Skip to main content
SpringerLink
Log in

Structural analysis of the intervertebral discs adjacent to an interbody fusion using multibody dynamics and finite element cosimulation

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

This work describes a methodology for the dynamic and structural analysis of complex (bio)mechanical systems that joins both multibody dynamics and finite element domains, in a synergetic way, through a cosimulation procedure that takes benefit of the advantages of each numerical formulation. To accomplish this goal, a cosimulation module is developed based on the gluing algorithm X-X, which is the key element responsible for the management of the information flux between the two software packages (each using its own mathematical formulation and code). The X-X algorithm uses for each cosimulated structure multiple pairs of reference points whose kinematics are solved by the multibody module and prescribed, as initial data, to the finite element counterpart. The finite element module, by its turn, solves the structural problem imposed by the prescribed kinematics, calculates the resulting generalized loads applied over the reference points and return these loads back to the multibody module that uses them to solve the dynamic problem and to calculate new reference kinematics to prescribe to the finite element module in the next time step. The proposed method is applied to study the cervical spine dynamics in a pathologic situation in which an intersomatic fusion is simulated to confirm its potential advantages. Taking into account the proposed simulation scenario, a cervical spine multibody model that includes the rigid vertebrae, the facet joints’ and spinous processes’ contacts, ligaments and the finite element models of the intervertebral discs, and their surrogates is developed. The proposed model is simulated for extension in a forward dynamics perspective.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Rouvière, H.: Anatomie Humaine—Descriptive et Topographique: Tome II Tronc, 10th edn. Masson, Paris (1970)

    Google Scholar 

  2. Ehlers, W., Markert, B., Karajan, N., Acartürk, A.: A coupled FE analysis of the intervertebral disc based on a multiphasic TPM formulation. In: Holzapfel, G.A., Ogden, R.W. (eds.) Proceedings of IUTAM Symposium on Mechanics of Biological Tissue, pp. 373–386. Springer, Berlin (2005)

    Google Scholar 

  3. White, A.A., Panjabi, M.M.: Clinical Biomechanics of the Spine, 2nd edn. Williams & Wilkins, Baltimore (1970)

    Google Scholar 

  4. Skaggs, D.L., Weidenbaum, M., Iatridis, J.C., Ratcliffe, A., Mow, V.C.: Regional variation in tensile properties and biochemical composition of the lumbar annulus fibrosus. Spine 19(12), 1310–1319 (1994)

    Article  Google Scholar 

  5. Harris, R.I., Macnab, I.: Structural changes in the lumbar intervertebral disc: Their relationship to low back pain and sciatica. J. Bone Jt. Surg. 36B(2), 304–322 (1954)

    Google Scholar 

  6. Brown, S.H.M., Gregory, D.E., McGill, S.M.: Vertebral endplate fractures as a result of high rate pressure loading in the nucleus of the young adult porcine spine. J. Biomech. 41, 122–127 (2008)

    Article  Google Scholar 

  7. Cusick, J.F., Yoganandan, N.: Biomechanics of the cervical spine 4: Major injuries. Clin. Biomech. 17, 1–20 (2002)

    Article  Google Scholar 

  8. Shirazi-Adl, A.: Finite element simulation of changes in the fluid content of human lumbar discs: Mechanical and clinical implications. Spine 17(2), 206–212 (1992)

    Article  Google Scholar 

  9. Dvorak, M., Pitzen, T., Zhu, O., Gordon, J., Fisher, C., Oxland, T.: Anterior cervical plate fixation: A biomechanical study to evaluate the effects of plate design, endplate preparation, and bone mineral density. Spine 30(3), 294–301 (2005)

    Article  Google Scholar 

  10. Lopez-Espina, C.G., Amirouche, F., Havalad, V.: Multilevel cervical fusion and its effect on disc degeneration and osteophyte formation. Spine 31(9), 972–978 (2006)

