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ELSEVIER
Finite element
spine unit
N. Yoganandan,
Department
of Veterans
Received
modeling
of the U-C6
S. C. Kumaresan, Liming Voo, F. A. Pintar and S. J. Larson
of Neurosurgery,
Medical College
Affairs Medical Center, Milwaukee,
25 October
cervical
1995, revised
18 December
1995, accepted
of Wisconsin and the Department
Wisconsin, USA
22 January
1996
ABSTRACT
This study was conducted
to develop a &tailed,
three-dimensional,
anatomically
accurateJnite
element model of the
human
cervical spine structure
using closeup
computed
tomography
scans and to validate
against experimental
data. Thefinite
element model of the three vertebra segment C&C6
unit consisted of 9178 solid elements and 1193
thin shell elements. The forcedisplacement
response under axial compression
correlated
well with expen’mental
data.
Because of the inclusion
of three levels in the spinal structure,
it was possible to determine
the internal
mechanics
of
the various
components
at each level. The applicability
of the model was illustrated
by adopting
a#o@iate
material
properties from literature.
Results indicated
that, the stresses in the anterior
column
were higher compared
to the
posterior column at the infm’or level, white the opposite was found
to be true at the superior
level. The superior and
infa’or
endplate stresses were higher in the middle vertebral
body compared
to the adjacent
vertebrae.
In addition,
the stresses in the cancellous
core of the middle,
unconstrained
vertebral
body were higher.
The present three
dimensional
finite
element model off em an additional
facet to a better understanding
of the biomechanics
of the
human
cervical spine. Published
by Elsevier Science Ltd for IPEMB.
Keywords: Finite
element
Med.
1996,
BACKGROUND
Eng.
Phys.,
method,
Vol.
cervical
18, 569-574,
AND LITERATURF,
spine,
computed
tomography,
stress
analysis
October
REVIEW
Finite element methods of structural analysis were
introduced
in 1956l. The first application
for the
method was in the aircraft industry. One of the
early a plications of the finite element technique
to me cfical and biological
problems was to analyse
the dynamics of cardiovascular
pulsatile flow in
.1969l. The use of this technique
to understand
the behavior
of the human spinal column
was
initiated in 1973 by Liu and Ray. Since then, there
have been a plethora
of finite element
applications to the human low back*. In contrast, little
research work has been done using the principles
of the finite element
technique
to analyse the
biomechanics
of the human cervical spine.
The earlier finite element models treated the
cervical columns as simple rigid masses connected
by beam and spring elements
representing
the
intervertebral
discs; ligaments;
facet joints; and
muscles. Simple rigid masses for the cervical vertebrae do not produce realistic responses. Hosey
and Liu’s finite element model of the head-neck
did not include
the cervical posterior
components, and the geometrical
features such as the
Correspondence
to: Professor
N. Yoganandan,
Medical
College of
Wisconsin,
Department
of Neurosurgery,
MCW Clinic
at FM1.H.
9200 West Wisconsin
Avenue,
Milwaukee,
WI 53226, USA.
orientation
of the disc from the anterior to the
posterior
and the uncinate
processes’.
The
detailed models are by Bozic et aZ.; Kleinberger;
Saito et aZ,; and Teo et ~1.~~ Bozic et al. created
a finite element model of the mid cervical vertebra from a 66 year old human cadaver specimen
based on computed
tomography
(CT) images.
The actual geometry of the C4 vertebra was represented by 8590 isoparametric
eight-noded
brick
elements. The modulus of the elasticity was based
on the CT density. Traumatic
loading was simulated by applying an axial compressive
displacement of 4 mm through
the 221 linear spring
elements attached to the superior vertebral body
surface such that the applied force was 3400 N.
This applied force was determined
from the analysis (as cited in the article). The restraint boundary
was provided by 241 linear spring elements in the
inferior direction. The total stiffness of the springs
at the superior and inferior
directions
approximated
the stiffness of the intervertebral
disc
(500 N/mm).
In addition,
restraints were applied
in the medial, lateral and anteroposterior
directions
by using
springs
of low stiffnesses
(60 N/mm).
