Medical Engineering & Physics 23 (2001) 155–164
www.elsevier.com/locate/medengphy
Evaluation of the role of ligaments, facets and disc nucleus in
lower cervical spine under compression and sagittal moments using
finite element method
E.C. Teo *, H.W. Ng
School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798
Received 22 November 2000; received in revised form 10 February 2001; accepted 21 March 2001
Abstract
Cervical spinal instability due to ligamentous injury, degenerated disc and facetectomy is a subject of great controversy. There
is no analytical investigation reported on the biomechanical response of cervical spine in these respects. Parametric study on the
roles of ligaments, facets, and disc nucleus of human lower cervical spine (C4–C6) was conducted for the very first time using
noninvasive finite element method.
A three-dimensional (3D) finite element (FE) model of the human lower cervical spine, consisted of 11,187 nodes and 7730
elements modeling the bony vertebrae, articulating facets, intervertebral disc, and associated ligaments, was developed and validated
against the published data under three load configurations: axial compression; flexion; and extension. The FE model was further
modified accordingly to investigate the role of disc, facets and ligaments in preserving cervical spine motion segment stability in
these load configurations. The passive FE model predicted the nonlinear force displacement response of the human cervical spine,
with increasing stiffness at higher loads. It also predicted that ligaments, facets or disc nucleus are crucial to maintain the cervical
spine stability, in terms of sagittal rotational movement or redistribution of load. FE method of analysis is an invaluable application
that can supplement experimental research in understanding the clinical biomechanics of the human cervical spine.  2001 IPEM.
Published by Elsevier Science Ltd. All rights reserved.
Keywords: Spinal stability; Disc nucleus; Ligaments; Facets; Force redistribution
1. Introduction
Definition of spinal instability has been a subject of
considerable debate and has not been established clearly.
Clinically, the spinal motion segment is defined to be
unstable if it exhibits abnormally large increase in
rotational or translational displacements under physiological load. Many in vitro biomechanical studies on
injured and stabilized cervical spines were conducted to
investigate the effects of facetectomy or ligamentous
injuries or degraded disc of cervical spinal motion under
physiological load configuration [1–6]. Analytical investigation using finite element (FE) model on the biomechanical response of cervical spine of the role of ligaments,
facets and disc nucleus has not been demonstrated.
* Corresponding author. Tel.: +65-790-5529.
E-mail address: [email protected] (E.C. Teo).
Yoganandan et al. [1] studied the dynamic response
of human cervical spine segment and spinal injuries. The
non-destructive biomechanical responses of cadaveric
cervical spine as well as the strength and the pattern of
failure for quasi-static load were measured by Coffee et
al. [2] and Shea et al. [3]. In 1993, Wen et al. [4] determined the biomechanical properties of the human spine
with ligamentous injuries. Eighteen functional spinal
units were obtained from nine human cadaveric cervical
spines. Experimental measurement was first performed
with intact functional spinal units, then to a series ligamentous injuries created artificially. These previous
analyses of ligamentous injuries showed detrimental
consequences of different ligamentous injuries and
helped them to assess the certain assumptions about
clinical stability of human spine.
In the study of cervical facetectomy, Raynor et al. [5]
studied 14 cervical spinal motion segments consisting of
two adjacent vertebral bodies and their connecting liga-
1350-4533/01/$20.00  2001 IPEM. Published by Elsevier Science Ltd. All rights reserved.
PII: S 1 3 5 0 - 4 5 3 3 ( 0 1 ) 0 0 0 3 6 - 4
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E.C. Teo, H.W. Ng / Medical Engineering & Physics 23 (2001) 155–164
ments in shear. The results showed that bilateral resection of more than 50% of the facet joint significantly
compromises the shear strength of a cervical spine
motion segment. In 1993, Zdeblick et al. [6] conducted
a study to examine the effect of resection of the facet
capsule alone, without disruption of the bony facet to
determine the degree of facet-capsule resection leads to
acute instability. The results show that under torsion, the
rotational displacement increased by 1% after a 25%
capsule resection; 19% after a 50% resection; and 25%
after a 75 or 100% resection.
