Computational Mechanics

, Volume 46, Issue 1, pp 3–16 | Cite as

A fully-coupled fluid-structure interaction simulation of cerebral aneurysms

  • Y. Bazilevs
  • M.-C. Hsu
  • Y. Zhang
  • W. Wang
  • X. Liang
  • T. Kvamsdal
  • R. Brekken
  • J. G. Isaksen
Open Access
Original Paper

Abstract

This paper presents a computational vascular fluid-structure interaction (FSI) methodology and its application to patient-specific aneurysm models of the middle cerebral artery bifurcation. A fully coupled fluid-structural simulation approach is reviewed, and main aspects of mesh generation in support of patient-specific vascular FSI analyses are presented. Quantities of hemodynamic interest such as wall shear stress and wall tension are studied to examine the relevance of FSI modeling as compared to the rigid arterial wall assumption. We demonstrate the importance of including the flexible wall modeling in vascular blood flow simulations by performing a comparison study that involves four patient-specific models of cerebral aneurysms varying in shape and size.

Keywords

Cerebral aneurysms Fluid-structure interaction Arterial wall tissue modeling Incompressible Navier–Stokes equations Boundary layer meshing Wall shear stress Wall tension 

References

  1. 1.
    Appanaboyina S, Mut F, Löhner R, Putman C, Cebral J (2009) Simulation of intracranial aneurysm stenting: techniques and challenges. Comput Methods Appl Mech Eng (published online) doi:10.1016/j.cma.2009.01.017
  2. 2.
    Badia S, Nobile F, Vergara C (2009) Robin-Robin preconditioned Krylov methods for fluid-structure interaction problems. Comput Methods Appl Mech Eng 198: 2768–2784CrossRefMathSciNetGoogle Scholar
  3. 3.
    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
  4. 4.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43: 3–37MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    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
  6. 6.
    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 (published online) doi:10.1016/j.cma.2009.04.015
  7. 7.
    Bazilevs Y, Hsu M-C, Benson DJ, Sankaran S, Marsden AL (2009) Computational fluid-structure interaction: methods and application to a total cavopulmonary connection. Comput Mech (in the same issue)Google Scholar
  8. 8.
    Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36: 12– 26MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov- Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32: 199–259MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    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
  11. 11.
    Custus X. A visualization and navigation system for image-guided surgery based on VTK and ITK. http://www.sintef.no/Home/Health-Research/Medical-technology/
  12. 12.
    Fernández MA, Gerbeau J-F, Gloria A, Vidrascu M (2008) A partitioned Newton method for the interaction of a fluid and a 3D shell structure. Technical Report RR-6623, INRIA, 2008Google Scholar
  13. 13.
    Figueroa CA, Baek S, Taylor CA, Humphrey JD (2008) A computational framework for fluid-solid-growth modeling in cardiovascular simulations. Comput Methods Appl Mech Eng (published online) doi:10.1016/j.cma.2008.09.013
  14. 14.
    Figueroa CA, Vignon-Clementel IE, Jansen KE, Hughes TJR, Taylor CA (2006) A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput Methods Appl Mech Eng 195: 5685–5706MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Formaggia L, Gerbeau JF, Nobile F, Quarteroni A (2001) On the coupling of 3D and 1D Navier–Stokes equations for flow problems in compliant vessels. Comput Methods Appl Mech Eng 191: 561–582MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Gerbeau J-F, Vidrascu M, Frey P (2005) Fluid-structure interaction in blood flows on geometries based on medical imaging. Comput Struct 83: 155–165CrossRefGoogle Scholar
  17. 17.
    Holzapfel GA (2000) Nonlinear solid mechanics, a continuum approach for engineering. Wiley, ChichesterMATHGoogle Scholar
  18. 18.
    Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194: 4135–4195MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Hughes TJR, Engel G, Mazzei L, Larson MG (2000) The continuous Galerkin method is locally conservative. J Comput Phys 163: 467–488MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Hughes TJR, Oberai AA (2003) Calculation of shear stresses in the Fourier–Galerkin formulation of turbulent channel flows: projection, the Dirichlet filter and conservation. J Comput Phys 188: 281–295MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Hughes TJR, Scovazzi G, Franca LP (2004) Multiscale and stabilized methods. In: Stein E, de Borst R, Hughes TJR (eds) Encyclopedia of Computational Mechanics, vol 3: Fluids, chapter 2. Wiley, LondonGoogle Scholar