    Article  Google Scholar 

  11. Gillet, P.: The fate of adjacent motion segments after lumbar fusion. J. Spinal Disord. Tech. 16(4), 338–345 (2003)

    Google Scholar 

  12. Rao, R.D., Wang, M., McGrady, L.H., Perlewitz, T.J., Dacid, K.S.: Does anterior plating of the cervical spine predispose to adjacent segment changes? Spine 30(24), 2788–2792 (2005)

    Article  Google Scholar 

  13. Wang, J., Ma, Z.-D., Hulbert, G.M.: A gluing algorithm for distributed simulation of multibody systems. Nonlinear Dyn. 34, 159–188 (2003)

    Article  MATH  Google Scholar 

  14. Rauter, F.G., Pombo, J., Ambrósio, J., Pereira, M.: Multibody modeling of pantographs for pantograph–catenary interaction. In: Eberhard, P. (ed.) IUTAM Symposium on Multiscale Problems in Multibody System Contacts, pp. 205–226. Springer, Berlin (2007)

    Chapter  Google Scholar 

  15. Esat, V., Acar, M.: A multibody human spine model for dynamic analysis in conjunction with the fe analysis of spinal parts. In: Proceedings of 1st Annual Injury Biomechanics Symposium, The Ohio State University, USA (2005)

  16. Esat, V., van Lopik, D.W., Acar, M.: Combined multi-body dynamic and fe models of human head and neck. In: Gilchrist, M.D. (ed.) IUTAM Proceedings on Impact Biomechanics: From Fundamental Insights to Application, pp. 91–100. Springer, Berlin (2005)

    Chapter  Google Scholar 

  17. Esat, V., Acar, M.: Viscoelastic finite element analysis of the cervical intervertebral discs in conjunction with a multi-body dynamic model of the human head and neck. Proc. Inst. Mech. Eng., Part H, J. Eng. Med. 249–262 (2009)

  18. Silva, M.T.: Human motion analysis using multibody dynamics and optimization tools. PhD. Thesis Instituto Superior Técnico—Technical University of Lisbon, Lisbon (2003)

  19. Ferreira, A.: Multibody model of the cervical spine and head for the simulation of traumatic and degenerative disorders. M.Sc. Thesis Instituto Superior Técnico—Technical University of Lisbon, Lisbon (2008)

  20. Ambrósio, J., Veríssimo, P.: Improved bushing models for general multibody systems and vehicle dynamics. Multibody Syst. Dyn. 22(4), 341–365 (2009)

    Article  MATH  Google Scholar 

  21. de Jager, M.: Mathematical head-neck models for acceleration impacts. Technische Universiteit Eindhoven—University of Technology, Eindhoven (2000)

  22. Monteiro, N.: Analysis of intervertebral discs adjacent to interbody fusion using a multibody and finite element cosimulation. M.Sc. Thesis Instituto Superior Técnico—Technical University of Lisbon, Lisbon (2009)

  23. Wheeldon, J.A., Pintar, F.A., Knowles, S., Yoganandan, N.: Experimental flexion/extension data corridors for validation of finite element models of the young, normal cervical spine. J. Biomech. 39, 375–380 (2004)

    Article  Google Scholar 

  24. Camacho, D.L., Nightingale, R.W., Robinette, J.J., Vanguri, S.K., Coates, D.J., Myers, B.S.: Experimental flexibility measurements for the development of a computational head–neck model validated for a near-vertex head impact. Society of Automotive Engineers, Paper No. 973345 (1997)

  25. Nightingale, R.W., Winkelstein, B.A., Knaub, K.E., Richardson, W.J., Luck, J.F., Myers, B.S.: Comparative strengths and structural properties of the upper and lower cervical spine in flexion and extension. J. Biomech. 35, 725–732 (2002)

    Article  Google Scholar 

  26. Nightingale, R.W., Chancey, V.C., Ottaviano, D., Luck, J.F., Tran, L., Prange, H., Myers, B.S.: Flexion and extension structural properties and strengths for male cervical spine segments. J. Biomech. 40, 535–542 (2007)