These in vitro studies are expensive, surgically invasive, time consuming coupled with limited availability of
specimens, and many investigators turn to FE analysis
to study the biomechanics of cervical spine [7–15]. This
FE analysis enjoys a distinct advantage as a versatile
tool and has significant biomechanics application in the
handling of complex geometry, material and geometrical
nonlinearity encountered in the modeling of the human
cervical spine.
The first validated FE model of human normal cervical spine reported in the literature under axial compressive loading was developed by Yoganandan et al. [11],
based on a cervical specimen and 1-mm computed tomographic (CT) scanned slices of C4–C6. In 1997, Maurel
et al. [12] developed a 3D spinal segment using simplified geometry parameters (planes, ellipses, cylinders,
blocks, etc.) and validated it under flexion, extension,
lateral bending and torsion. In 1998, Heitplatz et al. [13]
developed a simplified FE model of human spine and
validated it under compressive loading with the intervertebral disc modeled using a combination of solid
elements and nonlinear springs. In the same year, Goel
and Clausen [14] developed a more detailed 3D spinal
segment of C5–C6 from serial CT scans and validated
it under flexion, extension, lateral bending and torsion
again.
In the area of FE analysis of the injured human spine,
Sharma et al. [16] developed a 3D FE model of a lumbar
motion segment to study the effect of ligament and facet
and their geometry on segment responses. The results
show that rotational instability in flexion or posterior displacement is unlikely without prior damage of ligaments,
whereas instability in extension rotation or forward displacement is unlikely before facet degeneration or
removal. However, till now, no comprehensive analytical injuries studies of cervical spine had been reported
in the literature.
The goal of the present study was to develop a FE
model of lower cervical spine and validate it against the
published data under compressive displacement, flexion
and extension load configurations [3,11–14,17,18]. The
ability of FE model to predict the roles of the ligaments,
facets, and disc nucleus in the redistribution of loads and
movement of lower cervical spine under three load con-
figurations was evaluated for the three different FE models.
2. Materials and methods
A 3D FE model of the spinal motion segment C4–C6
was developed for FE analysis based on a 68-year-old
cadaveric cervical spine. Adopting the digitizing technique used in the simplified models of isolated cervical
vertebra by Teo et al. [15] and Maurel et al. [12], this
study utilized the digitized geometrical coordinates of a
dried cadaveric cervical specimen obtained using a flexible 3D movement digitizer.
The C4–C6 was assumed to be symmetrical about the
mid-sagittal plane [11–15], only half of the vertebrae
were modeled. With the vertebral model development
techniques similar for all the vertebrae, the digitizing and
FE mesh generation discussed in our previous study of
C1 [19] was adopted. Briefly, the geometrical coordinates were obtained by continuous digitizing over the
outer surface profile of the vertebra and the automatic
registered data of 0.1 mm intervals were then post processed to form the sections, surfaces and then “watertight” solid volumes for the final FE mesh generation.
Each vertebra (C4–C6) was defined using 1632 eightnoded isoparametric solid elements for the cortical bone,
the cancellous bone and the posterior arch.
The modeling of the biological tissues between the
adjacent vertebrae were based on mean values from
literature. For the intervertebral disc, some investigators
[11–14] represented the intervertebral disc as a continuous structure whose lateral limits can go to the base of
the uncinate processes or to the middle of these processes or as far as the external limit of the uncinate processes. (1) In this study, the intervertebral disc was modeled as three layers: (i) two layers (superior and inferior)
of 0.5 mm thick of endplate; and (ii) an encasing middle
layer of the intervertebral disk consisting of the annulus
and nucleus. An anterior disk height of 5.5-mm, a posterior disk height of 3.5-mm [20], and the thickness of
the annulus in the anterior region was taken to be 1.2
times that of the posterior region [21] were adopted. The
intervertebral disc were defined by 1032 eight-noded
solid. (2) In our model, the ligaments were defined using
183 3D tension cable elements to represent the true
physiological functions of the ligaments.
