Construction and Validation of a Hybrid Lumbar Spine Model for the Fast Evaluation of Intradiscal Pressure and Mobility

A novel hybrid model of the lumbar spine, allowing
fast static and dynamic simulations of the disc pressure
and the spine mobility, is introduced in this work. Our
contribution is to combine rigid bodies, deformable finite
elements, articular constraints, and springs into a unique model
of the spine. Each vertebra is represented by a rigid body
controlling a surface mesh to model contacts on the facet
joints and the spinous process. The discs are modeled using
a heterogeneous tetrahedral finite element model. The facet
joints are represented as elastic joints with six degrees of
freedom, while the ligaments are modeled using non-linear
one-dimensional elastic elements. The challenge we tackle
is to make these different models efficiently interact while
respecting the principles of Anatomy and Mechanics.
The mobility, the intradiscal pressure, the facet joint force and
the instantaneous center of rotation of the lumbar spine are
validated against the experimental and theoretical results of
the literature on flexion, extension, lateral bending as well as
axial rotation.
Our hybrid model greatly simplifies the modeling task and
dramatically accelerates the simulation of pressure within the
discs, as well as the evaluation of the range of motion and the
instantaneous centers of rotation, without penalizing precision.
These results suggest that for some types of biomechanical
simulations, simplified models allow far easier modeling and
faster simulations compared to usual full-FEM approaches
without any loss of accuracy.

• Ali Hamadi Dicko
• Nicolas Tong-Yette
• Benjamin Gilles
• François Faure
• Olivier Palombi

• Hybrid
• modeling
• fast simulation
• lumbar spine.

[1] H. Schmidt, F. Heuer, J. Drumm, Z. Klezl, L. Claes,
and H.-J. Wilke, “Application of a calibration method
provides more realistic results for a finite element model
of a lumbar spinal segment.” Clinical biomechanics
(Bristol, Avon), vol. 22, no. 4, pp. 377–84, May
2007. (Online). Available: http://www.ncbi.nlm.nih.gov/
pubmed/17204355
[2] H. Schmidt, F. Heuer, L. Claes, and H.-J. Wilke,
“The relation between the instantaneous center of
rotation and facet joint forces - A finite element
analysis.” Clinical biomechanics (Bristol, Avon), vol. 23,
no. 3, pp. 270–8, Mar. 2008. (Online). Available:
http://www.ncbi.nlm.nih.gov/pubmed/17997207
[3] H. Schmidt, F. Galbusera, A. Rohlmann, T. Zander,
and H.-J. Wilke, “Effect of multilevel lumbar disc
arthroplasty on spine kinematics and facet joint loads
in flexion and extension: a finite element analysis,”
European Spine Journal, vol. 21, no. 5, pp. 663–674,
2012. (Online). Available: http://dx.doi.org/10.1007/
s00586-010-1382-1
[4] D. S. Shin, K. Lee, and D. Kim, “Biomechanical study
of lumbar spine with dynamic stabilization device using
finite element method,” Comput. Aided Des., vol. 39,
no. 7, pp. 559–567, Jul. 2007. (Online). Available:
http://dx.doi.org/10.1016/j.cad.2007.03.005
[5] Y. Alapan, C. Demir, T. Kaner, R. Guclu, and
S. Inceo˘glu, “Instantaneous center of rotation behavior
of the lumbar spine with ligament failure.” Journal of
neurosurgery. Spine, vol. 18, no. 6, pp. 617–26, Jun.
2013. (Online). Available: http://www.ncbi.nlm.nih.gov/
pubmed/23600587
[6] T. Zander, A. Rohlmann, and G. Bergmann, “Influence
of ligament stiffness on the mechanical behavior of a
functional spinal unit.” Journal of biomechanics, vol. 37,
no. 7, pp. 1107–11, Jul. 2004. (Online). Available:
http://www.ncbi.nlm.nih.gov/pubmed/15165881
[7] B. Weisse, a. K. Aiyangar, C. Affolter, R. Gander,
G. P. Terrasi, and H. Ploeg, “Determination of the
translational and rotational stiffnesses of an L4-L5
functional spinal unit using a specimen-specific finite
element model.” Journal of the mechanical behavior
of biomedical materials, vol. 13, pp. 45–61, Sep.