    Article  Google Scholar 

  27. Goël, V., Clark, C., Gallaes, K., Liu, Y.K.: Moment–rotation relationships of the ligamentous occipito-axial complex. J. Biomech. 21(8), 673–680 (1988)

    Article  Google Scholar 

  28. van Lopik, D.W., Acar, M.: Dynamic verification of a multibody computational model of human head and neck for frontal, lateral and rear impacts. Proc. Inst. Mech. Eng., Part K, J. Multibody Dyn. 221(2), 199–217 (2007)

    Google Scholar 

  29. Ambrósio, J.A.C.: Multibody dynamics: Bridging for multidisciplinary applications. In: Gutkowski, W., Kowalewski (eds.) Mechanics of the 21st Century, pp. 61–88. Springer, Berlin (2005)

    Chapter  Google Scholar 

  30. Tseng, F.C.: Multibody dynamics simulation in network-distributed environments. PhD. Dissertation, University of Michigan (2000)

  31. de La Bourdonnaye, A., Farhat, C., Macedo, A., Magoules, F., Roux, F.-X.: A method of finite element tearing and interconnecting for the Helmholtz problem. In: Topping, B.H.V. (ed.) Advances in Computational Mechanics with High Performance Computing, pp. 41–54. CIVIL-COMP Press (1998)

  32. Ladeveze, P., Dureisseix, D.: Comparison of multi-level approaches in domain decomposition for structural analysis. In: Topping, B.H.V. (ed.) Advances in Computational Mechanics with High Performance Computing, pp. 55–63. CIVIL-COMP Press (1998)

  33. Tseng, F.-C., Hulbert, G.M.: A gluing algorithm for network-distributed multibody dynamics simulation. Multibody Syst. Dyn. 6, 377–396 (2001)

    Article  MATH  Google Scholar 

  34. Yen, J., Petzold, L.R.: An efficient Newton-type iteration for the numerical solution of highly oscillatory constrained multibody dynamic systems. SIAM J. Sci. Comput. 15(5), 1513–1534 (1998)

    Article  MathSciNet  Google Scholar 

  35. Monteiro, N., Folgado, J., Silva, M., Melancia, J.: Analysis of the intervertebral discs using a finite element and multibody dynamics approach. In: 8th World Congress on Computational Mechanics (WCCM8), 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), Venice, Italy, 30 June–5 July 2008

  36. Monteiro, N., Folgado, J., Silva, M., Melancia, J.: Co-simulação de sistemas multicorpo com modelos de elementos finitos: Aplicação à análise de tensões nos discos intervertebrais. In: 3° Congresso Nacional de Biomecânica, Bragança (2009)

  37. Monteiro, N., Folgado, J., Silva, M., Melancia, J.: Dynamic stress distribution on a multilevel cervical fusion using a MSD/FE cosimulation approach. In: Proceedings of Multibody Dynamics 2009. An ECCOMAS Thematic Conference, Warsaw, Poland, 29 June–2 July 2009

  38. Monteiro, N., Folgado, J., Silva, M., Melancia, J.: A new approach to analyze the stress distribution on a multilevel cervical/lumbar intersomatic fusion. In: Proceedings of ESMC2009, 7th EUROMECH Solid Mechanics Conference, Lisbon, Portugal, 7–11 September 2009

  39. Nikravesh, P.: Computer-Aided Analysis of Mechanical Systems. Prentice-Hall, Englewood Cliffs (1988)

    Google Scholar 

  40. Panjabi, M.M., Oxland, T.R., Parks, E.H.: Quantitative anatomy of cervical spine ligaments. Part I: Upper cervical spine. J. Spinal Disord. Tech. 4(3), 270–276 (1991)

    Google Scholar 

  41. Sharma, M., Langrana, N.A., Rodriguez, J.: Role of ligaments and facets in lumbar spinal stability. Spine 20(8), 887–900 (1995)

