Multibody System Dynamics

, Volume 30, Issue 4, pp 413–432 | Cite as

On the modeling of the intervertebral joint in multibody models for the spine

  • Miguel Christophy
  • Maurice Curtin
  • Nur Adila Faruk Senan
  • Jeffrey C. Lotz
  • Oliver M. O’Reilly
Article

Abstract

The need to develop feasible computational musculoskeletal models of the spine has led to the development of several multibody models. Central features in these works are models for the ligaments, muscles, and intervertebral joint. The purpose of the present paper is to show how experimental measurements of joint stiffnesses can be properly incorporated using a bushing element. The required refinements to existing bushing force functions in musculoskeletal software platforms are discussed and further implemented using a SpineBushing element specific to the intervertebral joint. Four simple lumbar spine models are then used to illustrate the accompanying improvements. Electronic supplemental material for this article includes a complementary review of formulations of stiffness matrices for the intervertebral joint.

Keywords

Spinal kinematics Musculoskeletal multibody models Stiffness matrix Bushing element 

Supplementary material

11044_2012_9331_MOESM1_ESM.pdf (200 kb)
Electronic supplementary material for On the modeling of the intervertebral joint in multibody models for the spine: Review of Stiffness Matrices for the Intervertebral Joint (PDF 200 kB)

