FE ANALYSIS OF MOMENT-ROTATION RELATIONSHIPS FOR HUMAN CERVICAL SPINE
Qing Hang Zhang1, Vee-Sin Lee2, Kok-Yong Seng2, Kian-Wee Tan2, Hong-Wan Ng1, Ee-Chon Teo1*
School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Ave, Singapore
2
Human Effectiveness Lab, Defense Medical Research Institute, Defense Science Technology Agency, Singapore
1
INTRODUCTION
RESULTS
A three-dimensional head-neck finite element (FE)
model was developed based on the actual geometry of
human cadaver specimen. The C0-C7 FE model
comprises of the skull, C1-C7 vertebrae, intervertebral
discs, facets joints and relating ligaments. Pure moment
loading of 1000Nmm was applied incrementally to the
skull to simulate the movements of the head/cervical
spine complex under flexion, tension, axial rotation and
lateral bending. The non-linear moment-rotation
relationship for human cervical spine is predicted.
Under same loading magnitude, the cervical spine
produces the largest rotation under extension, followed
by flexion and axial rotation. The upper cervical spines
are much flexible than the lower levels. The differences
of range of motions among the lower cervical spines are
relatively small. Validation study shows that the motion
values predicted from current FE model agree well with
the experimental data. The model can effectively reflect
the behaviour of human cervical spine and suitable for
further clinical study.
The
predicted
non-linear
moment-rotation
relationships of the whole structure (head respect to C7)
under the four moment loadings were shown in Figure
2. Under same loading magnitude, the cervical spine
produced the largest rotation under extension, followed
by flexion and axial rotation. The ROM under lateral
bending is the smallest. Under flexion, extension and
lateral bending, the ratios of rotation angles generated
by C0-C1 and C1-C2 to the whole cervical spine were
around 50%. Under axial rotation, this ratio is even up
to 65%. It is obvious that the upper cervical spine is
more flexible than the lower ones. In addition, the
differences of ROMs among the lower cervical levels
(C3-C7) are relatively small. These findings are
consistent with those obtained from experimental
studies[9,10].
The three-dimensional FE models of the skull and
cervical spine were developed based on the actual
geometry of human cadaver specimen. The anatomic
coordinates of the skull and vertebrae (C1-C7) were
measured from the cadaver specimen of a 68-year-old
man using a digitizer. The data for basic geometries of
the intervertebral discs were taken from average values
reported in literature[1]. The detailed process of
measurement and generation of the models were
described elsewhere[2,3]. Cortical bone, cancellous
bone, posterior elements, disc annulus, disc nucleus, and
endplate were modeled for each motion segment.
Furthermore, all spinal ligaments are also incorporated
in the model with insertion sites for various ligaments
based on anatomic text[4]. Figure 1 shows the C0-C7
FE models consists of 22,094 elements and 28,638
nodes.
Flexion
Extension
Axial Rotation
Lateral Bending
50
Rotation Angle (degree)
MATERIALS AND METHODS
60
40
30
20
10
0
0
200
400
600
800
1000
Moment (Nmm)
Fig.2. Predicted load-displacement curves of head
respect to C7
Figure 3 shows the comparisons of the predicted
primary ROM under extension and axial moment for
each motion segment with those obtained from Panjabi
et al[5]. Under extension, the predicted maximum
ROM occurred at C0-C1, which followed by C1-C2.
The ROMs of other motion segments are significantly
lower than these segments. Under axial rotation, the
motion was greatest at C1-C2, which was significantly
greater than all the other levels. These findings are
compatible with those observed from experiment.
Rotation Angle (degree)
30
Fig.1 Finite element mesh of the head and cervical
spine model
FE Result
25
Panjabi et al (2001)
20
15
10
5
0
C0-C1
13th ICMMB 12-15 Nov 2003 Tainan, Taiwan
C1-C2
C2-C3
C3-C4
C4-C5
C5-C6
C6-C7
Rotation Angle (degree)
70
60
Table 2: Range of motion of C5-C6 obtained from
different in vitro studies
50
40
Goel
et al[9]
30
20
10
0
C0-C1
C1-C2
C2-C3
C3-C4
C4-C5
C5-C6
C6-C7
Fig 3. Comparison of predicted ROMs for each motion
segment under moment of 1.0Nm with those obtained
from experiments under Extension and Axial Rotation
DISCUSSION AND CONCLUSIONS
In this study, a detailed C0-C7 FE model was developed
based on the actual geometries of human cadaver and
analysed. To the best knowledge of the authors, the
model developed is the most completed and complex for
biomechanical studies of human cervical spine. The
static studies under four rotational moment loadings
result show that the upper cervical spines are much
flexible than the lower segments. The motions of the
upper two motion segments are half (or higher) of the
whole structure under rotational loading conditions,
which agree with the experimental observations[5,6].