Using maximum
shear stress theory,
the model predicted the initiation
of failure in the
central cancellous core. This finding of potential
failure in the central regions of the body corre-
Cervical
spine finite
element model: N. Yoganandan
et al.
lates well with the findings from lumbar intervertebral joint
studies (under
axial compressive
loading),
wherein micro-trauma
initiates
at the
central
regions
of the vertebral
endplate
as
observed fluoroscopically
and in cryomicrotome
images, and derived from the biomedical
stiffnessdeflection responses7-g. Despite the detailed finite
element
modeling,
the isolated vertebra model
has limited applications
in the study of the biomechanics of the cervical column.
In another investigation,
Teo et aZ., developed
a finite model of the second cervical vertebra (CZ)
using an unembalmed
adult human
cadaver
spine6.
A coordinate
measuring
machine
extracted the data for the finite element input.
The model consisted of 328 isoparametric
brick
and triangle prism solid elements at 972 nodes.
Material properties were obtained from literature.
The vertebra was made of cortical bone and
ignored
the cancellous
bone. Spring elements
were introduced
to simulate the effects of transverse ligaments;
the disc; and the superior and
inferior
articulating
facets. A force of 1 kN was
applied at orientations
of zero, 45” and -45” in
the sagittal plane; it was distributed
over a 50 mm*
area on the anterior
articulating
surface of the
dens in the anteroposterior
direction.
For the
zero degree (e.g., head impact with windshield
with an upright
neck), the posterior junction
at
the lateral edges between the base of the odontoid
process and the vertebral body and the inner lateral edges of the superior facets, experienced
the
highest
compressive
stress. For
this
case,
maximum
tensile stress occurred at the mid sagittal surface at the base of the odontoid
process.
With the force applied at 45” (e.g., a head impact
with the neck in extension),
maximum
tensile
stress occurred in the posterior outer lateral sides
of the body and the localized compressive stress
occurred on the surface of the applied force. In
contrast, the force applied at an angle of -45”
(e.g., boxing), resulted in high compressive stress
at the posterior surface of the dens and inner lateral edges of the superior facets; the maximum
tensile stress occurred at the junction
of the dens
and the vertebral body.
Saito et al. constructed
a finite element model
of the ligamentous
cervical column (occiput/COT2) to study the cervical deformity
secondary to
laminectomy5.
The model simplified
the vertebral
geometry by dividing
the spine into four sagittal
slices. The first slice consisted of the spongiosa,
the endplates of the bodies from Cl to T2, annulus fibrosus, and the nucleus pulposus of the discs;
the laminae;
the spinous processes; the anterior
and posterior
longitudinal
ligaments;
the ligamentum flavum; and the interspinous
and supraspinous ligaments.
The second slice consisted of
the cortices of the vertebral bodies (C2-T2) and
the articular facets, The third slice included
the
transverse processes and the intertransverse
ligaments. The fourth slice simulated
the lower part
of the cranium and cortex of the atlas. Spanning
element
theory was used to connect these twodimensional
slices. The lower region of T2 was
fixed. TI-UP superior part of the lower cranium was
570
unconstrained
in the cranio-caudal
direction
and
restrained
in the anteroposterior
direction,
Linear elastic material properties from literature were
used. A load of 150 N applied between the hypophysial fossa and anterior
to the Cl-C2
facet
induced a slight displacement.
The loading was
repeated 13 times at the same location on the displaced model to produce a gradual deformity.
A
total of 1607 elements for the post laminectomy
model and 1743 for the normal model were used.
This model
is suitable for the study of gross
responses of the whole cervical column
rather
than the local changes at the individual
spinal levels. Owing to its over-simplification
of the vertebral geometry and the intervertebral
joints, the
load-sharing
and stress distributions
predicted by
the model may not be realistic. Further, the model
is limited to sagittal plane simulation.
In a more recent study, Kleinberger
developed
a three-dimensional
finite element model of the
ligamentous
cervical spine coupled with a rigid
head to study the biomechanics
of neck injury*.
The complex anatomic structures were simplified
to a combination
of regularly shaped blocks such
as cylinders, rectangles, and wedges. The superior
and inferior surfaces of the vertebral bodies were
flat. All facet angles were assumed to be 45”. The
cervical lordosis was simulated
by adjusting
the
angle between the vertebrae.
Interspinous
ligaments were replaced by supraspinous
ligaments.
The posterior
and anterior
disc heights were
4 mm and 5.3 mm, respectively.