    Article  Google Scholar 

  42. Chazal, J., Tanguy, A., Bourges, M., Gaurel, G., Escande, G., Guillot, M., Vanneuville, G.: Biomechanical properties of spinal ligaments and a histological study of the supraspinal ligament in traction. J. Biomech. 18(3), 167–176 (1985)

    Article  Google Scholar 

  43. Panjabi, M.M.: The stabilizing system of the spine—Part II: Neutral zone and instability hypothesis. J. Spinal Disord. Tech. 5, 390–396 (1992)

    Article  Google Scholar 

  44. Yoganandan, N., Kumaresan, S., Pintar, F.A.: Biomechanics of the cervical spine Part 2: Cervical spine soft tissue responses and biomechanical modeling. Clin. Biomech. 16, 1–27 (2001)

    Article  Google Scholar 

  45. Wisman, J.: A three-dimensional mathematical model of the human knee joint. PhD. Thesis, Technische Hogenschool Eindhoven (1980)

  46. van der Horst, M.: Human head neck response in frontal, lateral and rear end impact loading. Technisch Universiteit Eindhoven—University of Technology, Eindhoven (2002)

  47. Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. ASME J. Mech. Des. 112, 369–375 (1990)

    Article  Google Scholar 

  48. Ambrósio, J.A., Silva, M.: Multibody dynamics approaches for biomechanical modeling in human impact application. In: Gilchrist, M.D. (ed.) IUTAM Proceedings on Impact Biomechanics: From Fundamental Insights to Applications, pp. 61–80. Springer, Berlin (2005)

    Chapter  Google Scholar 

  49. Hertz, H.: On the Contact of Solids—On the Contact of Rigid Elastic Solids and on Hardness. Miscellaneous Papers, pp. 146–183. MacMillan, London (1896)

    Google Scholar 

  50. Burgin, L.V., Aspden, R.M.: Impact testing to determine the mechanical properties of articular cartilage in isolation and on bone. J. Mater. Sci. Mater. Med. 19, 703–711 (2008)

    Article  Google Scholar 

  51. Nissan, M., Gilad, I.: The cervical and lumbar vertebrae—an anthropometric model. Eng. Med. 13(3), 111–114 (1984)

    Article  Google Scholar 

  52. Panjabi, M.M., Duranceau, J., Goel, V., Oxland, T., Takata, K.: Cervical human vertebrae: Quantitative three-dimensional anatomy of the middle and lower regions. Spine 16(8), 861–869 (1991)

    Article  Google Scholar 

  53. Panjabi, M.M., Oxland, T., Takata, K., Goël, V., Duranceau, J., Krag, M.: Articular facets of the human spine: Quantitative three-dimensional anatomy. Spine 18(10), 1298–1310 (1993)

    Article  Google Scholar 

  54. Xu, R., Burgar, A., Ebraheim, N.A., Yeasting, R.A.: The quantitative anatomy of the laminas of the spine. Spine 24(2), 107–113 (1999)

    Article  Google Scholar 

  55. Yoganandan, N., Kumaresan, S., Pintar, F.A.: Geometrical and mechanical properties of human cervical spine ligaments. J. Biomech. Eng. 122, 623–629 (2000)

    Article  Google Scholar 

  56. Meertens, W.: Mathematical modelling of the upper cervical spine with MADYMO. Final Thesis, Eindhoven University of Technology (1995)

  57. Hukins, D.W.L., Kirby, M.C., Sikoryn, T.A., Aspden, R.M., Cox, A.J.: Comparison of structure, mechanical properties, and functions of lumbar spinal ligaments. Spine 15(8), 787–795 (1990)

    Google Scholar 

  58. Tkaczuk, H.: Tensile properties of human lumbar longitudinal ligaments. Acta Orthop. Scand. 115 (1968) (Supplement)

  59. Nachemson, A., Evans, J.: Some mechanical properties of the third lumbar inter-laminar ligament (ligamentum flavum). J. Biomech. 1(211) (1968)