Facet joints, in FE studies of spine, are often represented by solid element [11] or gap element [12,14]
of constant spring stiffness with gap. (3) And facet
articulation was treated as a moving contact problem,
defined by 202 contact elements to appropriately model
the changing areas of contact of the facet articulating
surfaces with increments in loading.
Generally, owing to the geometrical complexity of the
cervical spine, the FE mesh of C4–C6 was fairly fine.
E.C. Teo, H.W. Ng / Medical Engineering & Physics 23 (2001) 155–164
The generated 3D C4–C6 FE model consisting of 11,187
nodes and 7730 elements was developed and shown in
Fig. 1. To analyze the FE model, appropriate material
properties for each spinal component based on the published data [11,12,14,22–25] were assigned as listed in
Table 1.
3. FE analysis
3.1. Validation
As validation studies form the vital link between the
development of the FE model and its final intended use,
the present model was validated under compression,
flexion and extension load configurations. The predicted
responses were compared against the published experimental and existing analytical results [3,11–14,17,18]
under the same boundary and load configurations.
The present C4–C6 model was analyzed to evaluate
the force–displacement response under 1-mm axial dis-
Fig. 1.
157
placement and compared against in vitro experimental
measurements carried out by Shea et al. [3], linear FE
model by Yoganandan et al. [11], and the simplified nonlinear FE model by Heitplatz et al. [13]. The boundary
and loading conditions were imposed as shown in Fig. 2.
Due to the limited in vitro studies carried out on lower
cervical spine under sagittal moment (flexion, extension)
load configuration, the present C4–C6 model with C4
removed to form the C5–C6: (a) intact; and (b) disc segment models. The predicted responses were validated
against in vitro experimental results by Moroney et al.
[17] and analytical results by Goel and Clausen [14] and
Pelker et al. [18]. In these series of analysis, the boundary and load configurations similar to the published data
[17,14,18] for both the C5–C6 intact and disc model are
depicted in Fig. 3.
3.2. Significance of ligaments, facets and disc nucleus
studies
In this part of the study, the relative importance of
ligaments, facets, and disc nucleus under 1-mm com-
Iso-posterior view of the: (a) C4–C6 FE model; (b) intervertebral disc and articular contact surfaces.
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E.C. Teo, H.W. Ng / Medical Engineering & Physics 23 (2001) 155–164
Table 1
Element types and mechanical properties of different spinal components used in the present study
Description
Element type
Young’s
modulus
(MPa)
Poisson’s ratio
Cortical bone
Linear isotropic eight-noded solid
10 000
0.29
100
500
3500
3.4
1
0.29
0.4
0.29
0.4
0.499
54.5
–
20
20
1.5
1.5
1.5
–
–
–
–
–
Cancellous bone
Endplate
Posterior elements
Disc annulus
Disc nucleus
Anterior longitudinal ligaments
Posterior longitudinal ligaments
Capsular ligaments
Ligamentum flavum
Interspinous ligaments
Supraspinous ligaments
Facet articulation
3D cable, nonlinear cable with no
compression option
Nonlinear contact element
Reference
Saito et al., 1991 [21]; Yoganandan
et al., 1996 [11]; Goel et al., 1995
[22]
Maurel et al., 1997 [12]; Kumaresan
et al., 1997 [23]; Goel and Clausen,
1998 [14]
Ueno and Liu, 1987 [24]
4. Results
4.1. Validation
Fig. 2. Schematic illustrations of the loading and boundary conditions of C4–C6 cervical spine FE model under compression.
pressive displacement and sagittal moment of
1800 N mm load configurations were evaluated. The
validated models (C4–C6 and C5–C6) were modified
accordingly to form the corresponding three new models
(intact segment without ligaments, intact segment without ligaments and facets, and intact segment without disc
nucleus) and analyzed under these three load configurations. The corresponding responses of these models
were compared against the predicted responses of the
validated segment models.
All the analyses were performed using ansys 5.6
(ANSYS, Inc. Pennsylvania, USA) with nonlinear static
structural contact and automatic time stepping options.