The material
properties
of the discs and the facet joints were
identical. Anterior and posterior longitudinal
ligaments, supraspinous
ligament
and ligamentum
flavum were included. The effects of the capsular
ligament
were included
in the definition
of the
facet joint. Cervical lordosis was maintained
and
Tl was fixed. Motion of the occipital condyles was
constrained
to z-translation
(the right .handed
Cartesian system of reference was used with Sx,
+y and +z directions oriented along the posterior
to anterior,
right to left lateral and inferior
to
superior axes, respectively) without rotation. Lin‘ear elastic material properties were used. Loading
conditions
for the two simulations
included
the
following: A 200 ms distributed
pressure ramp was
applied to the superior surfaces of the occipital
condyles. This resulted in a total vertical force (zdirection)
of 250 N. The resulting axial stiffness
compared
favorably
with literature’&‘“.
The
second simulation
consisted of a 10 mm axial displacement
applied to Cl to determine
the large
strain response. The model predicted
shear displacements
agreed with earlier results1°-13. Currently,
this is the most comprehensive
finite
element model of the cervical spine. As the vertebrae are considered to be rigid, material properties are linear and isotropic,
and representation
of the cervical spine anatomy such as the orientation of the facet joints is based on assumed
geometry;
the finite element
model predictions
are only a first approximation.
The foregoing
review on the finite element
models of the cervical spine clearly highlights
the
potential of the finite element technique to inves-
Cemcal
spinefinite
ekmrnt
model:
et al.
A’, Yoganandan
tigate the biomechanics
of the human
cervical
spine. These studies also underscore
the importance and the complexity
of simulating
a structure
such as the human
cervical spine. The above
described
models lack the important
anatomic
features, such as the articular facet variation at different spinal levels and the saddle-shapes of the
superior and inferior surfaces of the cervical vertebral bodies; and, the application
is limited
to
mostly sagittal gross motions.
In other words,
none of the existing cervical spine models possess
the necessary detailed representation
of the cervical anatomy for the study of the biomechanical
responses such as the stress distribution
among
under
real-world
intervertebral
components
force vectors.
PURPOSE
A realistic model which incorporates
the actual
geometry
and appropriate
material
data, and
which is validated against experimental
results, is
of use in safety engineering
and clinical medicine.
For example, the model can be used to determine
stress-distributions,
i.e., relative contributions
of
each spinal component
in resisting the external
force vector. This output cannot be obtained easily from an experimental
study. The model can
also identify potential failure regions. The present
study was designed to develop a detailed,
threedimensional
anatomically
accurate finite element
model of the C4-C6 human cervical spine structure using close-up CT scans and validate against
of the
experimental
results. The applicability
finite element model has been illustrated
by analysing the stress distributions
in the various compoems of the spinal structure.
MATERIALS
AND
METHODS
To obtain the geometrical
data required for the
finite
element
model,
the
cervical
spine
(Occiput/CO-Tl)
was isolated from a 33 year old
female unembalmed
human cadaver. Medical records were reviewed and pre-radiography
was performed to ensure the absence of bony abnormalities, spine disease or trauma. Anteroposterior,
lateral and oblique radiographs
were taken. The
specimen
was positioned
in a Styrofoam
container. The specimen was aligned along the anatomical axes with respect to the exterior surfaces
of the container. The twodimensional
sagittal and
coronal CT images were obtained using a CT scanner (General Electric Model: High-Speed
Advantage, Waukesha, Wisconsin, USA). They were processed using an edge-detection
algorithm
to
extract accurate outlines of the vertebral cross-sections. By suitably combining
the coronal and sagittal slices across the entire anteroposterior
and leftto-right cross-sections, the solid model (for the
C4-C5-C6 cervical spine structure) was developed
according
to the principles
of three-dimensional
reconstruction’4.
Eight-noded
isoparametric
elements were chosen for the cancellous
bone;
transverse processes; pedicles; laminae;
spinous
processes; and the intervertebral
discs. Thin shell
Figure 1 Finite element
model of the three vertebra
(CPC5-C6)
cervical spinal segment.
The oblique
frontal view demonstrates
the
W-5
(top) and C5-6 (bottom)
discs along with the adjacent
vertebral bodies (C4: top; C5: middle; C6: bottom)
and the posterior
elements. The arrow indicates the superior
portion
of the G-6
disc
near the inferior
endplate
of the C5 vertebral
body
elements (1 mm thickness) were used to simulate
the cortical shell and the endplates.
