptative meshing method for fluid-structure interaction in heart valves. Int. J. Numer. Methods Fluids 2004, 46:533-544. IJNFDW, 0271-2091, 10.1002/fld.775.
42. 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. JCTPAH, 0021-9991, 10.1016/j.jcp.2006.01.032.
43. Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput. Methods Appl. Mech. Eng. 2006, 195:3776-3796. CMMECC, 0045-7825, 10.1016/j.cma.2005.04.014.
44. Weinberg EJ, Kaazempur-Mofrad MR. On the constitutive models for heart valve leaflet mechanics. Cardiovasc. Eng. 2005, 5:37-43. ZZZZZZ, 1567-8822, 10.1007/s10558-005-3072-x.
45. Weinberg EJ, Kaazempur-Mofrad MR. Transient, three-dimensional, multiscale simulations of the human aortic valve. Cardiovasc. Eng. 2007, 7:140-155. ZZZZZZ, 1567-8822, 10.1007/s10558-007-9038-4.
46. Wootton DM, Ku DN. Fluid mechanics of vascular systems, diseases, and thrombosis. Annu. Rev. Biomed. Eng. 1999, 1:299-329. ARBEF7, 1523-9829, 10.1146/annurev.bioeng.1.1.299.
47. Xu Z, Chen N, Shadden SC, Marsden JE, Kamocka MM, Rosen ED, Alber M. Study of blood flow impact on growth of thrombi using a multiscale model. Soft Matter 2009, 5:769-779. SMOABF, 1744-683X, 10.1039/b812429a.
48. Yilmaz F, Gundogdu MY. A critical review on blood flow in large arteries: Relevance to blood rheology, viscosity models, and physiologic conditions. Korea-Aust. Rheol. J. 2008, 20:197-211. ZZZZZZ, 1226-119X.
49. Yu Z. A DLM/FD method for fluid/flexible-body interactions. J. Comput. Phys. 2005, 207:1-27. JCTPAH, 0021-9991, 10.1016/j.jcp.2004.12.026.