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


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.


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)


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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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