RESULTS
The finite element
model of the three-segment
C4-6 cervical spinal unit consisted of 9178 solid
elements and 1193 thin shell elements, resulting
in a total of 10 371 elements
(Figure 1). Table 1
includes the material property data used in the
present study. The model was validated against in
vitro experimental
results under
axial compression. As no experimental
tests were conducted in this research, data from other sources were
used to define the material property information.
For example,
Kleinberger’s
study was used to
define the intervertebral
disc, and Saito’s study
was used to define the cortical shell and endplate
characteristics4,5.
The response was obtained
by
applying
uniform
axial compression
at the top
Table
1
Material
properties
used in the study
Description
Young’s
modulus
MPa
Poisson’s
ratio
Cortical bone (5)
Cancellous
bone (5)
Posterior
elements
(17)
Disc - anulus (4)
Disc - nucleus (4)
Endplate
(5)
10000
100
3500
3.4
3.4
500
0.29
0.29
0.29
0.40
0.49
0.40
Note: Numbers
in parentheses
denote
material
property
data were obtained.
the references
from
which
the
571
Gruical
S@W finite
eknent
model: N. Yoganandan
et al.
nodes of the model, i.e., at C4; the inferior nodes
of C6 were constrained.
In other words, the
superior nodes of the C4 vertebral body endplate
and the other components
of the vertebra were
displaced
along the vertical
direction.
These
boundary conditions
simulated
the exFerimenta1
setup reported in the Shea et al. study 5. For the
applied uniform
axial compressive displacement
at C4, the resulting vertical reaction force at C6
was computed
from the finite element
analysis
and this force corresponding
to the applied displacement
was compared
with the experimental
results. The finite element model forcedisplacement response shown in Figure 2 correlated
well
with the experimental
response of Shea et aZ.15.
Because of the inclusion
of three levels in the
spinal structure, it was possible to determine
the
internal mechanics of the various components
at
each level. Stresses were analysed to determine
the biomechanical
behavior of the spine under an
axial compressive displacement
of 1 .O mm applied
to the superior nodes of the C4 vertebra of the
model with the inferior nodes of the C6 vertebra
constrained.
Stresses in the anterior
column
(vertebral body-disc
medium)
were higher at the
inferior
level compared
to the superior
level
(Figure 3~). In contrast, stresses in the posterior
column
(structure
posterior
to the body of
vertebra)
were higher at the superior intervertebral joint level compared to its inferior counterpart. Minimum
principal
compressive
stresses in
the middle vertebral body cancellous core were
consistently higher compared to the stresses in the
superior or inferior vertebral bodies (Figure 3b).
Furthermore,
von Mises, stresses in the endplates
demonstrated
a higher magnitude
in the middle
vertebral body compared to the proximal
and distal cervical vertebrae (Figure 3~).
3
0
EZB
2
2
E
E
m
1
0
Anterior
Experiment
0
FE Model
Column
Posterior
Figure 3a Bar chart representation
the anterior
and posterior
column
Column
of the relative
stresses
contribution
of
1.5
c4
Figure
0
-L,
C4-c5
C5-C6
3b
Vertebral
body
c5
C6
stresses
T
0
B
-0.2
0.0
0.2
0.4
0.6
0.6
1.0
1.2
Displacement (mm)
Figure 2 Comparison
of the model output
with the experimental
data”.
Open squares correspond
to the finite element
output and
open circles correspond
to the experimental
data as reported
by
Shea et al. in their three-segment
cervical spine axial loading study.
Notice a good match between
the experimental
outcome
and the
finite element model output
572
C4 hf.
c5 sup.
C5 hf.
C6 Sup
Endplate
Fiie
3c
C6 superior
Stresses in the C4 inferior;
endplates
C5 superior
and inferior;
and
Cmvical
DISCUSSION
The objective
of the study was to develop a
detailed three-dimensional
finite ,element model
of the human cervical spinal structure using actual
human cadaver data from CT scanned images.
Both sagittal and coronal plane CT scans were
used. All the important
anatomic features of the
cervical spine vertebrae such as the facet articulation surfaces, uncinate processes and the spinal
canal were clearly defined
in our model. The
direct computerized
process of the CT data
reliably preserves the accurate topography
of the
original structure that is to be replicated.
Principles of linear structural analysis were used
in this study. It is well known that the human cervical spine is a structure with material and geometrical non linearities.