  60. Fagan, M.J., Julian, S., Siddall, D.J., Mohsen, A.M.: Patient-specific spine models. Part 1: Finite element analysis of the lumbar intervertebral disc—a material sensitivity study. Proc. Inst. Mech. Eng., Part H, J. Eng. Med. 216, 299–314 (2002)

    Article  Google Scholar 

  61. Tanaka, N., Fujimoto, Y., An, H.S., Ikuta, Y., Yasuda, M.: The anatomic relation among the nerve roots, intervertebral foramina, and intervertebral disc of the cervical spine. Spine 25(3), 286–291 (2000)

    Article  Google Scholar 

  62. Bogduk, N.: Clinical Anatomy of the Lumbar Spine and Sacrum. Churchill Livingstone, New York (1997)

    Google Scholar 

  63. Nachemson, A.: Lumbar intradiscal pressure: Experimental studies on postmortem material. Acta Orthop. Scand. 43, 9–104 (1960)

    Google Scholar 

  64. Moroney, S.P., Schultz, A.B., Miller, J.A.A., Andersson, G.B.J.: Load-displacement properties of lower cervical spine motion segments. J. Biomech. 21, 767–779 (1988)

    Article  Google Scholar 

  65. Marchand, F., Ahmed, A.: Investigation of the laminate structure of lumbar disc annulus fibrosus. Spine 15(5), 402–410 (1990)

    Article  Google Scholar 

  66. Little, J.P.: Finite element modeling of anular lesions in the lumbar intervertebral disc. PhD. Thesis, Queensland University of Technology (2004)

  67. Eyre, D., Muir, H.: Types I and II collagens in intervertebral disc: Interchanging radial distributions in annulus fibrosus. Biochem. J. 157(1), 267–270 (1976)

    Google Scholar 

  68. Chen, J.-F., Wu, C.-T., Lee, S.-C., Lee, S.-T.: Use of a polymethylmethacrylate cervical cage in the treatment of single-level cervical disc disease. J. Neurosurg. Spine 3, 24–28 (2005)

    Article  Google Scholar 

  69. Chen, J.-F., Lee, S.-T.: The polymethyl methacrylate cervical cage for treatment of cervical disc disease. Part III: Biomechanical properties. Surg. Neurol. 66, 367–370 (2006)

    Article  Google Scholar 

  70. Guan, Y., Yoganandan, N., Maiman, D.J., Pintar, F.A.: Internal and external responses of anterior lumbar/lumbosacral fusion: nonlinear finite element analysis. J. Spinal Disord. Tech. 21(4) (2008)

  71. Natarajan, R.N., Chen, B.H., An, H.S. Andersson, G.B.J.: Anterior cervical fusion: A finite element model study on the motion segment stability including the effect of osteoporosis. Spine 25(8), 955–961 (2000)

    Article  Google Scholar 

  72. Ivanov, A.A., Kiapour, A., Ebraheim, N.A., Goël, V.: Lumbar fusion leads to increases in angular motion and stress across sacroiliac joint. Spine 34(5), E162–E169 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IDMEC/IST—Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001, Lisboa, Portugal

    Nuno Miguel Barroso Monteiro, Miguel Pedro Tavares da Silva & João Orlando Marques Gameiro Folgado

  2. FML—Faculdade de Medicina de Lisboa, University of Lisbon, Av. Prof. Egas Moniz, 1649-028, Lisboa, Portugal

    João Pedro Levy Melancia

Authors
  1. Nuno Miguel Barroso Monteiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miguel Pedro Tavares da Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. João Orlando Marques Gameiro Folgado
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. João Pedro Levy Melancia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miguel Pedro Tavares da Silva.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Monteiro, N.M.B., da Silva, M.P.T., Folgado, J.O.M.G. et al. Structural analysis of the intervertebral discs adjacent to an interbody fusion using multibody dynamics and finite element cosimulation. Multibody Syst Dyn 25, 245–270 (2011). https://doi.org/10.1007/s11044-010-9226-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-010-9226-7

Keywords

Search

Navigation