A two-dimensional effective model describing fluid-structure interaction in blood flow: Analysis, simulation and experimental validation

Comptes Rendus - Mecanique

Volumn 333, Issue 12, 2005, Pages 867-883

  Čanić, Sunčica ^a   Mikelić, Andro ^b   Tambača, Josip ^c  

^a University of Houston   (United States)

^b UNIVERSITÉ LYON 1   (France)

^c UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

3D Navier Stokes equations; Asymptotic methods; Blood flow; Computational fluid mechanics; Fluid structure interaction

Indexed keywords

BLOOD FLOW; COMPUTATIONAL FLUID DYNAMICS;

EID: 28844490436     PISSN: 16310721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crme.2005.10.005     Document Type: Short Survey

References (28)

1. A. Quarteroni, M. Tuveri, and A. Veneziani Computational vascular fluid dynamics: problems, models and methods. Survey article Comput. Visual. Sci. 2 2000 163 197
2. W.W. Nichols, M.F. O'Rourke, McDonald's Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, fourth ed., Arnold and Oxford University
3. R. Glowinski, T.W. Pan, and J. Periaux A fictitious domain method for Dirichlet problem and applications Comput. Methods Appl. Mech. Engrg. 111 3-4 1994 283 303
4. R. Glowinski Finite element methods for incompressible viscous flow P.G. Ciarlet J.L. Lions Handbook of Numerical Analysis vol. IX 2003 North-Holland Amsterdam
5. F. Nobile, Numerical approximation of fluid-structure interaction problems with application to haemodynamics, Ph.D. Thesis, EPFL, Lausanne, 2001
6. K. Perktold, and G. Rappitsch Mathematical modeling of local arterial flow and vessel mechanics J. Crolet R. Ohayon Computational Methods for Fluid Structure Interaction Pitman Res. Notes in Math. vol. 306 1994 Longman Harlow 230 245
7. C.S. Peskin, and D.M. McQueen A three-dimensional computational method for blood flow in the heart - I. Immersed elastic fibers in a viscous incompressible fluid J. Comput. Phys. 81 2 1989 372 405
8. A.M. Robertson, and A. Sequeira A director theory approach to modeling blood flow in the arterial system Math. Models Methods Appl. Sci. 15 2005 871 906
9. S. Čanić, and E.-H. Kim Mathematical analysis of the quasilinear effects in a hyperbolic model of blood flow through compliant axi-symmetric vessels Math. Methods Appl. Sci. 26 14 2003 1161 1186
10. L. Formaggia, F. Nobile, and A. Quarteroni A one dimensional model for blood flow: application to vascular prosthesis I. Babuska T. Miyoshi P.G. Ciarlet Mathematical Modeling and Numerical Simulation in Continuum Mechanics Lect. Notes Comput. Sci. Eng. vol. 19 2002 Springer Berlin 137 153
11. Y.C. Fung Biomechanics: Circulation second ed. 1993 Springer New York
12. M.S. Olufsen, C.S. Peskin, W.Y. Kim, E.M. Pedersen, A. Nadim, and J. Larsen Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions Ann. Biomedical Engrg. 28 2000 1281 1299
13. L. Formaggia, J.F. Gerbeau, F. Nobile, and A. Quarteroni On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels Comput. Methods Appl. Mech. Engrg. 191 2001 561 582
14. P.G. Ciarlet, Mathematical Elasticity. Vol. III. Theory of Shells, in: Stud. Math. Appl., vol. 29, North-Holland, Amsterdam
15. P.G. Ciarlet, and V. Lods Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations Arch. Rational Mech. Anal. 136 2 1996 119 161
16. P.G. Ciarlet, and V. Lods Asymptotic analysis of linearly elastic shells. III. Justification of Koiter's shell equations Arch. Rational Mech. Anal. 136 2 1996 191 200
17. W.T. Koiter On the foundations of the linear theory of thin elastic shells. I, II Nederl. Akad. Wetensch. Proc. Ser. B 73 1970 169 182
18. P. Luchini, M. Lupo, and A. Pozzi Unsteady Stokes flow in a distensible pipe Z. Angew. Math. Mech. 71 10 1991 367 378
19. X. Ma, G.C. Lee, and S.G. Wu Numerical simulation for the propagation of nonlinear waves in arteries Trans. ASME 114 1992 490 496
20. S. Čanić, A. Mikelić, D. Lamponi, and J. Tambača Self-consistent effective equations modeling blood flow in medium-to-large compliant arteries SIAM J. Multisc. Anal. Simul. 3 2005 559 596
21. S. Čanić, and A. Mikelić Effective equations modeling the flow of a viscous incompressible fluid through a long elastic tube arising in the study of blood flow through small arteries SIAM J. Appl. Dynamical Systems 2 3 2003 431 463
22. C. Chmielewsky, Master's Thesis, North Carolina State University, 2004
23. M.A. Biot Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Lower frequency range J. Acoust. Soc. Am. 28 2 1956 168 178
24. M.A. Biot Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range J. Acoust. Soc. Am. 28 2 1956 179 191
25. J.-L. Auriault Poroelastic media U. Hornung Homogenization and Porous Media Interdiscip. Appl. Math. 1997 Springer Berlin 163 182
26. E. Sanchez-Palencia Non-Homogeneous Media and Vibration Theory Lecture Notes in Phys. vol. 127 1980 Springer
27. A. Mikelić M. Kirkilionis S. Krömker R. Rannacher F. Tomi Trends in Nonlinear Analysis 2002 Springer-Verlag Heidelberg 225 267
28. S. Čanić, and A. Mikelić Effective equations describing the flow of a viscous incompressible fluid through a long elastic tube C. R. Mecanique 330 2002 661 666