Computational Mechanics

, 43:151 | Cite as

Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling

  • Ryo Torii
  • Marie Oshima
  • Toshio Kobayashi
  • Kiyoshi Takagi
  • Tayfun E. Tezduyar
Original Paper


Fluid–structure interaction (FSI) simulations of a cerebral aneurysm with the linearly elastic and hyper-elastic wall constitutive models are carried out to investigate the influence of the wall-structure model on patient-specific FSI simulations. The maximum displacement computed with the hyper-elastic model is 36% smaller compared to the linearly elastic material model, but the displacement patterns such as the site of local maxima are not sensitive to the wall models. The blood near the apex of an aneurysm is likely to be stagnant, which causes very low wall shear stress and is a factor in rupture by degrading the aneurysmal wall. In this study, however, relatively high flow velocities due to the interaction between the blood flow and aneurysmal wall are seen to be independent of the wall model. The present results indicate that both linearly elastic and hyper-elastic models can be useful to investigate aneurysm FSI.


Fluid–structure interaction Cerebral aneurysm Patient-specific modeling Structural model 


  1. 1.
    Steiger HJ (1990) Pathophysiology of development and rupture of cerebral aneurysms. Acta Neurochir Suppl 48: 1–57Google Scholar
  2. 2.
    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: 482–490CrossRefzbMATHGoogle Scholar
  3. 3.
    Komatsu Y, Yasuda S, Shibata T, Ono Y, Hyodo A, Nose T (1994) Management for subarachnoid hemorrhage with negative initial angiography. Neurol Surg (in Japanese) 22: 43–49Google Scholar
  4. 4.
    Taylor CL, Yuan Z, Selman WR, Ratcheson RA, Rimm AA (1995) Cerebral arterial aneurysm formation and rupture in 20,767 elderly patients: hypertension and other risk factors. J Neurosurg 83: 812–819Google Scholar
  5. 5.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Fluid–structure interaction modeling of blood flow and cerebral aneurysm: significance of arterial and aneurysm shape. In: Proceedings of USNCCM9, San Francisco, JulyGoogle Scholar
  6. 6.
    Fung YC (1993) Biomechanics: mechanicsl properties of living tissue, 2 edn. Springer, New YorkGoogle Scholar
  7. 7.
    Humphrey JD (2002) Cardiovascular solid mechanics. Cells, tissues, and organs. Springer, New YorkGoogle Scholar
  8. 8.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Influence of wall elasticity in patient-specific hemodynamic simulations. Comput Fluids 36: 160–168zbMATHCrossRefGoogle Scholar
  9. 9.
    Baek S, Gleason RL, Rajagopal KR, Humphrey JD (2007) Theory of small on large: Potential utility in computations of fluid–solid interactions in arteries. Comput Methods Appl Mech Eng 196: 2070–3078CrossRefMathSciNetGoogle Scholar
  10. 10.
    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 Meth Appl Mech Eng 195: 5685–5706zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Raghavan ML, Vorp DA (2000) Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. J Biomech 33(4): 475–482CrossRefGoogle Scholar
  12. 12.
    DI Martino ES, Vorp D (2003) Effect of variation in intraluminal thrombus constitutive properties on abdominal aortic aneurysm wall stress. Ann Biomed Eng 31: 804–809CrossRefGoogle Scholar
  13. 13.
    Leung JH, Wright AR, Cheshire N, Crane J, Thom SA, Hughes AD, Xu Y (2006) Fluid structure interaction of patient specific abdominal aortic aneurysms: a comparison with solid stress models. Biomed Eng 5 (online)Google Scholar
  14. 14.
    Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38: 310–322CrossRefMathSciNetzbMATHGoogle Scholar
  15. 15.
    Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modeling of fluid–structure interactions with the space–time finite elements: Arterial fluid mechanics. Int J Numer Meth Fluids 54: 901–922zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    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 Meth Fluids 57: 601–629. doi: 10.1002/fld.1633 zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Holzapfel GA, Gasser TC (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61: 1–48zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Humphrey JD, Na S (2002) Elastodynamics and arterial wall stress. Ann Biomed Eng 30: 509–523CrossRefGoogle Scholar
  19. 19.
    Gasser TC, Holzapfel GA (2007) Finite element modeling of balloon angioplasty by considering overstretch of remnant non-diseased tissues in lesions. Comput Mech 40: 47–60CrossRefzbMATHGoogle Scholar
  20. 20.
    Hariton I, deBotton G, Gasser TC, Holzapfel GA (2005) How to incorporate collagen fibers orientations in an arterial bifurcation? In: Proceedings of 3rd IASTED international conference on biomechanics, Benidorm, Spain, SeptemberGoogle Scholar
  21. 21.
    Williamson SD, Lam Y, Younis HF, Huang H, Patel S, Kaazempur-Mofrad MR, Kamm RD (2003) On the sensitivity of wall stresses in diseased arteries to variable material properties. J Biomech Eng 125: 147–155CrossRefGoogle Scholar
  22. 22.
    Karino T, Takeuchi S, Kobayashi N, Motomiya M, Mabuchi S (1993) Fluid dynamics of cerebrovascular disease (in Japanese). Neurosurgeons 12: 15–24Google Scholar
  23. 23.
    Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44zbMATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces – the deforming-spatial-domain/space–time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94(3): 339–351zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space–time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94(3): 353–371zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Hughes TJR, Brooks AN (1979) A multi-dimensional upwind scheme with no crosswind diffusion. In: Hughes TJR (ed) Finite element methods for convection dominated flows, AMD, vol 34, ASME, New York, pp 19–35Google Scholar
