Numerical models for the simulation of flexible artificial heart valves: Part I - Computational methods

Computer Methods in Biomechanics and Biomedical Engineering

Volumn 4, Issue 4, 2001, Pages 323-339

  Fenlon, A J ^a   David, T ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Conjugate gradients; Coupled motion; Flexible heart valves; Fluid mechanics; Lagrangian dynamics; Panel method

Indexed keywords

CONJUGATE GRADIENT; COUPLED MOTIONS; HEART VALVES; LAGRANGIAN DYNAMICS; PANEL METHODS;

CONJUGATE GRADIENT METHOD; DYNAMIC MODELS; FLUID MECHANICS; LAGRANGE MULTIPLIERS;

NUMERICAL MODELS;

POLYURETHAN;

ARTICLE; BIOLOGICAL MODEL; BIOMECHANICS; BLOOD FLOW; COMPUTER SIMULATION; CORONARY ARTERY BLOOD FLOW; HEART VALVE PROSTHESIS; MECHANICAL STRESS; MOTION; NONLINEAR SYSTEM; PROSTHESIS; SURFACE PROPERTY;

BIOMECHANICS; COMPUTER SIMULATION; CORONARY CIRCULATION; HEART VALVE PROSTHESIS; MODELS, CARDIOVASCULAR; MOTION; NONLINEAR DYNAMICS; POLYURETHANES; PROSTHESIS DESIGN; REGIONAL BLOOD FLOW; STRESS, MECHANICAL; SURFACE PROPERTIES;

EID: 0035223019     PISSN: 10255842     EISSN: 14768259     Source Type: Journal    
DOI: 10.1080/10255840108908012     Document Type: Article

References (29)

1. Bellhousc, B. J. and Talbot, L, (1969) The fluid mechanics of the aortic valve. Journal of Fluid Mechanics, 35, 721-735.
2. Brewer, R. J., Mentzer, R. M. Jr., Deck, J. D., Ritter, R. C., Tretil, J. S. and Nolan, S. P. (1977) An in vivo study of the dimensional changes of the aortic valve leaflets during the cardiac cycle. The Journal of Throacic and Cardiovascular Surgery, 74(4), 645-650.
3. Butterfield, M. and Fisher, J. (1999) Stresses and modes of failure in polyurethane heart valves. Personal Communication, University of Leeds, Leeds, England.
4. Carling, J. C., Bowtcll, G. and Williams, T. L. (1995) Swimming in the lamprey, modelling the neural pattern generation, the body dynamics and the fluid mechanics. Cambridge press.
5. Cordon, J. (1995) The fluid mechanics and leaflet dynamics of the Leeds polyurethane trileaflet heart valve. Ph.D. Thesis, University of Leeds, Leeds, England.
6. Corden, J., David, T. and Fisher, J. (1995a) Determination of the curvatures and bending strains acting in open tri-leaflet heart valves. Proc. Inst. Mech. Engrs., 209, 121-128.
7. Corden, J., David, T. and Fisher, J. (1995b) In vitro determination of the curvatures and bending strains acting on the leaflets of polyurethane tri-leaflet heart valves during leaflet motion. Proc. Inst. Mech. Engrs., 209, 243-253.
8. Embree, M. and Trefethen, L. M. (1999) Green's Functions for Multiply connected Domains via Conformal Mapping. SIAM Review, 41, 745-761.
9. Fauci, L. J. and McDonald, A. (1995) Sperm motility in the presence of boundaries. Bulletin of mathematical biology, 57, 679-699.
10. Fenlon, A. J. (1999) Mathematical models for flexible leaflet heart valves. Ph.D. Thesis, Department of Mechanical Engineering, University of Leeds.
11. Fenlon, A, J. and David, T. (2000) Numerical models for the simulation of flexible artificial heart valves: Part II-valve Studies. Computer Methods in Biomechanics and Biomedical Engineering (to appear).
12. Gear, C. W. (1971) Numerical initial value problems in ordinary differential equations. Prentice-Hall, Englewood Cliffs, New Jersey.
13. Horsten, J. (1990) On the analysis of moving heart valves. Ph.D. Thesis, Technical Univeristy, Eindhoven, Hollnad.
14. Jones, K. and Platzer, M. (1995) Time-domain aeroelastic analysis of a two airfoil system with application to unsteady rotary wing flowfields. Technical Report, Naval Postgraduate School, California, USA.
15. Katz, J. and Plotkin, A. (1991) Low Speed Aerodynamics from wing theory to panel methods. McGraw-Hill, New York, international edition.
16. Katz, J, and Weihs, D. (1979) Large amplitude unsteady motion of a flexible slender propulsar. Journal of Fluid Mechanics, 90(4), 713-723.
17. Lighthill, J. (1990a) Biofluiddynamics of balistiform and gymnotiform locomotion. Part 1. Biological background, and analysis by elongated body theory. Journal of Fluid Mechanics, 212, 183-207.
18. Lighthill, J. (1990b) Biofluiddynamics of balistiform and gymnotiform locomotion. Part 2. The pressure distribution arising in two-dimensional irrotational flow from a general symmetrical motion of a flexible plate normal to itself. Journal of Fluid Mechanics, 213, 1-11.
19. NAG (1996) NAG Fortran Library Mark 14. The Numerical Algorithms Group, Ltd.
20. Peskin, C. S. (1980) Modeling prosthetic heart valves for numerical analysis of blood flow in the heart. Journal of Computational Physics, 37, 113-132.
21. Peskin, C. S. (1982) The fluid dynamics of heart valves: Experimental, theoretical and computational methods. Ann. Rev. Fluid Mech., 14, 235-259.
22. Swanson, W. M. and Clark, R. E. (1974a) Aortic valve motion during systole (Numerical graphical determination). Circ. Res., 32, 871-882.
23. Swanson, W. M. and Clark, R. E. (1974b) Dimensions and geometric relationships of the human aortic valve as a function of pressure. Circ. Res., 34, 42-48.
24. Thubrikar, M., Heckman, J. L. and Nolan, S. P. (1993) High speed cineradiographic study of aortic valve motion. J. Heart Valve Dis., 2(6), 653-661.
25. Thubrikar, M., Selim, G., Robicsek, F. and Fowler, B. (1997) Effect of Sinus geometry on the dynamics of bioprosthetic heart valves. In: Gabbay, S. and Wheatley, D. J. Eds., Advances in anticalciftc and antidegenerative treatment of heart valve prolheses, pp. 13-34, Washington, D.C. Silent Partners, Inc.
26. Thubrikar, M. J., Bosher, L. P. and Nolan, S. P. (1979) The mechanism of opening of the aortic valve. The Journal of Throacic and Cardiovascular Surgery, 77(6), 863-870.
27. Van der Vorst, H. A. (1992) Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 13(2), 631-644.
28. Van Steenhoven, A. A., Verlaan, C. W. J., Veenstra, P. C. and Reneman, R. S. (1981) In vivo cinematographic analysis of the aortic valve. American Physiological Society, 81, 286-292.
29. Wells, D. (1967) Schaum's outline series of theory and problems in Lagrangian dynamics. McGraw-Hill, New York.