Computational Mechanics

, Volume 45, Issue 1, pp 77–89

Computational fluid–structure interaction: methods and application to a total cavopulmonary connection

  • Yuri Bazilevs
  • M.-C. Hsu
  • D. J. Benson
  • S. Sankaran
  • A. L. Marsden
Open Access
Original Paper

Abstract

The Fontan procedure is a surgery that is performed on single-ventricle heart patients, and, due to the wide range of anatomies and variations among patients, lends itself nicely to study by advanced numerical methods. We focus on a patient-specific Fontan configuration, and perform a fully coupled fluid–structure interaction (FSI) analysis of hemodynamics and vessel wall motion. To enable physiologically realistic simulations, a simple approach to constructing a variable-thickness blood vessel wall description is proposed. Rest and exercise conditions are simulated and rigid versus flexible vessel wall simulation results are compared. We conclude that flexible wall modeling plays an important role in predicting quantities of hemodynamic interest in the Fontan connection. To the best of our knowledge, this paper presents the first three-dimensional patient-specific fully coupled FSI analysis of a total cavopulmonary connection that also includes large portions of the pulmonary circulation.

Keywords

Blood flow Fontan surgery Fluid–structure interaction Variable wall thickness Hyperelasticity Wall shear stress 

References

  1. 1.
    Bazilevs Y, Calo VM, Cottrel JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197: 173–201MATHCrossRefGoogle Scholar
  2. 2.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43: 3–37MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38: 310–322MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng. doi:10.1016/j.cma.2009.04.015
  5. 5.
    Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Liang X, Kvamsdal T, Brekken R, Isaksen JG (2009) A fully-coupled fluid–structure interaction simulation of cerebral aneurysms. Comput Mech, In the same issueGoogle Scholar
  6. 6.
    Bischoff M, Wall WA, Bletzinger K-U, Ramm E (2004) Models and finite elements for thin-walled structures. In: Stein E, de Borst R, Hughes TJR (eds) Encyclopedia of computational mechanics, vol 2, Solids, structures and coupled problems, chap 3. WileyGoogle Scholar
  7. 7.
    Bove EL, de Leval MR, Migliavacca F, Guadagni G, Dubini G (2003) Computational fluid dynamics in the evaluation of hemodynamic performance of cavopulmonary connections after the Norwood procedure for hypoplastic left heart syndrome. J Thorac Cardiovasc Surg 126: 1040–1047CrossRefGoogle Scholar
  8. 8.
    Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. J Appl Mech 60: 371–375MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    de Leval MR, Dubini G, Migliavacca F, Jalali H, camporini G, Redington A, Pietrabissa R (1996) Use of computational fluid dynamics in the design of surgical procedures: application to the study of competitive flows in cavo-pulmonary connections. J Thorac Cardiovasc Surg 111(3): 502–513CrossRefGoogle Scholar
  10. 10.
    Dubini G, de Leval MR, Pietrabissa R, Montevecchi FM, Fumero R (1996) A numerical fluid mechanical study of repaired congenital heart defects: application to the total cavopulmonary connection. J Biomech 29(1): 111–121CrossRefGoogle Scholar
  11. 11.
    Ensley AE, Ramuzat A, Healy TM, Chatzimavroudis GP, Lucas C, Sharma S, Pettigrew R, Yoganathan AP (2000) Fluid mechanic assessment of the total cavopulmonary connection using magnetic resonance phase velocity mapping and digital particle image velocimetry. Ann Biomed Eng 28: 1172–1183CrossRefGoogle Scholar
  12. 12.
    Farhat C, Geuzaine P, Grandmont C (2001) The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids. J Comput Phys 174(2): 669–694MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Fontan F, Baudet E (1971) Surgical repair of tricuspid atresia. Thorax 26: 240–248CrossRefGoogle Scholar
  14. 14.
    Giardini A, Balducci A, Specchia S, Gaetano G, Bonvicini M, Picchio FM (2008) Effect of sildenafil on haemodynamic response to exercise capacity in fontan patients. Eur Heart J 29: 1681–1687CrossRefGoogle Scholar
