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

  • Henry Y. Chen
  • Luoding Zhu
  • Yunlong Huo
  • Yi Liu
  • Ghassan S. Kassab


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.


Immerse Boundary Arbitrary Lagrangian Eulerian Immerse Boundary Method Flexible Fiber Surgical Ventricular Restoration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research was supported in part by the National Institute of Health-National Heart, Lung, and Blood Institute Grant HL055554-11, HL084529, and HL087235 (G. Kassab), and U.S. National Science Foundation grant DMS-0713718 (L. Zhu).


  1. 1.
    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.Google Scholar
  2. 2.
    Peskin CS Flow patterns around heart valves: a numerical method. J Comput Phys. 1977;25:220.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Peskin CS. The immersed boundary method. Acta Numer. 2002;11:479.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Hughes, TJR, Liu, WK, Zimmermann, TK. Lagrangian Eulerian finite element formulation in incompressible viscous flows. Comput Methods Appl Mech Eng. 1981;29:329–49MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    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;33:689–723MATHCrossRefGoogle Scholar
  6. 6.
    Formaggia L, Nobile F. A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements. EastWest J Numer Math. 1999;7:105–31.MathSciNetMATHGoogle Scholar
  7. 7.
    Fefferman C/L. Existence & smoothness of the Navier–Stokes equation. Princeton, NJ: Princeton University, Department of Mathematics. 2000.Google Scholar
  8. 8.
    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.Google Scholar
  9. 9.
    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.CrossRefGoogle Scholar
  10. 10.
    Tawhai MH, Hunter PJ. Multibreath washout analysis: modeling the influence of conducting airway asymmetry. Respir Physiol. 2001 Sep;127(2-3):249–58.CrossRefGoogle Scholar
  11. 11.
    Bathe KJ. Finite element procedures. Englewood Cliffs: Prentice-Hall, 1995, 1037 pp.Google Scholar
  12. 12.
    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.Google Scholar
  13. 13.
    McQueen DM, Peskin CS. Computer-assisted design of pivoting-disc prosthetic mitral valves. J Thorac Cardiovasc Surg. 1983;86:126–35.Google Scholar
  14. 14.
    McQueen DM, Peskin CS. Computer-assisted design of butterfly bileaflet valves for the mitral position. Scand J Thorac Cardiovasc Surg. 1985;19:139–48.CrossRefGoogle Scholar
  15. 15.
    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.CrossRefGoogle Scholar
  16. 16.
    Kovacs SJ, McQueen DM, Peskin CS. Modelling cardiac fluid dynamics and diastolic function. Philos Transact A Math Phys Eng Sci. 2001;359(1783):1299–314MATHCrossRefGoogle Scholar
  17. 17.
    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.CrossRefGoogle Scholar
  18. 18.
    Peskin CS, McQueen DM. Computational biofluid dynamics. Contemp Math. 1993:141:161.MathSciNetCrossRefGoogle Scholar
  19. 19.
    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.MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Chorin AJ. Numerical solution of the Navier–Stokes equations. Math Comp. 1968;22:745.MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Chorin AJ. On the convergence of discrete approximations to the Navier–Stokes equations. Math Comp. 1969;23:341MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    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.CrossRefGoogle Scholar
  23. 23.
    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.CrossRefGoogle Scholar
  24. 24.
    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.Google Scholar
  25. 25.
    STS Adult CV Surgery National Database. (2007) Executive summary. Durham, NC:Duke University Medical Center.Google Scholar
  26. 26.
    Gasser TC, Schulze-Bauer CA, Holzapfel GA. A three-dimensional finite element model for arterial clamping. J Biomech Eng. 2002;124(4):355–63.CrossRefGoogle Scholar
  27. 27.
    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.MATHCrossRefGoogle Scholar
  28. 28.
    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.Google Scholar
  29. 29.
    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.CrossRefGoogle Scholar
  30. 30.
    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.CrossRefGoogle Scholar
  31. 31.
    Jung E, Peskin CS. 2-D simulation of valveless pumping using the immersed boundary method. SIAM J Sci Comput. 2001;23(1):19–45.MathSciNetMATHCrossRefGoogle Scholar
  32. 32.
    Zhu L, Peskin CS. Interaction of two flapping filaments in a flowing soap film. Phys Fluids 2003;15(7):1954–60.MathSciNetCrossRefGoogle Scholar
  33. 34.
    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.CrossRefGoogle Scholar
  34. 35.
    Fung YC. Biomechanics: motion, flow, stress, and growth. Springer-Verlag, New York, 1998.Google Scholar
  35. 36.
    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.CrossRefGoogle Scholar
  36. 37.
    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.CrossRefGoogle Scholar
  37. 38.
    Ross DE.. Chasing the wrong villain. http://www.ctsnet.orgsections/newsandviews/inmyopinion/articles/article-58.html, 2006
  38. 39.
    Slayback JB, Bowen WW, Hinshaw DB. Intimal injury from arterial clamps. Am J Surg. 1976;132(2):183–8.CrossRefGoogle Scholar
  39. 40.
    Zhang W, Chen HY, Kassab GS. A rate-insensitive linear viscoelastic model for soft tissues. Biomaterials. 2007 Aug;28(24):3579–86.CrossRefGoogle Scholar
  40. 41.
    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.Google Scholar
  41. 42.
    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.Google Scholar
  42. 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.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Henry Y. Chen
    • 1
  • Luoding Zhu
    • 2
  • Yunlong Huo
    • 3
  • Yi Liu
    • 4
  • Ghassan S. Kassab
    • 5
    • 6
  1. 1.Weldon School of Biomedical EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.Department of Mathematical SciencesIUPUIIndianapolisUSA
  3. 3.Department of Biomedical Engineering, Surgery, and Cellular and Integrative PhysiologyIUPUIIndianapolisUSA
  4. 4.Department of Biomedical EngineeringIUPUIIndianapolisUSA
  5. 5.Weldon School of Biomedical EngineeringPurdue UniversityWest LafayetteUSA
  6. 6.Department of Biomedical Engineering Department of Surgery Department of Cellular and Integrative Physiology Indiana Center for Vascular Biology and MedicineIUPUIIndianapolisUSA

Personalised recommendations