References

  1. 1.
    Ambrósio, J., Verissimo, P.: Improved bushing models for general multibody systems and vehicle dynamics. Multibody Syst. Dyn. 22, 341–365 (2009). doi:10.1007/s11044-009-9161-7 CrossRefMATHGoogle Scholar
  2. 2.
    Blundell, M., Harty, D.: The Multibody Systems Approach to Vehicle Dynamics. Butterworth Heinemann, London (2004) Google Scholar
  3. 3.
    Christophy, M., Faruk Senan, N.A., Lotz, J.C., O’Reilly, O.M.: A musculoskeletal model for the lumbar spine. Biomech. Model. Mechanobiol. 11(1–2), 19–34 (2012). doi:10.1007/s10237-011-0290-6 CrossRefGoogle Scholar
  4. 4.
    Crisco, J.J., Fujita, L., Spenciner, D.: The dynamic flexion/extension properties of the lumbar spine in vitro using a novel pendulum system. J. Biomech. 40(12), 2767–2773 (2007). doi:10.1016/j.jbiomech.2006.12.013 CrossRefGoogle Scholar
  5. 5.
    de Zee, M., Hansen, L., Wong, C., Rasmussen, J., Simonsen, E.B.: A generic detailed rigid-body lumbar spine model. J. Biomech. 40(6), 1219–1227 (2007). doi:10.1016/j.jbiomech.2006.05.030 CrossRefGoogle Scholar
  6. 6.
    Delp, S., Suryanarayanan, S., Murray, W., Uhlir, J., Triolo, R.: Architecture of the rectus abdominis, quadratus lumborum, and erector spinae. J. Biomech. 34(3), 371–375 (2001) CrossRefGoogle Scholar
  7. 7.
    Delp, S.L., Anderson, F.C., Arnold, A.S., Loan, P., Habib, A., John, C.T., Guendelman, E., Thelen, D.G.: OpenSim: open-source software to create and analyze dynamic simulations of movement. IEEE Trans. Biomed. Eng. 54(11), 1940–1952 (2007) CrossRefGoogle Scholar
  8. 8.
    Ferreira, A., Silva, M.T., Levy-Melancia, J.: A multibody model of the human cervical spine for the simulation of traumatic and degenerative disorders. In: 8th World Congress on Computational Mechanics (WCCM8), Venice, Italy, pp. 1–2 (2008) Google Scholar
  9. 9.
    Gardner-Morse, M.G., Stokes, I.A.F.: The effects of abdominal muscle coactivation on lumbar spine stability. Spine 23(1), 86–92 (1998). doi:10.1097/00007632-199801010-00019 CrossRefGoogle Scholar
  10. 10.
    Gardner-Morse, M.G., Stokes, I.A.F.: Physiological axial compressive preloads increase motion segment stiffness, linearity and hysteresis in all six degrees of freedom for small displacements about the neutral posture. J. Orthop. Res. 21(3), 547–552 (2003) CrossRefGoogle Scholar
  11. 11.
    Gardner-Morse, M.G., Stokes, I.A.F.: Structural behavior of the human lumbar spinal motion segments. J. Biomech. 37(2), 205–212 (2004). doi:10.1016/j.jbiomech.2003.10.003 CrossRefGoogle Scholar
  12. 12.
    Gardner-Morse, M.G., Laible, J.P., Stokes, I.A.F.: Incorporation of spinal flexibility measurements into finite element analysis. J. Biomech. Eng. 112, 481–483 (1990) CrossRefGoogle Scholar
  13. 13.
    Gercek, E., Hartmann, F., Kuhn, S., Degreif, J., Rommens, P., Rudig, L.: Dynamic angular three-dimensional measurement of multisegmental thoracolumbar motion in vivo. Spine 33(21), 2326–2333 (2008) CrossRefGoogle Scholar
  14. 14.
    Hill, A.: The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. Lond. B, Biol. Sci. 126(843), 136–195 (1938) CrossRefGoogle Scholar
  15. 15.
    Huynh, K.T., Gibson, I., Lu, W.F., Jagdish, B.N.: Simulating dynamics of thoracolumbar spine derived from LifeMOD under haptic forces. World Acad. Sci., Eng. Technol. 64, 278–285 (2010) Google Scholar
  16. 16.
    Janevic, J., Ashton-Miller, J.A., Schultz, A.B.: Large compressive preloads decrease lumbar motion segment flexibility. J. Orthop. Res. 9(2), 228–236 (1991) CrossRefGoogle Scholar
  17. 17.
    Kwang, T., Gibson, I., Jagdish, B.: Detailed spine modeling with LifeMOD™. In: Proceedings of the 3rd International Convention on Rehabilitation Engineering & Assistive Technology, pp. 1–5 (2009). doi:10.1145/1592700.1592729 Google Scholar
  18. 18.
    Lambrecht, J.M., Audu, M.L., Triolo, R.J., Kirsch, R.F.: Musculoskeletal model of trunk and hips for development of seated-posture-control neuroprosthesis. J. Rehabil. Res. Dev. 46(4), 515–528 (2009) CrossRefGoogle Scholar
  19. 19.
    Ledesma, R., Ma, Z.D., Hulbert, G., Wineman, A.: A nonlinear viscoelastic bushing element in multibody dynamics. Comput. Mech. 17, 287–296 (1996). doi:10.1007/BF00368551 CrossRefMATHGoogle Scholar
  20. 20.
    Lee, S.H.: Biomechanical modeling and control of the human body for computer animation. Ph.D. thesis, University of California, Los Angeles (2008) Google Scholar
  21. 21.
    Lee, S.H., Eftychios Sifakis, E., Terzopoulos, D.: Comprehensive biomechanical modeling and simulation of the upper body. ACM Trans. Graph. 28, 1–17 (2009). doi:10.1145/1559755.1559756 Google Scholar
  22. 22.
    Metzger, M.F., Faruk Senan, N.A., O’Reilly, O.M.: On Cartesian stiffness matrices in rigid body dynamics: an energetic perspective. Multibody Syst. Dyn. 24(4), 441–472 (2010). doi:10.1007/s11044-010-9205-z MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Monteiro, N.M.B., da Silva, M.P.T., Folgado, J.O.M.G., Melancia, J.P.L.: 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). doi:10.1007/s11044-010-9226-7 CrossRefGoogle Scholar