The predicted mechanical response of the C4–C6
model under axial compressive loading agreed reasonably well with the published experimental measurements
and existing analytical models [3,11,13] (Fig. 4). The
nonlinear and stiffening effects of the relationship
between the axial compressive force and axial displacement were predicted in the present FE model. A difference of less than 10% was shown between the results
predicted by the present model and the mean experimental values. The FE models proposed by Yoganadan
et al. and Heiplatz et al. showed a difference of 15 and
25%, respectively, from the mean experimental values
at final compressive load of 1-mm. Generally, the three
FE models agreed reasonably well with the experimental
data. However, closer agreement was shown between
our C4–C6 FE model and the experimental measurements.
Table 2 shows the comparison of results between the
present C5–C6 models, experimental data and analytical
models under sagittal moments [12,14,17,18]. The predicted results of C5–C6 intact model and C5–C6 disc
segment model were in good agreement with mean
experimental data [17]. As the present models were
assumed to be symmetrical about the mid-sagittal plane,
no coupled motion was predicted for the flexion or
extension load configurations. The load–displacement
curve of C5–C6 intact model under 1800 N mm of sagittal moments shown in Fig. 5 demonstrated a marked
nonlinearity with a large increase of stiffness at higher
E.C. Teo, H.W. Ng / Medical Engineering & Physics 23 (2001) 155–164
Fig. 3.
159
Schematic illustrations of the boundary and loading conditions of C5–C6: (a) intact; and (b) disc segment FE model under sagittal moments.
Fig. 4. Validation analysis. Comparison of the C4–C6 model predicted responses with experimental values by Shea et al. [3], analytical results
by Yoganandan et al. [11] and Heitplatz et al. [13] under compression.
magnitude of sagittal moment. Fig. 6 shows the comparison of results between the present C5–C6 intact model,
experimental values and analytical model by Goel and
Clausen [14] under 1000 N mm of sagittal moments at
four equal incremental steps.
4.2. Significance of ligaments, facets and disc nucleus
Fig. 7 showed the predicted redistribution of forces
transmitted to the inferior body of C6 under axial compressive displacement load of the different arbitrary
simulated injured models. The magnitude of force transmitted down to the inferior portion of the model was
reduced under the compressive displacement load. The
complete section of ligaments was not significant, obviously, in this load configuration. The differences in the
redistribution of force transmission between the segment
model without ligaments and facet and segment without
disc nucleus against the validated intact C4–C6 showed
a shift in the load carrying capacity of the disc to facets
as compressive displacement increased. At lower compressive load, the disc transmitted 100% of the force but
reduced to about 55% at higher load.
The predicted results of the C5–C6 motion segment
under 1800 N mm flexion and extension for the intact
segment, segment without ligaments, segment without
ligaments and facets, and segment without disc nucleus
were shown in Fig. 8. Comparing against the predicted
response of the validated C5–C6 intact segment model,
there was a marked increase of about 75 and 26% under
flexion moment and extension moment, respectively, for
the segment without ligaments. There was no difference
in the predicted response for segment model without
ligaments and segment model with both ligaments and
facets removed under flexion. Under extension moment
this deflection increased significantly to about 95% difference, against the normal C5–C6 intact model, when
both the ligaments and facets were removed. The
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Table 2
Comparisons of results between the present C5–C6 model, published experimental values and analytical models [12,14,17,18]
(73.6 N preload)
Rotation (SD) in degrees
Experimental
Moroney et al., 1988
[17]
C5–C6 intact model
At 1800 N mm flexion moment
5.55 (1.84)
Flexiona
Axial rotation
0.34 (0.60)
Lateral bending
0.34 (0.66)
At 1800 N mm extension moment
3.52 (1.94)
Extensiona
Axial rotation
0.04 (0.44)
Lateral bending
0.11 (0.38)
C5–C6 disc segment
At 1600 N mm flexion moment
7.02 (2.23)
Flexiona
Axial rotation
0.48 (0.69)
Lateral bending
0.52 (0.60)
At 1600 N mm extension moment
4.80 (1.41)
Extensiona
Axial rotation
0.21 (0.39)
Lateral bending
⫺0.54 (1.72)
a
Finite element models
Pelker et al., 1991 [18] Maurel et al., 1997
[12]
Goel et al., 1998 [14]
Present model
6.1
–
–
7 (1.3)
–
–
5.17
–
–
4.83
–
–
3.45
–
–
7.5 (1.2)
–
–
3.69
–
–
3.95
–
–
–
–
–
7.80
–
–
–
–
–
6.50
-
–
–
–
8.70
–
–
–
–
–
6.83
–
–
Denotes the primary motion.