  22. 22.
    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
  23. 23.
    Jansen KE, Collis SS, Whiting C, Shakib F (1999) A better consistency for low-order stabilized finite element methods. Comput Methods Appl Mech Eng 174: 153–170MATHMathSciNetGoogle Scholar
  24. 24.
    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
  25. 25.
    Lagana K, Dubini G, Migliavacca F, Pietrabissa R, Pennati G, Veneziani A, Quarteroni A (2002) Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures. Biorheology 39: 359–364Google Scholar
  26. 26.
    Lipton S, Evans JA, Bazilevs Y, Elguedj T, Hughes TJR (2009) Robustness of isogeometric structural discretizations under severe mesh distortion. Comput Methods Appl Mech Eng (published online) doi:10.1016/j.cma.2009.01.022
  27. 27.
    Marsden AL, Feinstein JA, Taylor CA (2008) A computational framework for derivative-free optimization of cardiovascular geometries. Comput Methods Appl Mech Eng 197: 1890–1905CrossRefMathSciNetGoogle Scholar
  28. 28.
    Oshima M, Hughes TJR, Jansen K (1998) Consistent finite element calculations of boundary and internal fluxes. Int J Comput Fluid Dyn 9: 227–235MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Pope SB (2001) Large-eddy simulation using projection onto local basis functions. In: Lumley JL (eds) Fluid mechanics and the environment: dynamical approaches. Springer, Heidelberg, pp 239–265CrossRefGoogle Scholar
  30. 30.
    Rank E, Düster A, Nübel V, Preusch K, Bruhns OT (2005) High order finite elements for shells. Comput Methods Appl Mech Eng 194: 2494–2512MATHCrossRefGoogle Scholar
  31. 31.
    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. CIMNE, BarcelonaGoogle Scholar
  32. 32.
    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
  33. 33.
    Taylor CA, Hughes TJR, Zarins CK (1998) Finite element modeling of blood flow in arteries. Comput Methods Appl Mech Eng 158: 155–196MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575MATHCrossRefMathSciNetGoogle Scholar
  35. 35.
    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
  36. 36.
    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
  37. 37.
    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
  38. 38.
    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
  39. 39.
    Tezduyar TE, Takizawa K (2008) Private communicationGoogle Scholar
  40. 40.
    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
  41. 41.
    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
  42. 42.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Influence of the wall elasticity in patient-specific hemodynamic simulations. Comput Fluids 36: 160–168MATHCrossRefGoogle Scholar
  43. 43.
    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
  44. 44.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2008) Fluid-structure interaction modeling of blood flow and cerebral aneurysm: significance of artery and aneurysm shapes. Comput Methods Appl Mech Eng (published online) doi:10.1016/j.cma.2008.08.020
  45. 45.
    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
  46. 46.
    Zhang Y, Bajaj C, Sohn BS (2005) 3D finite element meshing from imaging data. Comput Methods Appl Mech Eng 194: 5083–5106MATHCrossRefGoogle Scholar
  47. 47.
    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: 131–150Google Scholar
  48. 48.
    Zhang Y, Xu G, Bajaj C (2006) Quality meshing of implicit salvation models of biomolecular structures. Comput Aided Geom Des 23: 510–530MATHCrossRefMathSciNetGoogle Scholar
  49. 49.
    Zunino P, D’Angelo C, Petrini L, Vergara C, Capelli C, Migliavacca F (2008) Numerical simulation of drug eluting coronary stents: Mechanics, fluid dynamics and drug release. Comput Methods Appl Mech Eng (published online) doi:10.1016/j.cma.2008.07.019

Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Y. Bazilevs
    • 1
  • M.-C. Hsu
    • 1
  • Y. Zhang
    • 2
  • W. Wang
    • 2
  • X. Liang
    • 2
  • T. Kvamsdal
    • 3
  • R. Brekken
    • 4
  • J. G. Isaksen
    • 5
    • 6
  1. 1.Department of Structural EngineeringUniversity of California, San DiegoLa JollaUSA
  2. 2.Department of Mechanical EngineeringCarnegie Mellon UniversityPittsburghUSA
  3. 3.Department of Applied MathematicsSINTEF Information and Communication TechnologyTrondheimNorway
  4. 4.Department of Medical TechnologySINTEF Health ResearchTrondheimNorway
  5. 5.Departments of Neurosurgery and NeurologyUniversity Hospital of North NorwayTromsøNorway
  6. 6.Institute of Clinical MedicineUniversity of TromsøTromsøNorway

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