  24. 24.
    O’Reilly, O.M., Metzger, M.F., Buckley, J.M., Moody, D.A., Lotz, J.C.: On the stiffness matrix of the intervertebral joint: application to total disk replacement. J. Biomech. Eng. 131, 081007 (2009). doi:10.1115/1.3148195 CrossRefGoogle Scholar
  25. 25.
    Panjabi, M.M.: Theoretical treatment of vibrations in single and multiple body suspension systems based on matrix methods. Ph.D. thesis, Chalmers University of Technology, Goteborg, Sweden (1971) Google Scholar
  26. 26.
    Panjabi, M., Abumi, K., Duranceau, J., Oxland, T.R.: Three-dimensional mathematical model of the human spinal structure. J. Biomech. 6, 671–680 (1973) CrossRefGoogle Scholar
  27. 27.
    Panjabi, M.M., Brand, R.A. Jr., White III, A.A.: Three-dimensional flexibility and stiffness properties of the human thoracic spine. J. Biomech. 9(4), 185–192 (1976). doi:10.1016/0021-9290(76)90003-8 CrossRefGoogle Scholar
  28. 28.
    Patwardhan, A.G., Havey, R.M., Carandang, G., Simonds, J., Voronov, L.I., Ghanayem, A.J., Meade, K.P., Gavin, T.M., Paxinos, O.: Effect of compressive follower preload on the flexion-extension response of the human lumbar spine. J. Orthop. Res. 21(3), 540–546 (2006). doi:10.1016/S0736-0266(02)00202-4 CrossRefGoogle Scholar
  29. 29.
    Silva, M.T.: Human motion analysis using multibody dynamics and optimization tools. Ph.D. thesis, Technical University of Lisbon, Lisbon (2003) Google Scholar
  30. 30.
    Stokes, I.A.F., Gardner-Morse, M.: Lumbar spine maximum efforts and muscle recruitment patterns predicted by a model with multijoint muscles and joints with stiffness. J. Biomech. 28(2), 173–186 (1995) CrossRefGoogle Scholar
  31. 31.
    Stokes, I.A.F., Gardner-Morse, M.: Lumbar spinal muscle activation synergies predicted by multi-criteria cost function. J. Biomech. 34, 733–740 (2001) CrossRefGoogle Scholar
  32. 32.
    Stokes, I.A.F., Gardner-Morse, M.G.: Spinal stiffness increases with axial load: another stabilizing consequence of muscle action. J. Electromyogr. Kinesiol. 13(4), 397–402 (2003). doi:10.1016/S1050-6411(03)00046-4 CrossRefGoogle Scholar
  33. 33.
    Stokes, I.A.F., Iatridis, J.C.: Basic Orthopaedic Biomechanics and Mechano-Biology. In: Mow, V.C., Huiskes, R. (eds.) Biomechanics of the Spine, 3rd edn., pp. 529–561. Lippincott Williams & Wilkins, Philadelphia (2005) Google Scholar
  34. 34.
    Stokes, I.A.F., Gardner-Morse, M., Henry, S.M., Badger, G.J.: Decrease in trunk muscular response to perturbation with preactivation of lumbar spinal musculature. Spine 25(15), 1957–1964 (2000). doi:10.1097/00007632-200008010-00015 CrossRefGoogle Scholar
  35. 35.
    Stokes, I.A.F., Gardner-Morse, M.G., Churchill, D., Laible, J.P.: Measurement of a spinal motion segment stiffness matrix. J. Biomech. 35(4), 517–521 (2002) CrossRefGoogle Scholar
  36. 36.
    Tawackoli, W., Marco, R., Liebschner, M.A.K.: The effect of compressive axial preload on the flexibility of the thoracolumbar spine. Spine 29(9), 988–993 (2004) CrossRefGoogle Scholar
  37. 37.
    Thelen, D.G.: Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults. J. Biomech. Eng. 125, 70–77 (2003) CrossRefGoogle Scholar
  38. 38.
    Thelen, D.G., Anderson, F.: Using computed muscle control to generate forward dynamic simulations of human walking from experimental data. J. Biomech. Eng. 39, 1107–1115 (2006) CrossRefGoogle Scholar
  39. 39.
    Thelen, D.G., Anderson, F., Delp, S.: Generating dynamic simulations of movement using computed muscle control. J. Biomech. Eng. 36, 321–328 (2003) CrossRefGoogle Scholar
  40. 40.
    van Lopik, D.W., Acar, M.: Development of a multi-body computational model of human head and neck. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 221(2), 175–197 (2007). doi:10.1243/14644193JMBD84 CrossRefGoogle Scholar
  41. 41.
    Vasavada, A.N., Li, S., Delp, S.L.: Influence of muscle morphometry and moment arms on the moment-generating capacity of human neck muscles. Spine 23(4), 412–422 (1998) CrossRefGoogle Scholar
  42. 42.
    White III, A.A., Panjabi, M.M.: Clinical Biomechanics of the Spine. Lippincott, Philadelphia (1978) Google Scholar
  43. 43.
    Wong, K.W.N., Luk, K.D.K., Leong, J.C.Y., Wong, S.F., Wong, K.K.Y.: Continuous dynamic spinal motion analysis. Spine 31(4), 414–419 (2006) CrossRefGoogle Scholar
  44. 44.
    Zajac, F.E.: Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17(4), 359–411 (1989) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Miguel Christophy
    • 1
  • Maurice Curtin
    • 2
  • Nur Adila Faruk Senan
    • 1
  • Jeffrey C. Lotz
    • 3
  • Oliver M. O’Reilly
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of California at BerkeleyBerkeleyUSA
  2. 2.School of Electrical, Electronic and Communications EngineeringUniversity College DublinDublinIreland
  3. 3.Department of Orthopaedic SurgeryUniversity of California at San FranciscoSan FranciscoUSA

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