Fig. 5. Validation analysis. Load–displacement response curves of C5–C6 intact model prediction and experimental values by Moroney et al.
[17] and Pelker et al. [18] under sagittal moments.
increase in rotational angle for segment without disc
nucleus was about 40 and 18% different from the C5–C6
intact model under flexion and extension, respectively.
5. Discussion
To investigate the mechanical response of human
spine under physiological loads, many in vitro experimental ex vivo analytical studies have been conducted.
FE analysis has been applied successfully in the field of
biomechanics. As the cervical spine is a complex biomechanical system containing both passive structural and
active neuromuscular components, the FE method is well
suited for parameterized analytical study. The FE
method offers the advantages in handle complex geometric configurations as well as material and geometric nonlinearity.
In this project, a detailed 3D FE model of the human
lower cervical spine (C4–C6) using actual geometric
data of the dried specimens was developed. All the
important anatomic features of the lower cervical spine
E.C. Teo, H.W. Ng / Medical Engineering & Physics 23 (2001) 155–164
161
Fig. 6. Validation analysis. Predicted response of the C5–C6 intact model and experimental values and analytical values of study by Goel and
Clausen [14] under 1000 N mm sagittal moments.
Fig. 7. Predicted redistribution of load of C4–C6 model under 1-mm axial compressive displacement load configuration for intact segment,
segment without ligaments, segment without ligaments and facets, and segment without disc nucleus.
Fig. 8. Predicted rotations of intact C5–C6 FE model under 1.8 N m pure sagittal moments for intact segment model, segment model without
ligaments, segment model without ligaments and facets, and segment without disc nucleus.
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E.C. Teo, H.W. Ng / Medical Engineering & Physics 23 (2001) 155–164
such as the facet articulation surfaces, posterior arch,
intervertebral disc were defined clearly. The model was
analyzed in flexion, extension and axial compressive
load configurations with specific purposes.
As validation is the most important step in the FE
analysis in anatomical structures modeling, the use of
FE models beyond their validated conditions is a common error [10]. Model validation is important in
enabling an analytical model to produce reliable predictions for a variety of complex investigations. Therefore,
in this study, the loads and constraints of the validation
step for flexion, extension and axial compressive load
configurations were identical to the published literature.
The loads applied to the C4–C6 and C5–C6 FE model
for the analysis corresponded to the experimental values
used in the studies carried out by Shea et al., Pelker et
al., Moroney et al and Goel and Clausen [3,18,17,14].
For the applied compressive displacement at C4, the predicted vertical reaction at C6 (i.e. the force transmitted
to C6) was compared with the published experimental
results and analytical models’ predictions [3,11,13]. For
the applied moment at C5, the rotational responses of the
C5 vertebra with respect to C6 in the plane of moment
application were computed and compared with the published results [12,14,17,18]. Once the initial validation
studies have been completed, the authors believe that the
model can be used as a specimen with repeatability and
reproducibility characteristics that is ideal for various
biomechanical studies, such as ligamentous, facets, and
disc injuries.
It is well known that the force–displacement of the
human cervical spine is nonlinear, with increasing stiffness at higher loads [7–14]. It is important to develop a
realistic FE model that can effectively simulate this general nonlinear behavior of the human cervical spine. In
this study, the FE models developed are the first to predict the nonlinear response of the human cervical spine
function unit (C4–C6) under axial compressive loading
and (C5–C6) under flexion and extension loading conditions. Furthermore, all the validations were done without changing the materials characteristics defined for the
spinal components of the different models analyzed.
