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2010 | OriginalPaper | Buchkapitel

9. Fluid–Structure Interaction (FSI) Modeling in the Cardiovascular System

verfasst von : Henry Y. Chen, Luoding Zhu, Yunlong Huo, Yi Liu, Ghassan S. Kassab

Erschienen in: Computational Cardiovascular Mechanics

Verlag: Springer US

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Abstract

The cardiovascular system experiences strong fluid–structure interaction (FSI). This chapter presents the theoretical formulations for two powerful FSI techniques: the arbitrary Lagrangian Eulerian (ALE) and the immersed boundary (IB) methods. Examples of FSI applications to aortic cross-clamping used during surgical treatment of heart failure and valveless pumping are also presented.

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Literatur
1.
Zurück zum Zitat Peskin CS. Flow patterns around heart valves: a digital computer method for solving the equations of motion. (PhD thesis). Physiol., Albert Einstein Coll. Med, Univ. Microfilms. 1972;378:72–80. Peskin CS. Flow patterns around heart valves: a digital computer method for solving the equations of motion. (PhD thesis). Physiol., Albert Einstein Coll. Med, Univ. Microfilms. 1972;378:72–80.
4.
Zurück zum Zitat Hughes, TJR, Liu, WK, Zimmermann, TK. Lagrangian Eulerian finite element formulation in incompressible viscous flows. Comput Methods Appl Mech Eng. 1981;29:329–49MathSciNetMATHCrossRef Hughes, TJR, Liu, WK, Zimmermann, TK. Lagrangian Eulerian finite element formulation in incompressible viscous flows. Comput Methods Appl Mech Eng. 1981;29:329–49MathSciNetMATHCrossRef
5.
Zurück zum Zitat Donea J, Giuliani S, Halleux JP. An arbitrary Lagrangian Eulerian finite element method for transient dynamic fluid structure interactions. Comput Methods Appl Mech Eng. 1982;33:689–723MATHCrossRef Donea J, Giuliani S, Halleux JP. An arbitrary Lagrangian Eulerian finite element method for transient dynamic fluid structure interactions. Comput Methods Appl Mech Eng. 1982;33:689–723MATHCrossRef
6.
Zurück zum Zitat Formaggia L, Nobile F. A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements. EastWest J Numer Math. 1999;7:105–31.MathSciNetMATH Formaggia L, Nobile F. A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements. EastWest J Numer Math. 1999;7:105–31.MathSciNetMATH
7.
Zurück zum Zitat Fefferman C/L. Existence & smoothness of the Navier–Stokes equation. Princeton, NJ: Princeton University, Department of Mathematics. 2000. Fefferman C/L. Existence & smoothness of the Navier–Stokes equation. Princeton, NJ: Princeton University, Department of Mathematics. 2000.
8.
Zurück zum Zitat Boukir K, Nitrosso B, Maury, B. A characteristics-ALE method for variable domain Navier–Stokes equations. In: Wrobel LC, Sarler B, and Brebbia CA, Eds., Computational modeling of free and moving boundary problems III. Boston: Computational Mechanics Publications Southampton, 1995, pp. 57–65. Boukir K, Nitrosso B, Maury, B. A characteristics-ALE method for variable domain Navier–Stokes equations. In: Wrobel LC, Sarler B, and Brebbia CA, Eds., Computational modeling of free and moving boundary problems III. Boston: Computational Mechanics Publications Southampton, 1995, pp. 57–65.
9.
