ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

ABSTRACT
CONSTITUTIVE MODELLING OF THE LUMBAR SPINE
MUSCULATURE
Th. Toumanidou 1 , G. Fortuny 2 , D. Lacroix 3 and J. Noailly 4
Spinal muscles provide stability of the trunk and transmit loading onto the vertebra and
intervertebral discs. Current lumbar spine finite element models overlook such muscle
contribution or suggest simplifications far from the reality. This study proposes to
address this limitation by developing a novel active lumbar spine muscle model. A
modified quasi-incompressible fibre-reinforced hyperelastic constitutive model was
adopted for the passive and active behavior of the lumbar musculature. The constitutive
relation was expressed in terms of muscle fibre, matrix deviatoric and volumetric
stresses. A single unidirectional element was used to assess the model under 30%
traction and 20% compression strains. For the active fibre stress, a parametric study
defined suitable values for a strain-like parameter ζCE that controls muscle activation
through deformation thresholds. Stress analysis revealed that ζCE values derived for the
different lumbar muscles from literature-based morphometric criteria were unable to
induce any active response. Thus, alternative values were proposed keeping the relative
activations of the muscles modelled as suggested by the relation of ζCE to the functional
geometrical characteristics of these muscles. Stress results for all models were in the
plausible range of values reported in literature for the erect posture. The Psoas Major,
though, showed an unrealistic high activation for compression strains over 15%.
Therefore, a phenomenological calibration of the parameter ζCE would allow further
implementation of the constitutive model proposed in a lumbar spine model, given the
limited number of parameters involved.
1. INTRODUCTION
Mechanical factors have a significant influence on the degenerative progression of spine
tissues. The muscles of the spine provide stability of the trunk and transfer most of the
kinematical forces to the vertebra and intervertebral discs. Mechanistic simulations of
the boundary conditions through explicit muscle modeling, using tension-only
unidirectional elements representing muscle fascicles were initially proposed to capture
the effect of in vivo loading conditions [1]. Advanced kinematical models deriving
1
PhD student, Biomechanics and Mechanobiology, Institute for Bioengineering of Catalonia (IBEC),
C/Baldiri Reixac, 4, 08028 Barcelona, Spain
2
Associate Professor, Department of Computational Engineering and Mathematics , University of Rovira
i Virgili, Av.Paisos Catalans, 26, 43007 Tarragona, Spain
3
Professor, Department of Mechanical Engineering , University of Sheffield, Mappin Street, Sheffield,
S1 3JD, UK
4
Senior Researcher, Biomechanics and Mechanobiology, Institute for Bioengineering of Catalonia
(IBEC), C/Baldiri Reixac, 4, 08028 Barcelona, Spain
1