  15. 15.
    Hjortdal VE, Emmertsen K, Stenbog E, Frund T, Rahbek Schmidt M, Kromann O, Sorensen K, Pedersen EM (2003) Effects of exercise and respiration on blood flow in total cavopulmonary connection: a real-time magnetic resonance flow study. Circulation 108: 1227–1231CrossRefGoogle Scholar
  16. 16.
    Holzapfel GA (2000) Nonlinear solid mechanics, a continuum approach for engineering. Wiley, ChichesterMATHGoogle Scholar
  17. 17.
    Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis. Dover Publications, MineolaGoogle Scholar
  18. 18.
    Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian- Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29: 329–349MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Isaksen JG, Bazilevs Y, Kvamsdal T, Zhang Y, Kaspersen JH, Waterloo K, Romner B, Ingebrigtsen T (2008) Determination of wall tension in cerebral artery aneurysms by numerical simulation. Stroke 39: 3172–3178CrossRefGoogle Scholar
  20. 20.
    Jansen KE, Whiting CH, Hulbert GM (1999) A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190: 305–319CrossRefMathSciNetGoogle Scholar
  21. 21.
    Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119: 73–94MATHCrossRefGoogle Scholar
  22. 22.
    Khunatorn Y, Mahalingam S, DeGroff CG, Shandas R (2002) Influence of connection geometry and SVC-IVC flow rate ratio on flow structures within the total cavopulmonary connection: a numerical study. J Biomech Eng Trans ASME 124: 364–377CrossRefGoogle Scholar
  23. 23.
    Kulik TJ, Bass JL, Fuhrman BP, Moller JH, Lock JE (1983) Exercise induced pulmonary vasoconstriction. Br Heart J 50: 59–64CrossRefGoogle Scholar
  24. 24.
    Marsden AL, Vignon-Clementel IE, Chan F, Feinstein JA, Taylor CA (2007) Effects of exercise and respiration on hemodynamic efficiency in CFD simulations of the total cavopulmonary connection. Ann Biomed Eng 35(2): 250–263CrossRefGoogle Scholar
  25. 25.
    Marsden AL, Bernstein AD, Reddy VM, Shadden S, Spilker R, Chan FP, Taylor CA, Feinstein JA (2009) Evaluation of a novel Y-shaped extracardiac fontan baffle using computational fluid dynamics. J Thorac Cardiovasc Surg, To appearGoogle Scholar
  26. 26.
    Marsden AL, Vignon-Clementel IE, Chan F, Feinstein JA, Taylor CA (2007) Effects of exercise and respiration on hemodynamic efficiency in CFD simulations of the total cavopulmonary connection. Ann Biomed Eng 35: 250–263CrossRefGoogle Scholar
  27. 27.
    Masters JC, Ketner M, Bleiweis MS, Mill M, Yoganathan A, Lucas CL (2004) The effect of incorporating vessel compliance in a computational model of blood flow in a total cavopulmonary connection (tcpc) with caval centerline offset. J Biomech Eng 126: 709–713CrossRefGoogle Scholar
  28. 28.
    Migliavacca F, Dubini G, Bove EL, de Leval MR (2003) Computational fluid dynamics simulations in realistic 3-D geometries of the total cavopulmonary anastomosis: the influence of the inferior caval anastomosis. J Biomech Eng 125: 805–813CrossRefGoogle Scholar
  29. 29.
    Migliavacca F, Dubini G, Pietrabissa R, de Leval MR (1997) Computational transient simulations with varying degree and shape of pulmonic stenosis in models of the bidirectional cavopulmonary anastomosis. Med Eng Phys 19: 394–403CrossRefGoogle Scholar
  30. 30.
    Pedersen EM, Stenbog EV, Frund T, Houlind K, Kromann O, Sorensen KE, Emmertsen K, Hjortdal VE (2002) Flow during exercise in the total cavopulmonary connection measured by magnetic resonance velocity mapping. Heart 87: 554–558CrossRefGoogle Scholar
  31. 31.
    Petrossian E, Reddy VM, Collins KK, Culbertson CB, MacDonald MJ, Lamberti JJ, Reinhartz O, Mainwaring RD, Francis PD, Malhotra SP, Gremmels DB, Suleman S, Hanley FL (2006) The extracardiac conduit Fontan operation using minimal approach extracorporeal circulation: early and midterm outcomes. J Thorac Cardiovasc Surg 132(5): 1054–1063CrossRefGoogle Scholar
  32. 32.
    Sahni O, Muller J, Jansen KE, Shephard MS, Taylor CA (2006) Efficient anisotropic adaptive discretization of the cardiovascular system. Comput Methods Appl Mech Eng 195: 5634–5655MATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Shachar GB, Fuhrman BP, Wang Y, Lucas RV Jr, Lock JE (1982) Rest and exercise hemodynamics after the fontan procedure. Circulation 65: 1043–1048Google Scholar