The unique anatomic articulating characteristics of the
segments (C0-C2) with no intervertebral disc in these
two levels, and the links between the vertebrae are only
ligaments and joint articulations. The lax ligaments in
this region make it possible for a relative small load to
produce large rotations across the complex[6].
There are differences in the predicted values and those
from in vivo or in vitro studies. Table 1 and 2 list the
ROMs obtained from different in vitro studies of upper
cervical spine (C0-C1 and C1-C2) and C5-C6 segment,
respectively. The different specimens used results in
different anatomical geometrical forms and tissues
biological materials characteristics, hence diverse and
controversial results are expected. For the upper
cervical spine, the data in Table 1 shows that the
greatest extension occurs at C0-C1 and the greatest axial
rotation occurs at C1-C2. The same phenomena also
observed for C5-C6 segment as shown in Table 2. The
values of motions obtained by Goel et al[7] are
significantly lower than those from Panjabi et al[5]
under the same magnitudes of load.
Moment
(Nm)
Extension
(deg)
Axial
Rotation
(deg)
Level
Moment
(Nm)
Extension
(deg)
Axial
Rotation
(deg)
C0-C1
C1C2
0.3
Panjabi et al[5]
C0-C1
C1C2
1.0
1.0
1.0
1.4 (0.3)
3.52 (1.94)
2.8 (0.8)
4.4 (2.8)
2.3 (1.4)
1.85 (0.67)
1.5 (0.5)
2.5 (1.0)
The values in ( ) are standard deviations
In conclusion:
1. The moment-rotation relationship for human cervical
spine is nonlinear. Under same loading magnitude, the
cervical spine produces the largest rotation under
extension, followed by flexion and axial rotation. The
range of motion under lateral bending is the smallest.
2. The upper cervical spines are much flexible than the
lower levels. The motions of the upper two motion
segments can be half (or higher) of the whole structure
under rotational loading conditions. The differences of
range of motions among the lower cervical spines (C3C7) are relatively small.
REFERENCES
[1] Gilad I and Nissan M (1986) Spine, 11(2):154-157.
[2] Teo EC and Ng HW (2001) J Biomech, 34:13-21.
[3] Ng HW and Teo EC (2001) J Spinal Disord, 14:201210
[4] The cervical spine research society, editorial
committee (1988) The cervical spine, Lippincott-Raven,
Philadelphia.
[5] Panjabi MM, Crisco JJ, Vasavada A, Oda T,
Cholewicki J, Nibu K and Shin E (2001) Spine,
26:2692-2700.
[6] Goel VK, Clark CR, Gallaes K and Liu YK (1988) J
Biomech, 21: 673-680.
[7] Goel VK and Clausen JD (1988) Spine, 23:684-691.
[8] Panjabi M, Dvorak J, Duranceau J, Yamamoto I,
Gerber M, Rauschning W and Bueff HU (1988) Spine,
13: 726-730.
[9] Goel VK, Clark CR, McGowan D and Goyal S
(1984) J Biomech, 17:363-376.
[10] Moroney SP, Schultz AB, Miller JA and Anderson
GB (1988) J Biomech, 21:769-779.
C1C2
1.5
16.5
(7.6)
5.2
(2.9)
20.2
(4.6)
12.1
(6.5)
21.0
(1.9)
10.9
(1.1)
2.4
(1.2)
23.3
(11.2)
4.9
(3.0)
28.4
(4.8)
7.9
(0.6)
38.3
(1.7)
Panjabi
et al[5]
1.8
Panjabi et al[8]
C0-C1
Goel
&
Clausen[7]
0.3
Table 1. Range of motion of upper cervical spine
obtained from different in vitro studies
Goel et al[6]
Moroney
et al[10]
The values in ( ) are standard deviations
13th ICMMB 12-15 Nov 2003 Tainan, Taiwan