AN ACCURATELY REPRESENTED FINITE ELEMENT MODEL OF
LUMBAR MOTION SEGMENT (L2-L3)
Ee-Chon Teo and Kim-Kheng Lee
School of Mechanical & Production Engineering, Nanyang Technological University, Singapore
Corresponding author: Ee-Chon Teo E-mail: mecteo@ntu.edu.sg
Abstract
In the present study, a three-dimensional geometrical and mechanical accurate finite element model
of the human lumbar L2-L3 segment was developed using digitized geometrical data of embalmed
lumbar L2 and L3 vertebrae. The direct digitizing process provides an alternative method in
capturing the highly irregular geometry of spine as compared to the commonly use of CT/MRI
images. All complex anatomical features of the spine such as lamina, superior/inferior facet,
pedicle, pars interarticularis, spinous process and transverse process were explicitly represented in
the unprecedented finite element model. The analysis accounts for geometrical, material and
contact non-linearities. The computed results of lumbar L2-L3 segment were closely correlated
with published results in terms of axial displacement, intradiscal pressure, disc bulge, end-plate
bulge and tensile stress in the peripheral annulus fiber.
1. Introduction
For the past decade, numerical method (such
as finite element method) has proved to be a
useful adjunct to the experimental
approaches for investigating clinical
problems of the spine. Investigators have
always accentuated the importance on need
for more accurate model in terms of
geometry, material property and advanced
simulation of intervertebral disc to better
simulate in vivo and in vitro situations.
Though the geometry of lumbar spine is
highly irregular, it is important to define the
actual geometry of the structure as closely as
possible to obtain reasonable results
applicable to clinical and in vivo situations.
It is well know that the anatomic structure
and surface geometry of the vertebrae detect
the motion of the spine and its related
biomechanical responses. Generally, CT
scans or MRI data of patients or cadaveric
spine are used for mesh geometry. But the
quality of mesh produced using these two
methods is not satisfactory as the meshes
align inherently with orthogonal plane of
images and the undefined borders between
the junctions of two adjacent vertebrae.
Therefore, the aim of this study is to develop
an accurately represented finite element
model of lumbar L2-L3 motion segment
using direct digizitizing process, which
provides
another
mean
for
mesh
construction. The model was validated
against published results under compression
loading. The validated FE model was further
analyzed to investigate disc and end-plates
bulge, intradiscal pressure and stress in the
annulus
fibers
under
compressive
physiological range of loading with
confidence.
2. Material and Methods
The 3-D finite element model of the L2-L3
spinal unit was developed based on
geometrical data of embalmed lumbar spine
obtained using a flexible highly accurate
touch-point digitizer of an accuracy of
The cadaveric spine was
0.01mm.
inspected to be free from spinal disease,
metastasis and trauma. Figure 1 shows the
steps undertaken to capture its intricate
details for mesh generation.
compressive displacement of 1.5 mm was
applied in 5 increments over the superior
surface of the L2 vertebral body
(displacement control).
3. Results and Discussion
Fig 1: FlowChart
The
geometrical
non-linearity
of
intervertebral disc is currently modeled by
representing the annulus as a composite
structure with fiber embedded in solid matrix
elements and the nucleus pulposus is
modeled as nearly incompressible fluid
(Shirazi et al). The nonlinear stress-strain
behaviors of the ligaments represented by
tension-only cable elements were obtained
from literature. In order to appropriately
model the changing areas of contact of the
facet articulating surface with increments in
loading, facet articulation is treated as a
moving contact problem. The final FE
model (fig 2) consists of 8281 solid 8-noded
elements and 817 cable elements with 32,641
degrees of freedoms.
As seen from Fig 2, the meshes developed
herein are observed to be as regular as
possible, of which is an important
requirement in finite element analysis. This
would be necessary in the study of stress
distribution pattern and injury mechanisms in
the spine.
The predicted results regarding the axial
displacement, intradiscal pressure, disc bulge
and end-plate bulge shown in the following
figures are in good agreement with the
previously experimental data in the literature.
With increasing prescribed compressive
displacement the stiffening behavior of the
disc is predicted.
Fig 2: FE Model of L2-L3 Motion Segment
For analysis, the inferior surface of L3
vertebral body was fixed, and a uniform axial
The FE model also predicts the intradiscal
pressure increased nearly linearly with
increasing compressive load, and these
finding compare favourably with published
results.
With the model validated under static
loading, it could serve as a platform for
developing more advanced finite element
model to better simulate in vivo and in vitro
situations. Our focus of future work would
be in the development of poroelastic model
for lumbar spine to better simulate the fluidflow mechanism for intervertebral disc so as
to have a better insight on the nutrition to
the disc and pathology of interverterbral
disc.
References
Disc stiffness along the radial direction
(bulge stiffness) similarly increased with
compressive load.
For the normal disc, the end-plate bulge is
upwards (convex outward with respect to the
nucleus) to provide the volume for the
incompressible nucleus. With increasing
load, the end-plate bulge increased.
4. Conclusions
In conclusion, a well-represented finite
element model of L2-L3 motion segment was
developed with the adoption of direct
digitizing process and advanced modeling
technique. The predicted results exhibit nonlinear behaviors except intradiscal pressure,
which exhibits a linear relationship with
compressive stress.
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