Zurück zum Zitat Huo Y, Guo X, Kassab GS. The flow field along the entire length of mouse aorta and primary branches. Ann Biomed Eng. 2008 May;36(5):685–99.CrossRef Huo Y, Guo X, Kassab GS. The flow field along the entire length of mouse aorta and primary branches. Ann Biomed Eng. 2008 May;36(5):685–99.CrossRef
10.
Zurück zum Zitat Tawhai MH, Hunter PJ. Multibreath washout analysis: modeling the influence of conducting airway asymmetry. Respir Physiol. 2001 Sep;127(2-3):249–58.CrossRef Tawhai MH, Hunter PJ. Multibreath washout analysis: modeling the influence of conducting airway asymmetry. Respir Physiol. 2001 Sep;127(2-3):249–58.CrossRef
11.
Zurück zum Zitat Bathe KJ. Finite element procedures. Englewood Cliffs: Prentice-Hall, 1995, 1037 pp. Bathe KJ. Finite element procedures. Englewood Cliffs: Prentice-Hall, 1995, 1037 pp.
12.
Zurück zum Zitat McQueen DM, Peskin CS, Yellin EL. Fluid dynamics of the mitral valve: Physiological aspects of a mathematical model. Am J Physiol. 1982;242:H1095–110. McQueen DM, Peskin CS, Yellin EL. Fluid dynamics of the mitral valve: Physiological aspects of a mathematical model. Am J Physiol. 1982;242:H1095–110.
13.
Zurück zum Zitat McQueen DM, Peskin CS. Computer-assisted design of pivoting-disc prosthetic mitral valves. J Thorac Cardiovasc Surg. 1983;86:126–35. McQueen DM, Peskin CS. Computer-assisted design of pivoting-disc prosthetic mitral valves. J Thorac Cardiovasc Surg. 1983;86:126–35.
14.
Zurück zum Zitat McQueen DM, Peskin CS. Computer-assisted design of butterfly bileaflet valves for the mitral position. Scand J Thorac Cardiovasc Surg. 1985;19:139–48.CrossRef McQueen DM, Peskin CS. Computer-assisted design of butterfly bileaflet valves for the mitral position. Scand J Thorac Cardiovasc Surg. 1985;19:139–48.CrossRef
15.
Zurück zum Zitat McQueen DM, Peskin CS. A three-dimensional computer model of the human heart for studying cardiac fluid dynamics. Comput Graph. 2000;34(1):56–60.CrossRef McQueen DM, Peskin CS. A three-dimensional computer model of the human heart for studying cardiac fluid dynamics. Comput Graph. 2000;34(1):56–60.CrossRef
16.
Zurück zum Zitat Kovacs SJ, McQueen DM, Peskin CS. Modelling cardiac fluid dynamics and diastolic function. Philos Transact A Math Phys Eng Sci. 2001;359(1783):1299–314MATHCrossRef Kovacs SJ, McQueen DM, Peskin CS. Modelling cardiac fluid dynamics and diastolic function. Philos Transact A Math Phys Eng Sci. 2001;359(1783):1299–314MATHCrossRef
17.
Zurück zum Zitat Vigmond EJ, Clements C, McQueen DM, Peskin CS. Effect of bundle branch block on cardiac output: A whole heart simulation study. Prog Biophys Mol Biol. 2008;97(2–3):520–42.CrossRef Vigmond EJ, Clements C, McQueen DM, Peskin CS. Effect of bundle branch block on cardiac output: A whole heart simulation study. Prog Biophys Mol Biol. 2008;97(2–3):520–42.CrossRef
19.
Zurück zum Zitat Zhu L, Peskin CS. Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J Comput Phys. 2002;179(2):452–68.MathSciNetMATHCrossRef Zhu L, Peskin CS. Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J Comput Phys. 2002;179(2):452–68.MathSciNetMATHCrossRef
21.
22.
Zurück zum Zitat Jackiewicz TA, McGeachie JK, Tennant M. Structural recovery of small arteries following clamp injury: a light and electron microscopic investigation in the rat. Microsurgery. 1996;17(12):674–80.CrossRef Jackiewicz TA, McGeachie JK, Tennant M. Structural recovery of small arteries following clamp injury: a light and electron microscopic investigation in the rat. Microsurgery. 1996;17(12):674–80.CrossRef
23.