2012. (Online). Available: http://www.ncbi.nlm.nih.gov/
pubmed/22842275
[8] T. Yoshimura, K. Nakai, and G. Tamaoki, “Multi-body
dynamics modelling of seated human body under
exposure to whole-body vibration.” Industrial health,
vol. 43, no. 3, pp. 441–7, Jul. 2005. (Online). Available:
http://www.ncbi.nlm.nih.gov/pubmed/16100921
[9] M. Christophy, N. Faruk Senan, J. Lotz, and O. O’Reilly,
“A musculoskeletal model for the lumbar spine,”
Biomechanics and Modeling in Mechanobiology, vol. 11,
no. 1-2, pp. 19–34, 2012. (Online). Available: http:
//dx.doi.org/10.1007/s10237-011-0290-6
[10] K. T. Huynh, I. Gibson, B. N. Jagdish, and W. F. Lu,
“Development and validation of a discretised multi-body
spine model in LifeMOD for biodynamic behaviour
simulation.” Computer methods in biomechanics and
biomedical engineering, vol. 0, no. June 2013, pp.
37–41, Apr. 2013. (Online). Available: http://www.ncbi.
nlm.nih.gov/pubmed/23621475
[11] E. Sifakis, T. Shinar, G. Irving, and R. Fedkiw, “Hybrid
simulation of deformable solids,” in Proceedings of
the 2007 ACM SIGGRAPH/Eurographics symposium on
Computer animation. Eurographics Association, 2007,
pp. 81–90.
[12] S.-H. Lee, E. Sifakis, and D. Terzopoulos,
“Comprehensive biomechanical modeling and simulation
of the upper body,” ACM Trans. Graph., vol. 28,
no. 4, pp. 99:1–99:17, Sep. 2009. (Online). Available:
http://doi.acm.org/10.1145/1559755.1559756
[13] F. Faure, B. Gilles, G. Bousquet, and D. K. Pai, “Sparse
meshless models of complex deformable solids,” ACM
Trans. Graph., vol. 30, no. 4, pp. 73:1–73:10, Jul. 2011.
(Online). Available: http://doi.acm.org/10.1145/2010324.
1964968
[14] I. Stavness, J. E. Lloyd, Y. Payan, and S. Fels,
“Coupled hard–soft tissue simulation with contact and
constraints applied to jaw–tongue–hyoid dynamics,”
International Journal for Numerical Methods in
Biomedical Engineering, vol. 27, no. 3, pp. 367–390,
2011.
[15] M. Dreischarf, T. Zander, A. Shirazi-Adl, C. Puttlitz,
C. Adam, C. Chen, V. Goel, A. Kiapour, Y. Kim,
K. Labus et al., “Comparison of eight published static
finite element models of the intact lumbar spine:
Predictive power of models improves when combined
together,” Journal of biomechanics, vol. 47, no. 8, pp.
1757–1766, 2014.
[16] N. Mitsuhashi, K. Fujieda, T. Tamura, S. Kawamoto,
T. Takagi, and K. Okubo, “Bodyparts3d: 3d structure
database for anatomical concepts,” Nucleic Acids
Research, vol. 37, no. suppl 1, pp. D782–D785, 2009.
[17] S. J. Ferguson, K. Ito, and L.-P. Nolte, “Fluid flow and
convective transport of solutes within the intervertebral
disc,” Journal of Biomechanics, vol. 37, no. 2, pp.
213 – 221, 2004, spinal Biomechanics. (Online).
Available: http://www.sciencedirect.com/science/article/
pii/S0021929003002501
[18] A. Malandrino, J. A. Planell, and D. Lacroix, “Statistical
factorial analysis on the poroelastic material properties
sensitivity of the lumbar intervertebral disc under
compression, flexion and axial rotation,” Journal of
Biomechanics, vol. 42, no. 16, pp. 2780 – 2788,
2009. (Online). Available: http://www.sciencedirect.com/
science/article/pii/S0021929009004679
[19] A. Shirazi-Adl, A. M. AHMED, and S. C.
SHRIVASTAVA, “Mechanical response of a lumbar
motion segment in axial torque alone and combined
with compression,” Spine, vol. 11, no. 9, pp. 914–927, 1986.
[20] J. Chazal, a. Tanguy, M. Bourges, G. Gaurel,
G. Escande, M. Guillot, and G. Vanneuville,
“Biomechanical properties of spinal ligaments and
a histological study of the supraspinal ligament
in traction.” Journal of biomechanics, vol. 18,
no. 3, pp. 167–76, Jan. 1985. (Online). Available:
http://www.ncbi.nlm.nih.gov/pubmed/3997901
[21] Y. Masharawi, B. Rothschild, G. Dar, S. Peleg,
D. Robinson, E. Been, and I. Hershkovitz,
“Facet Orientation in the Thoracolumbar Spine:
Three-dimensional Anatomic and Biomechanical
Analysis,” Spine, vol. 29, no. 16, 2004. (Online).