Understanding
the response
with the linearity assumption
is a first step in the
process. Furthermore,
the spine resists static,
dynamic and fatigue loads under physiologic
and
traumatic situations. Our model can be extended
to study the behavior under these loading situations. It should be emphasized
that the principal
focus of the present investigation
was to develop
an accurate
three-dimensional
model
of the
human cervical spine structure based on actual
geometry measured from in &JO type scans (e.g.,
CT scans). The model was analysed under a single
physiologic
loading vector (axial compression)
to
illustrate
the feasibility
of our modeling
technique.
In the present study, the finite element model
computed
force-deformation
responses agreed
closely with experimental
results of Shea et al.“.
As expected, the stress distributions
demonstrated
- .._--_--Figure
ing
4
Stress distribution
pattern
in the superior
spine finite
element model: IV. Yoganandan
et al.
variations indicating
differences in the load-carrying capacities in the components
of the cervical
spine (F&ZLW 3). Because of the presence of the
adjacent vertebra together with the two interconnecting
intervertebral
discs, and the unconstrained nature of the middle vertebra simulating
a realistic physiologic
situation, the present finite
element
model should provide
better realistic
biomechanical
variables (e.g., stress distribution)
compared to the earlier research wherein a single
vertebra was used 3*6. Results from these earlier
studies may be confounded
due to the ‘endeffects
secondary
to the assumed
boundary
restraints at the two end surfaces of the vertebra
during the execution of the finite element model.
The output
stress distribution
in the spinal
components
provide
insight
into the internal
mechanics
of the cervical spine (Figure 4). The
increases in the endplate stresses in the middle
vertebral body may indicate a plausible mechanism of the initiation
of failure from this component under compressive
loads. In fact, this has
been experimentally
verified in lumbar functional
spinal unit studies which have reported
that,
under axial loading,
although
the disc is more
flexible,
microtrauma
initiates
in the endplate
resulting in a loss of integrity of the structure7s8.
Furthermore,
the increase in the stresses in the
middle
vertebral
body (C5) compared
to the
adjacent vertebrae (C4 and C6) maysbe secondary
to the inward bending
(towards the vertebral
centrum)
of both the superior and inferior endplates of the mid-body 16. This phenomenon
which
occurs in viuo cannot be described using a single
vertebra/vertebral
body.
The
unconstrained,
.
surface
of the cervical
\ertehral
ho+
and posterior
elements
under-
aria1 compressivr
load-
573
Cervical
spine@ite
element model: N. Yoganandan
et al.
more physiologic
middle intervertebral
joint can-.
not be incorporated
in a single-level
functional
unit (C4-5 or C5-6) model. From this viewpoint,
the three vertebrae-two
disc model is a better
approximation
to the spinal response than a single-level (two vertebrae-one
disc) functional
unit.
The role of the posterior column with respect to
the anterior
column
in terms of resisting the
external load was also demonstrated
by the finite
element
model.
It should be emphasized
that
these results cannot be obtained
by any single
experimental
study and consequently,
the present
finite element model offers an additional
facet to
a better understanding
of the biomechanics
of the
human cervical spine.
6.
7.
8.
9.
Analysis and prevention of spinal column deformity following cervical laminectomy,
pathogenetic
analysis of
post laminectomy deformities. Spine 1991, 16: 494-502.
Teo EC, Paul JP, Evans JH. Finite element stress analysis
of a cadaver second cervical vertebra. h4ed and Biol Eng
and Comput
1994, 32: 236238.
Yoganandan N, Ray G, Pintar FA, Myklebust JB, Sances
A, Jr. Stiffness and strain energy criteria to evaluate the
threshold of injury to an intervertebral
joint. J Biomech
1989; 22(2): 135-142.
Yoganandan N, Maiman DJ, Pintar FA, Ray G, Myklebust
JB, Sances A, Jr, Larson SJ. Microtrauma
in the lumbar
spine: a cause of low back pain. Neurosurm
1988; 23(2):
162-168.
Yoganandan N, Larson SJ, Gallagher M, Pintar FA, Reinartz J, Droese K. Correlation
of microtrauma
in the lumbar spine with intraosseous pressures. Spine 1994; 19(4):
435-440.
ACKNOWLEDGEMENT
This study was supported in part by the PHS CDC
R49-CCR 507370, DOT NHTSA Grant DTNH2293-Y-17028,
and the Department
of Veterans
Affairs Medical
Research Service. This research
was presented in part at the ASME Bioengineering
Conference,
Beaver Creek, CO, June 1995.
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