Zurück zum Zitat Margovsky AI, Chambers AJ, Lord RS. The effect of increasing clamping forces on endothelial and arterial wall damage: an experimental study in the sheep. Cardiovasc Surg. 1999;7(4):457–63.CrossRef Margovsky AI, Chambers AJ, Lord RS. The effect of increasing clamping forces on endothelial and arterial wall damage: an experimental study in the sheep. Cardiovasc Surg. 1999;7(4):457–63.CrossRef
24.
Zurück zum Zitat Deiwick M, Glasmacher B, Baba HA, Roeder N, Reul H, Bally G, Scheld HH. In vitro testing of bioprostheses: influence of mechanical stresses and lipids on calcification. Ann Thorac Surg. 1998;66(6 Suppl):S206–11. Deiwick M, Glasmacher B, Baba HA, Roeder N, Reul H, Bally G, Scheld HH. In vitro testing of bioprostheses: influence of mechanical stresses and lipids on calcification. Ann Thorac Surg. 1998;66(6 Suppl):S206–11.
25.
Zurück zum Zitat STS Adult CV Surgery National Database. (2007) Executive summary. Durham, NC:Duke University Medical Center. STS Adult CV Surgery National Database. (2007) Executive summary. Durham, NC:Duke University Medical Center.
26.
Zurück zum Zitat Gasser TC, Schulze-Bauer CA, Holzapfel GA. A three-dimensional finite element model for arterial clamping. J Biomech Eng. 2002;124(4):355–63.CrossRef Gasser TC, Schulze-Bauer CA, Holzapfel GA. A three-dimensional finite element model for arterial clamping. J Biomech Eng. 2002;124(4):355–63.CrossRef
27.
Zurück zum Zitat Calvo B, Martínez MA, Peña E, Doblaré M. A directional damage model for fibred biological soft tissues. Int J Numer Methods Eng. 2007;69:2036–57.MATHCrossRef Calvo B, Martínez MA, Peña E, Doblaré M. A directional damage model for fibred biological soft tissues. Int J Numer Methods Eng. 2007;69:2036–57.MATHCrossRef
28.
Zurück zum Zitat Barone GW, Conerly JM, Farley PC, Flanagan TL, Kron IL. Assessing clamp-related vascular injuries by measurement of associated vascular dysfunction. Surgery. 1989;105(4):465–71. Barone GW, Conerly JM, Farley PC, Flanagan TL, Kron IL. Assessing clamp-related vascular injuries by measurement of associated vascular dysfunction. Surgery. 1989;105(4):465–71.
29.
Zurück zum Zitat Kassab GS, Navia JA, Lu X. Proper orientation of the graft artery is important to ensure physiological flow direction. Ann Biomed Eng. 2006;34(6):953–7.CrossRef Kassab GS, Navia JA, Lu X. Proper orientation of the graft artery is important to ensure physiological flow direction. Ann Biomed Eng. 2006;34(6):953–7.CrossRef
30.
Zurück zum Zitat Lu X, Kassab GS. Nitric oxide is significantly reduced in ex vivo porcine arteries during reverse flow because of increased superoxide production. J Physiol. 2004;561:575–82.CrossRef Lu X, Kassab GS. Nitric oxide is significantly reduced in ex vivo porcine arteries during reverse flow because of increased superoxide production. J Physiol. 2004;561:575–82.CrossRef
31.
Zurück zum Zitat Jung E, Peskin CS. 2-D simulation of valveless pumping using the immersed boundary method. SIAM J Sci Comput. 2001;23(1):19–45.MathSciNetMATHCrossRef Jung E, Peskin CS. 2-D simulation of valveless pumping using the immersed boundary method. SIAM J Sci Comput. 2001;23(1):19–45.MathSciNetMATHCrossRef
32.
Zurück zum Zitat Zhu L, Peskin CS. Interaction of two flapping filaments in a flowing soap film. Phys Fluids 2003;15(7):1954–60.MathSciNetCrossRef Zhu L, Peskin CS. Interaction of two flapping filaments in a flowing soap film. Phys Fluids 2003;15(7):1954–60.MathSciNetCrossRef