Thus, it is now feasible to investigate the asymmetric
injuries of our intended study with confidence.
Till now, definition of stability or instability of the
cervical spine is incomplete and confused. Some investigators studied the mechanisms of injury to the cervical
spine and evaluation of the forces and moments and
localized motions of the cervical column under injury
producing load vectors [25]. Panjabi et al. [27] found
out that for an functional unit that has all its anterior
elements “plus one” additional posterior structure, or all
of its posterior elements “plus one” additional anterior
structure, then the functional unit will remain stable in
the sagittal plane under physiological loads. Goel et al.
[28] found the determinant role of capsular ligaments in
flexion, extension, lateral bending and axial rotation of
lower human cervical spine segment. In 1993, Wen et
al. [4] studied the mechanical tolerance and the instability of the cervical spine due to some ligamentous
injuries. The results shows significant increase in flexibility after sectioning of some ligamentous structures in
certain directions in the intact state. Ulrich et al. [26]
found that flexion stability is preserved with posterior
ligamentous elements and capsular ligaments severed.
The definite roles of the ligamentous tissues, articulating facets and disc nucleus in the stability of the human
cervical spine cannot be disputed. As a logical extension,
the basic model was exercised to evaluate the role of
these individual components in resisting physiological
mode of loading under compression and sagittal
moments.
Under compressive loading (Fig. 7), a significant difference in the magnitude of redistribution of force has
been predicted for the model without the disc nucleus.
The predicted results show that the nearly incompressible disc nucleus is highly effective for the transmission
of force in the cervical spine under axial loading and the
removal of the disc nucleus reduced the this compressive
load by 75%. For healthy cervical spine, the results predicted that the facets and disc shared the load quite equally at higher loads, but the role of facets in load carrying
capacity reduced significantly at lower compressive load.
The results predicted the facets articulations contribute
considerably to the stability of the cervical spine under
larger axial compressive loading. The removal of either
the facets or the disc nucleus affected the stiffness of the
cervical spine drastically, and the segment became more
flexible in mobility under compression, resulting in
instability of the cervical spine under physiological load.
The removal of ligaments did not affect the stability of
the human spine under compression.
Under sagittal moments (Fig. 8), the segment model
without the ligaments was more flexible (7.67°) in
flexion than in extension (4.96°) at 1800 N mm moment.
The passively stretched ligaments provided the more
needed role for cervical stability under flexion. This was
shown by the significant increase in moment deflection
from 4.83 to 7.67° after sectioning of ligamentous structures. Under extension moments, the slight increase of
moment deflection from 3.95 to 4.96° for the basic intact
spinal segment to spinal segment without ligaments suggested the determinant role of articulating facets in this
load configuration. This behavior was also reported by
Wen et al. [4]. The model also predicted an increase in
instability under extension with the removal of ligaments
and facets together (deflection increases from 4.96 to
7.71°) reducing the cervical spine segment stiffness significantly and nonlinearly.
For segment with the disc nucleus removed, the predicted rotation was 6.13 and 4.67° at 1800 N mm flexion
and extension, respectively. The relatively smaller dif-
E.C. Teo, H.W. Ng / Medical Engineering & Physics 23 (2001) 155–164
ferences in rotational motion between intact segment and
segment without disc nucleus suggested that the intervertebral disc was less significant for resisting sagittal
moments, whereas the ligaments and facets play dominant major role in resisting large flexion and extension, respectively.
The nucleus pulposus portion of the intervertebral disc
is known to play an important role in the mechanics of
the human cervical spine. Under loads, the normal or
slightly degenerated nucleus generates hydrostatic pressure [21]. This pressure increases the disc stiffness
directly by resisting the compression force and indirectly
by pre-stressing the annulus layers. The confined nucleus
fluid may be lost into the surrounding structures as a
result of horizontal and vertical prolapses. It could be
resolved by injection of nucleolytic enzymes, which are
used to treat the disc herniation. Moreover, the nucleus
material may be intentionally removed during surgery,
or could mechanically alter with age to become dry and
semisolid. Therefore, our analysis on the total removal
of disc nucleus to simulate the extreme case of disc
degeneration, whereby the functional compressibility of
the nucleus is totally lost, predicts significant changes in
terms of both force redistribution and rotational resistance under the load configurations studied. Cervical spinal motion segments without the disc nucleus causes the
disc to be less effective in its load-bearing role. These
observations for the C4–C6 were in good agreement with
the conclusions reported by Shirazi-Adl et al. for the
lumbar spine segment [21]. Therefore, it is apparent that
such a structure, from a mechanical point of view, is no
more optimal to take full advantage of its constituent
substructures.
