Biomechanics and Modeling in Mechanobiology

, Volume 14, Issue 5, pp 1081–1105 | Cite as

A forward dynamics simulation of human lumbar spine flexion predicting the load sharing of intervertebral discs, ligaments, and muscles

  • T. K. Rupp
  • W. Ehlers
  • N. Karajan
  • M. Günther
  • S. SchmittEmail author
Original Paper


Determining the internal dynamics of the human spine’s biological structure is one essential step that allows enhanced understanding of spinal degeneration processes. The unavailability of internal load figures in other methods highlights the importance of the forward dynamics approach as the most powerful approach to examine the internal degeneration of spinal structures. Consequently, a forward dynamics full-body model of the human body with a detailed lumbar spine is introduced. The aim was to determine the internal dynamics and the contribution of different spinal structures to loading. The multi-body model consists of the lower extremities, two feet, shanks and thighs, the pelvis, five lumbar vertebrae, and a lumped upper body including the head and both arms. All segments are modelled as rigid bodies. 202 muscles (legs, back, abdomen) are included as Hill-type elements. 58 nonlinear force elements are included to represent all spinal ligaments. The lumbar intervertebral discs were modelled nonlinearly. As results, internal kinematics, muscle forces, and internal loads for each biological structure are presented. A comparison between the nonlinear (new, enhanced modelling approach) and linear (standard modelling approach, bushing) modelling approaches of the intervertebral disc is presented. The model is available to all researchers as ready-to-use C/C++ code within our in-house multi-body simulation code demoa with all relevant binaries included.


Biomechanics Direct dynamics Multi-body model  Impact Shock wave Computer simulation 



Intervertebral disc


Muscle–tendon complex




Finite element


Degree of freedom


Computed tomography


Contractile element


Intervertebral flexion–extension


Range of motion


Anterior longitudinal ligament


Posterior longitudinal ligament


Ligamentum flavum


Supraspinal ligament


Interspinal ligament


Rectus abdominis muscle


External oblique muscle


Internal oblique muscle


Psoas major muscle




Intertransversarii mediales


Longissimus thoracis pars lumborum


Iliocostalis lumborum pars lumborum


Cervical vertebrae


Thoracic vertebrae


Lumbar vertebrae


Sacral vertebrae

Sagittal axis

Dorsal to ventral (\(=\!x\)-axis)

Longitudinal axis

Caudal to cranial (\(=\!z\)-axis)

Graphic primitive

Geometric primitive, describes the simplest geometric objects that the system can handle; in this model, the graphic primitives represent respective body segments



The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart.

T.R. and S.S. have received funding from the (European Union) Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 246994.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • T. K. Rupp
    • 1
    • 2
  • W. Ehlers
    • 2
    • 3
  • N. Karajan
    • 2
    • 3
    • 4
  • M. Günther
    • 1
  • S. Schmitt
    • 1
    • 2
    Email author
  1. 1.Institute of Sports and Movement ScienceUniversity of StuttgartStuttgartGermany
  2. 2.Cluster of Excellence for Simulation Technology (SimTech)University of StuttgartStuttgartGermany
  3. 3.Institute of Applied Mechanics (Civil Engineering)University of StuttgartStuttgartGermany
  4. 4.DYNAmore GmbH - Gesellschaft für FEM Ingenieurdienstleistungen, HeadquarterStuttgartGermany

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