Available: http://journals.lww.com/spinejournal/
Fulltext/2004/08150/Facet\ Orientation\ in\ the\
Thoracolumbar\ Spine\ .9.aspx
[22] M. Nordin and V. H. V. H. Frankel, Basic biomechanics
of the musculoskeletal system. Philadelphia (Pa.):
Lippincott Williams & Wilkins, 2001. (Online).
Available: http://opac.inria.fr/record=b1133407
[23] A. De Luca, “Feedforward/feedback laws for the control
of flexible robots,” in Robotics and Automation, 2000.
Proceedings. ICRA ’00. IEEE International Conference
on, vol. 1, 2000, pp. 233–240 vol.1.
[24] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P.
Flannery, Numerical Recipes 3rd Edition: The Art of
Scientific Computing, 3rd ed. New York, NY, USA:
Cambridge University Press, 2007.
[25] W. M. Park, K. Kim, and Y. H. Kim, “Effects
of degenerated intervertebral discs on intersegmental
rotations, intradiscal pressures, and facet joint forces
of the whole lumbar spine,” Computers in biology and
medicine, vol. 43, no. 9, pp. 1234–1240, 2013.
[26] U. M. Ayturk and C. M. Puttlitz, “Parametric
convergence sensitivity and validation of a finite element
model of the human lumbar spine,” Computer methods in
biomechanics and biomedical engineering, vol. 14, no. 8,
pp. 695–705, 2011.
[27] C.-L. Liu, Z.-C. Zhong, H.-W. Hsu, S.-L. Shih, S.-T.
Wang, C. Hung, and C.-S. Chen, “Effect of the cord
pretension of the dynesys dynamic stabilisation system
on the biomechanics of the lumbar spine: a finite element
analysis,” European Spine Journal, vol. 20, no. 11, pp.
1850–1858, 2011.
[28] J. P. Little, H. De Visser, M. J. Pearcy, and C. J. Adam,
“Are coupled rotations in the lumbar spine largely due
to the osseo-ligamentous anatomy?—a modeling study,”
Computer methods in biomechanics and biomedical
engineering, vol. 11, no. 1, pp. 95–103, 2008.
[29] A. Shirazi-Adl, “Biomechanics of the lumbar spine in
sagittal/lateral moments,” Spine, vol. 19, no. 21, pp.
2407–2414, 1994.
[30] T. Zander, A. Rohlmann, and G. Bergmann, “Influence
of different artificial disc kinematics on spine
biomechanics,” Clinical biomechanics, vol. 24, no. 2,
pp. 135–142, 2009.
[31] A. Kiapour, D. Ambati, R. W. Hoy, and V. K. Goel,
“Effect of graded facetectomy on biomechanics of
dynesys dynamic stabilization system,” Spine, vol. 37,
no. 10, pp. E581–E589, 2012.
[32] M. J. PEARCY and N. BOGDUK, “Instantaneous
Axes of Rotation of the Lumbar Intervertebral
Joints,” Spine, vol. 13, no. 9, 1988. (Online).
Available: http://journals.lww.com/spinejournal/Fulltext/
1988/09000/Instantaneous\ Axes\ of\ Rotation\ of\
the\ Lumbar.11.aspx
[33] M.-A. Rousseau, D. S. Bradford, T. M. Hadi, K. L.
Pedersen, and J. C. Lotz, “The instant axis of rotation
influences facet forces at L5/S1 during flexion/extension
and lateral bending.” European spine journal : official
publication of the European Spine Society, the European
Spinal Deformity Society, and the European Section
of the Cervical Spine Research Society, vol. 15,
no. 3, pp. 299–307, Mar. 2006. (Online). Available:
http://www.pubmedcentral.nih.gov/articlerender.fcgi?
artid=3489304\&tool=pmcentrez\&rendertype=abstract
[34] P. Bifulco, M. Cesarelli, T. Cerciello, and M. Romano,
“A continuous description of intervertebral motion by
means of spline interpolation of kinematic data extracted
by videofluoroscopy.” Journal of biomechanics, vol. 45,
no. 4, pp. 634–41, Feb. 2012. (Online). Available:
http://www.ncbi.nlm.nih.gov/pubmed/22277152
[35] Faure, F., Duriez, C., Delingette, H., Allard, J., Gilles, B.,
Marchesseau, S., Talbot, H., Courtecuisse, H., Bousquet,
G., Peterlik, I. and Cotin S., “SOFA: A Multi-Model
Framework for Interactive Physical Simulation,” Soft
Tissue Biomechanical Modeling for Computer Assisted
Surgery, vol. 11, pp. 283–321, 2012.
[36] A. Shirazi-Adl and M. Parnianpour, “Load-bearing and
stress analysis of the human spine under a novel
wrapping compression loading,” Clinical Biomechanics,
vol. 15, no. 10, pp. 718–725, 2000.