A comprehensive nonlinear FE model of the lower
cervical spine has been used to study the role of ligaments, facets and disc nucleus in cervical spine stability.
The results indicate that the ligaments play an important
role in resisting flexion. The result shows that the disc
nucleus fluid plays a major role in cervical spine mechanics. The nucleus carries a significant portion of the
applied compression load. Under other physiologic loading (flexion/extension), the disc nucleus is responsible
for the initial stiffness of the cervical spine. The results
also highlight the importance of facets in resisting compression, extension.
Although the model and analysis are quite comprehensive, several factors, besides mechanical properties
variations, can account for the difference between the
predicted results and the experimental data. The current
model is mid-sagittally symmetric and thus will not predict any coupled motions associated with flexion–extension loading modes.
It has been pointed out that a mathematical model
based on detailed physical data is likely to represent the
real structure successfully with a limited validation [29].
Two of the most important physical data in constructing
163
a FE model of the C4–C6 are geometric and material
properties, which our present model has processed highquality representations of these aspects. The bony
geometry of the cervical spine greatly affects its biomechanical response [30]. Although our model is very
realistic, the current results are limited by the use of linear elastic and homogeneous material properties. However, because of the good prediction from a combination
of linear material properties and nonlinear geometry in
the present study, we may speculate that nonlinear
material properties of the disc and ligaments may not be
significant in the range of loading forces used in current study.
6. Conclusions
In summary, a 3D geometrical and mechanical accurate FE model based on actual geometry has been successfully developed for lower cervical spine (C4–C6).
The passive FE model was validated against the published data under axial compressive, flexion and
extended load configurations. The FE model predicted
the nonlinear response of the lower cervical spine segment. The parametric study undertaken to investigate the
roles of facets and ligaments reviewed the distinct role
of these spinal components in preserving cervical spine
stability passively under these load configurations. The
FE method of analysis adopted here could supplement
experimental research in understanding the clinical
biomechanics of human cervical spine under different
modes of load–displacement vectors.
References
[1] Yoganandan N, Sances A, Pintar F. Biomechanical evaluation of
the axial compressive responses of the human cadaveric and
manikin necks. J Biomech Engng 1989;111:250–5.
[2] Coffee MS, Edwards WT, Hays WC, White AA III. Biomechanical properties and strength of the human cervical spine. Orthop
Trans 1988;12:476.
[3] Shea M, Edwards WT, White AA, Hayes WC. Variations of stiffness and strength along the human cervical spine. J Biomech
1991;24(2):92–107.
[4] Wen N, Lavaste F, Santin JJ, Lassau. Three-dimensional biomechanical properties of the human cervical spine in vitro: II. Analysis of instability after ligamentous injuries. J Eur Spine
1993;2:12–5.
[5] Raynor RB, Pugh J, Shapiro I. Cervical facetectomy and its effect
on spine strength. J Neurosurg 1985;63:278–82.
[6] Zdeblick TA, Abitbol JJ, Kunz DN, Mccabe RP, Garfin S. Cervical Stability after sequential capsule resection. Spine
1993;18:22–7.
[7] Yoganandan N, Myklebust JB, Gautam R, Sances A. Mathematical and finite element analysis of spine injuries. CRC Crit Rev
Biomed Engng 1987;15(1):29–93.
[8] Gilbertson LG, Goel VK, Kong WZ, Clausen JD. Finite element
164
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
E.C. Teo, H.W. Ng / Medical Engineering & Physics 23 (2001) 155–164
methods in spine biomechanics research. CRC Crit Rev Biomed
Engng 1995;23(5/6):411–73.