  34. 34.
    Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70: 58–63MATHCrossRefGoogle Scholar
  35. 35.
    Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193: 2019–2032MATHCrossRefGoogle Scholar
  36. 36.
    Takizawa K, Christopher J, Moorman C, Martin J, Purdue J, McPhail T, Chen PR, Warren J, Tezduyar TE (2009) Space-time finite element computation of arterial FSI with patient-specific data. In: Schrefler B, Onate E, Papadrakakis M (eds) Computational methods for coupled problems in science and engineering, coupled problems 2009Google Scholar
  37. 37.
    Takizawa K, Christopher J, Tezduyar TE, Sathe S (2009) Space-time finite element computation of arterial fluid–structure interactions with patient-specific data. Commun Numer Methods Eng, published online. doi:10.1002/cnm.1241
  38. 38.
    Tezduyar TE, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite element computation of 3D flows. Computer 26: 27–36CrossRefGoogle Scholar
  39. 39.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575MATHCrossRefMathSciNetGoogle Scholar
  40. 40.
    Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the stabilized finite element methods—space-time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis, PVP-Vol. 246/ AMD-Vol. 143, pp 7–24. ASME, New YorkGoogle Scholar
  41. 41.
    Tezduyar TE, Sathe S (2007) Modelling of fluid–structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54: 855–900MATHCrossRefMathSciNetGoogle Scholar
  42. 42.
    Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modelling of fluid–structure interactions with the space-time finite elements: arterial fluid mechanics. Int J Numer Methods Fluids 54: 901–922MATHCrossRefMathSciNetGoogle Scholar
  43. 43.
    Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space-time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195: 2002–2027MATHCrossRefMathSciNetGoogle Scholar
  44. 44.
    Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2008) Arterial fluid mechanics modeling with the stabilized space-time fluid–structure interaction technique. Int J Numer Methods Fluids 57: 601–629MATHCrossRefMathSciNetGoogle Scholar
  45. 45.
    Tezduyar TE, Schwaab M, Sathe S (2008) Sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng, published online. doi:10.1016/j.cma.2008.05.024
  46. 46.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Computer modeling of cardiovascular fluid–structure interactions with the deforming-spatial-domain/stabilized space-time formulation. Comput Methods Appl Mech Eng 195: 1885–1895MATHCrossRefMathSciNetGoogle Scholar
  47. 47.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Fluid–structure interaction modeling of aneurysmal conditions with high and normal blood pressures. Comput Mech 38: 482–490MATHCrossRefGoogle Scholar
  48. 48.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2008) Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling. Comput Mech 43: 151–159MATHCrossRefGoogle Scholar
  49. 49.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2009) Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms. Commun Numer Methods Eng, published online. doi:10.1002/cnm.1289
  50. 50.
    Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA (2006) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Methods Appl Mech Eng 195: 3776–3796MATHCrossRefMathSciNetGoogle Scholar
  51. 51.
    Zhang Y, Wang W, Liang X, Bazilevs Y, Hsu M-C, Kvamsdal T, Brekken R, Isaksen JG (2009) High-fidelity tetrahedral mesh generation from medical imaging data for fluid–structure interaction analysis of cerebral aneurysms. Comput Model Eng Sci 42: 131–149Google Scholar

Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Yuri Bazilevs
    • 1
  • M.-C. Hsu
    • 1
  • D. J. Benson
    • 1
  • S. Sankaran
    • 2
  • A. L. Marsden
    • 2
  1. 1.Department of Structural EngineeringUniversity of California, San DiegoLa JollaUSA
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of California, San DiegoLa JollaUSA

Personalised recommendations