Implementation of physiological functional spinal units in a rigid-body model of the thoracolumbar spine

Scope of the method

The Method relates to
  • Human health
The Method is situated in
  • Basic Research
Type of method
  • In silico


Method keywords
  • Rigid-body modelling
  • Functional spinal unit
  • Nonlinear stiffness
  • Spinal kinematics
  • Follower compressive loadRigid-body modelling
  • Follower compressive load
Scientific area keywords
  • biomechanics
Method description

Most of the current rigid-body models of the complete thoracolumbar spine do not properly model the intervertebral joint as the highly nonlinear stiffness is not incorporated comprehensively and the effects of compressive load on stiffness are commonly being neglected. Based on published in vitro data of individual intervertebral joint flexibility, multi-level six degree-of-freedom nonlinear stiffness of functional spinal units was modelled and incorporated in a rigid-body model of the thoracolumbar spine. To estimate physiological in vivo conditions of the entire spine, stiffening effects caused by directly applied compressive loads, and contributions to mono-segmental stiffness from the rib cage as well as multi-segmental interactions in the thoracic spine were analysed and implemented. Forward dynamic simulations were performed to simulate in vitro tests that measured the load-displacement response of the spine under various loading conditions. The predicted kinematic responses of the model were in agreement with in vitro measurements, with correlations between simulated and measured segmental displacements varying between 0.66 to 0.97 (p<0.05) and average deviations below 1.6°. Coupling relationships were found between lateral bending and axial rotation. Under compressive loads, the model behaved stiffer and showed a decreased range of motion: The flexion/extension response of the full thoracolumbar spine under compressive loads up to 800N was found to strongly correlate with the literature (r=0.99, p<0.0001). The implementation of physiological functional spinal units with nonlinear stiffness properties into rigid-body models can enhance accuracy of biomechanical simulations, and enable detailed analysis of spinal kinematics under complex loading conditions seen in vivo.

Method status
  • Published in peer reviewed journal

Pros, cons & Future potential


We presented a novel model of non-linear FSU stiffness and integrated this model in an existing rigid-body model of the thoracolumbar spine. The stiffness formulations are comprehensive enough to capture the physiological response of spinal kinematics under various loading conditions, and are also simple and generic enough to be used for various spine modelling studies.


We presented a generic model of spine stiffness that does not account for geometrical factors like disc height and area or pathological conditions.

Future & Other applications

In future work, combining the proposed generic stiffness formulation with stiffness calibration methods (e.g., optimization technique) will be developed to better describe subject-specific FSU mechanical behavior in pathological conditions.

References, associated documents and other information

Implementation of physiological functional spinal units in a rigid-body model o…

Contact person

Wei Wang


Katholieke Universiteit Leuven (KUL)
Department of Movement Sciences
Flemish Region


Shanghai Jiao Tong University