Goel VK, Gilbertson LG. Applications of the finite element
method to thoracolumbar spine research — past, present and
future. Spine 1995;20(15):1719–27.
Yoganandan N, Kumaresan S, Voo L, Pintar FA. Finite element
applications in human cervical spine modeling. Spine
1996;21(15):1824–34.
Yoganandan N, Kumaresan SC, Voo L, Pintar FA, Larson SJ.
Finite element modeling of the C4–C6 cervical spine unit. Med
Engng Phys 1996;18(7):569–74.
Maurel N, Lavaste F, Skalli W. A three-dimensional parameterized finite element model of the lower cervical spine. Study
of the influence of the posterior articular facets. J Biomech
1997;30(9):921–31.
Heitplatz, P., Hartle, S.L., Gentle, C.R., 1998. A 3-dimensional
large deformation FEA of a ligamentous C4–C7 spine unit. Third
International Symposium on Computer Methods in Biomechanics
and Biomedical Engineering, Barcelona, Spain, pp. 387–394.
Goel VK, Clausen JD. Prediction of load sharing among spinal
components of a C5–C6 motion segment using the finite element
approach. Spine 1998;23(6):684–91.
Teo EC, Paul JP, Evans JH. Finite element stress analysis of a
cadaver second cervical vertebra. Med Biol Engng Comput
1994;32:236–8.
Sharma M, Langrana NA, Rodriguez J. Role of ligaments and
facets in lumbar spinal stability. Spine 1995;20(8):887–900.
Moroney SP, Schultz AB, Miller JAA, Andersson GBJ. Load–
displacement properties of lower cervical spine motion segments.
J Biomech 1988;21:767–79.
Pelker RR, Duranceau JS, Panjabi MM. Cervical spine stabilization. A three dimensional biomechanical evaluation of rotational
stability,
strength
and
failure
mechanism.
Spine
1991;16(2):117–22.
Teo EC, Ng HW. First cervical vertebra (Atlas) fracture mech-
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
anism studies using finite element method. J Biomech
2001;34(1):13–21.
Gilad I, Nissan M. A study of vertebra and disc geometric
relations of the human cervical and lumbar spine. Spine
1986;11(2):154–7.
Shirazi-Adl SA, Shrivastava SC, Ahmed AM. Stress analysis of
the lumbar disc-body unit compression. A three-dimensional nonlinear finite element study. Spine 1984;9(2):120–34.
Saito T, Yamamuro T, Shikata J, Oka M, Tsutsumi S. Analysis
and prevention of spinal column deformity following cervical
laminectomy, pathogenetic analysis of post laminectomy deformities. Spine 1991;16:494–502.
Goel VK, Monroe BT, Gilbertson LG, Brinckmann P, Nat R.
Interlaminar shear stresses and laminae separation in a disc. Spine
1995;20(6):689–98.
Kumaresan S, Yoganandan N, Pintar FA, Voo LM, Cusick JF,
Larson SJ. Finite element modeling of cervical laminectomy with
graded facetectomy. J Spinal Disord 1997;10:40–6.
Ueno K, Liu YK. A three-dimensinoal nonlinear finite element
model of lumbar intervertebral joint in torsion. J Biomed Engng
1987;109:200–9.
Ulrich C, Woersdoerfer O, Klalff R, Claes L, Wilke HJ. Biomechanics of fixation systems to the cervical spine. Spine
1991;16(Suppl.):4–92.
Panjabi MM, White A III, Johnson RM. Cervical spine mechanics
as a function of transection of components. J Biomech
1987;11:327–36.
Goel VK, Clark CR, Mcgowan D, Goyal S. An in-vitro study of
the kinematics of the normal, injured and stabilized cervical
spine. J Biomech 1984;17:363–76.
Panjabi MM. Validation of mathematical models. J Biomech
1979;12:238.
Yoganandan N, Pintar FA, Sances A, Reinsartz J, Larson SJ.
Strength and motion analysis of the human head–neck complex.
J Spinal Disord 1991;4:73–85.