  28. 28.
    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: 199–259zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95: 221–242zbMATHCrossRefGoogle Scholar
  30. 30.
    Hughes TJR, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška–Brezzi condition: a stable Petrov–Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Eng 59: 85–99zbMATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10): 27–36CrossRefGoogle Scholar
  32. 32.
    Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119: 157–177zbMATHCrossRefGoogle Scholar
  33. 33.
    Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18: 397–412zbMATHCrossRefGoogle Scholar
  34. 34.
    Tezduyar TE (1999) CFD methods for three-dimensional computation of complex flow problems. J Wind Eng Ind Aerodyn 81: 97–116CrossRefGoogle Scholar
  35. 35.
    Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8: 83–130zbMATHCrossRefGoogle Scholar
  36. 36.
    Tezduyar TE (2006) Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces. Comput Methods Appl Mech Eng 195: 2983– 3000zbMATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36: 191–206CrossRefMathSciNetGoogle Scholar
  38. 38.
    Tezduyar TE (2007) Finite elements in fluids: special methods and enhanced solution techniques. Comput Fluids 36: 207–223CrossRefMathSciNetGoogle Scholar
  39. 39.
    Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows—fluid–structure interactions. Int J Numer Methods Fluids 21: 933–953zbMATHCrossRefGoogle Scholar
  40. 40.
    Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid–structure interactions in parachute systems. Comput Methods Appl Mech Eng 190: 321–332zbMATHCrossRefGoogle Scholar
  41. 41.
    Tezduyar T, Osawa Y (2001) Fluid–structure interactions of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191: 717–726zbMATHCrossRefGoogle Scholar
  42. 42.
    Stein KR, Benney RJ, Tezduyar TE, Leonard JW, Accorsi ML (2001) Fluid–structure interactions of a round parachute: modeling and simulation techniques. J Aircraft 38: 800–808CrossRefGoogle 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: 2002–2027zbMATHCrossRefMathSciNetGoogle Scholar
  44. 44.
    Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195: 5743–5753zbMATHCrossRefMathSciNetGoogle Scholar
  45. 45.
    Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space–time finite elements: solution techniques. Int J Numer Methods Fluids 54: 855–900zbMATHCrossRefMathSciNetGoogle Scholar
  46. 46.
    Hisada T, Noguchi H (1995) Fundamentals and applications of nonlinear finite element method (in Japanese). Maruzen, TokyoGoogle Scholar
  47. 47.
    Delfino A, Stergiopulos N, Moore JE Jr, Meister JJ (1997) Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. J Biomech 30: 777–786CrossRefGoogle Scholar
  48. 48.
    Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, De Borst R, Hughes TJR (eds) Encyclopedia of computational mechanics, vol 3, Fluids, Chap 17, Wiley, New YorkGoogle Scholar
  49. 49.
    Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the finite element methods—space–time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis, PVP-vol 246/AMD-vol 143, ASME, New York, pp 7–24Google Scholar
  50. 50.
    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: 1885–1895zbMATHCrossRefMathSciNetGoogle Scholar
  51. 51.
    McDonald DA (1974) Blood flow in arteries, 2nd edn. Edward Arnold, LondonGoogle Scholar
  52. 52.
    Hayashi K, Handa H, Nagasawa S, Okumura A, Moritake K (1980) Stiffness and elastic behavior of human intracranial and extracranial arteries. J Biomech 13: 175–184CrossRefGoogle Scholar
  53. 53.
    Womersley JR (1955) Method for the calculation of velocity, rate of flow and viscos drag in arteries when the pressure gradient is known. J Physiol 127: 553–563Google Scholar
  54. 54.
    Ujiie H, Tamano Y, Sasaki K, Hori T (2001) Is the aspect ratio a reliable index for predicting the rupture of a saccular aneurysm. Neurosurgery 48(3): 495–503CrossRefGoogle Scholar
  55. 55.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Numerical investigation of the effect of hypertensive blood pressure on cerebral aneurysm—dependence of the effect on the aneurysm shape. Int J Numer Methods Fluids 54: 995–1009zbMATHCrossRefMathSciNetGoogle Scholar
  56. 56.
    Holzapfel GA (2003) Biomechanics of Soft Tissue in Cardiovascular Systems, chapter Structural and numerical models for the (visco)elastic response of arterial walls with residual stresses. Number 141 in CISM courses and lectures. Springer, New YorkGoogle Scholar
  57. 57.
    Raghavan ML, Trivedi S, Nagaraj A, McPherson DD, Chandran KB (2004) Three-dimensional finite element analysis of residual stress in arteries. Ann Biomed Eng 32: 257–263CrossRefGoogle Scholar
  58. 58.
    Malek AM, Alper SL, Izumo S (1999) Hemodynamic shear stress and its role in atherosclerosis. J Am Med Assoc 282: 2035–2042CrossRefGoogle Scholar
  59. 59.
    Abruzzo T, Shengelaia GG, Dawson RC III, Owens DS, Cawley CM, Gravanis MB (1998) Histologic and morphologic comparison of experimental aneurysms with human intracranial aneurysm. Am J Neuroradiol 19: 1309–1314Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Ryo Torii
    • 1
  • Marie Oshima
    • 2
  • Toshio Kobayashi
    • 3
  • Kiyoshi Takagi
    • 2
    • 4
  • Tayfun E. Tezduyar
    • 5
  1. 1.Department of Chemical EngineeringImperial CollegeLondonUK
  2. 2.Institute of Industrial ScienceThe University of TokyoTokyoJapan
  3. 3.Japan Automobile Research InstituteTsukubaJapan
  4. 4.Department of NeurosurgeryFujita Health UniversityToyoakeJapan
  5. 5.Mechanical EngineeringRice UniversityHoustonUSA

Personalised recommendations