34.
Zurück zum Zitat Zhang J, Childress S, Libchaber A, Shelley M. Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 2000;408:835.CrossRef Zhang J, Childress S, Libchaber A, Shelley M. Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 2000;408:835.CrossRef
35.
Zurück zum Zitat Fung YC. Biomechanics: motion, flow, stress, and growth. Springer-Verlag, New York, 1998. Fung YC. Biomechanics: motion, flow, stress, and growth. Springer-Verlag, New York, 1998.
36.
Zurück zum Zitat Margovsky AT, Lord RSA, Meek AC, Bobryshev YV. Artery wall damage and platelet uptake from so-called atraumatic arterial clamps: an experimental study. Cardiovasc Surg. 1997;5:42–47.CrossRef Margovsky AT, Lord RSA, Meek AC, Bobryshev YV. Artery wall damage and platelet uptake from so-called atraumatic arterial clamps: an experimental study. Cardiovasc Surg. 1997;5:42–47.CrossRef
37.
Zurück zum Zitat Okazaki Y, Takarabe K, Murayama J, Suenaga E, Furukawa K, Rikitake K, Natsuaki M, Itoh T. Coronary endothelial damage during off-pump CABG related to coronary-clamping and gas insufflation. Eur J Cardiothorac Surg. 2001;19:834–39.CrossRef Okazaki Y, Takarabe K, Murayama J, Suenaga E, Furukawa K, Rikitake K, Natsuaki M, Itoh T. Coronary endothelial damage during off-pump CABG related to coronary-clamping and gas insufflation. Eur J Cardiothorac Surg. 2001;19:834–39.CrossRef
39.
Zurück zum Zitat Slayback JB, Bowen WW, Hinshaw DB. Intimal injury from arterial clamps. Am J Surg. 1976;132(2):183–8.CrossRef Slayback JB, Bowen WW, Hinshaw DB. Intimal injury from arterial clamps. Am J Surg. 1976;132(2):183–8.CrossRef
40.
Zurück zum Zitat Zhang W, Chen HY, Kassab GS. A rate-insensitive linear viscoelastic model for soft tissues. Biomaterials. 2007 Aug;28(24):3579–86.CrossRef Zhang W, Chen HY, Kassab GS. A rate-insensitive linear viscoelastic model for soft tissues. Biomaterials. 2007 Aug;28(24):3579–86.CrossRef
41.
Zurück zum Zitat Glowinski R, Pan T, Periaux J. A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations. Comp. Methods in Appl. Mech. and Eng. 1994;112(1–4):113–148. Glowinski R, Pan T, Periaux J. A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations. Comp. Methods in Appl. Mech. and Eng. 1994;112(1–4):113–148.
42.
Zurück zum Zitat Glowinski R, Pan T, Hesla T, Joseph D, Periaux J. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow. J. Comput. Phys. 2001;169(2):363–426. Glowinski R, Pan T, Hesla T, Joseph D, Periaux J. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow. J. Comput. Phys. 2001;169(2):363–426.
43.
Zurück zum Zitat Prosi M, Perktold K, Schima H. Effect of continuous arterial blood flow in patients with rotary cardiac assist device on the washout of a stenosis wake in the carotid bifurcation: a computer simulation study. J. Biomech. 2007;40(10):2236–43. Prosi M, Perktold K, Schima H. Effect of continuous arterial blood flow in patients with rotary cardiac assist device on the washout of a stenosis wake in the carotid bifurcation: a computer simulation study. J. Biomech. 2007;40(10):2236–43.
Metadaten
Titel
Fluid–Structure Interaction (FSI) Modeling in the Cardiovascular System
verfasst von
Henry Y. Chen
Luoding Zhu
Yunlong Huo
Yi Liu
Ghassan S. Kassab
Copyright-Jahr
2010
Verlag
Springer US
DOI
https://doi.org/10.1007/978-1-4419-0730-1_9

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