Leitlinien & Studien
LABORATORY INVESTIGATION
C1–2 hypermobility and its impact on the spinal cord:
a finite element analysis
Arpan A. Patel, MD,1,2 Jacob K. Greenberg, MD, MSCI,3 Michael P. Steinmetz, MD,1,2
Sarel Vorster, MD,1,2 Edin Nevzati, MD,4,5 and Alexander Spiessberger, MD1,2
1Center for Spine Health, Cleveland Clinic, Cleveland, Ohio; 2Department of Neurosurgery, Cleveland Clinic Lerner College of
Medicine, Cleveland, Ohio; 3Department of Neurological Surgery, Washington University School of Medicine, St. Louis, Missouri;
4Department of Neurosurgery, Cantonal Hospital of Lucerne, Switzerland; and 5Faculty of Medicine, University of Basel,
Switzerland
OBJECTIVE The authors present a finite element analysis (FEA) evaluating the mechanical impact of C1–2 hypermobil-
ity on the spinal cord.
METHODS The Code_Aster program was used to perform an FEA to determine the mechanical impact of C1–2 hyper-
mobility on the spinal cord. Normative values of Young’s modulus were applied to the various components of the model,
including bone, ligaments, and gray and white matter. Two models were created: 25° and 50° of C1-on-C2 rotation, and
2.5 and 5 mm of C1-on-C2 lateral translation. Maximum von Mises stress (VMS) throughout the cervicomedullary junc-
tion was calculated and analyzed.
RESULTS The FEA model of 2.5 mm lateral translation of C1 on C2 revealed maximum VMS for gray and white matter
of 0.041 and 0.097 MPa, respectively. In the 5-mm translation model, the maximum VMS for gray and white matter was
0.069 and 0.162 MPa. The FEA model of 25° of C1-on-C2 rotation revealed maximum VMS for gray and white matter of
0.052 and 0.123 MPa. In the 50° rotation model, the maximum VMS for gray and white matter was 0.113 and 0.264 MPa.
CONCLUSIONS This FEA revealed significant spinal cord stress during pathological rotation (50°) and lateral transla-
tion (5 mm) consistent with values found during severe spinal cord compression and in patients with myelopathy. While
this finite element model requires oversimplification of the atlantoaxial joint, the study provides biomechanical evidence
that hypermobility within the C1–2 joint leads to pathological spinal cord stress.
KEYWORDS finite element analysis; Ehlers-Danlos syndrome; atlantoaxial instability; hypermobility; cervical
hlErs-Danlos syndromes (EDSs) have been asso-
(CMS) with symptoms of syncope, dizziness, sleep apnea,
autonomous dysregulation, motor weakness, and hyperre-
ciated with a constellation of spinal conditions as
a consequence of underlying ligamentous laxity,
2,4
E
flexia. Similar to hypermobility within the occiput–C1
including craniocervical instability (CCI), atlantoaxial
joint leading to brainstem functional impairment, liga-
mentous laxity in the transverse and alar ligaments within
1–5
instability (AAI), and basilar invagiation. AAI, in par-
1,4
ticular, is observed in multiple disorders of connective
tissue including Marfan syndrome, Down syndrome, and
the C1–2 junction can lead to hypermobility and AAI.
However, the mechanism of brainstem injury in AAI may
be secondary to repetitive strain and stress rather than
compression. Our study aims to examine various normal
and hypermobile anatomical scenarios within the atlanto-
axial joint to evaluate whether hypermobility can lead to
significant spinal cord stress using finite element analysis
(FEA).
1
rheumatoid arthritis. The deficient ligamentous architec-
ture and consequential hypermobility in conditions such
as CCI can lead to cranial settling and clivoaxial kypho-
1–3
sis. This well-studied phenomenon (cranial settling and
clivoaxial kyphosis) has been shown to lead to brainstem
compression and associated cervicomedullary syndrome
ABBREVIATIONS AAI = atlantoaxial instability; CAD = computer-aided design; CCI = craniocervical instability; CMS = cervicomedullary syndrome; EDS = Ehlers-Danlos
syndrome; FEA = finite element analysis; FEM = finite element modeling; VMS = von Mises stress.
SUBMITTED December 5, 2023. ACCEPTED February 21, 2024.
INCLUDE WHEN CITING Published online May 3, 2024; DOI: 10.3171/2024.2.SPINE231327.
©AANS 2024, except where prohibited by US copyright law
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Patel et al.
FIG. 1. CAD developed within the Code_Aster program. Components of the discretization process are labeled. Figure is available
in color online only.
Previous studies have utilized finite element modeling
unteer was used to develop a 3D finite element model of
the human cervical osteoligamentous spine and spinal
cord. Thin-sectioned (1-mm) DICOM files were used to
model the C1–2 junction, which was subsequently used to
develop a computer-aided design (CAD) model (Fig. 1).
The FEA program, Code_Aster, was used to compute the
magnitude and location of stress within the spinal cord.
Similar to the Spinal Cord Stress Injury Assessment sys-
tem, FEM provides a model of the brainstem with sim-
plified biomechanics including isotropy of gray and white
(FEM) to investigate the mechanical impact on neural
structures associated with pathological or postsurgical
conditions within the craniocervical junction such as
Chiari malformation, basilar invagination, degenerative
cervical myelopathy, spinal cord contusion, and surgical
6–13
decompression and fusion. These studies have signifi-
cantly improved our understanding of the relationship be-
tween the biomechanics of the cervical spine and their
mechanical impact on the spinal cord through assessing
stress and strain. Additionally, FEA allows the study of
unique anatomical and pathological scenarios that would
be difficult to produce in ex vivo cadaveric studies due
to tissue quality, high cost, and limited measurement of
11,14
matter and constant material property. A complete list
of biomechanical properties, including Young’s modulus
and Poisson’s ratio for anatomical components, is found in
15–18
Table 1.
All measures of stress were reported in mega-
6,12
pascal (MPa).
biomechanical parameters. Our study contributes to
the collective understanding of cervical biomechanics
derived from FEA studies by investigating the gray and
white matter von Mises stress (VMS) in two anatomical
settings: C1–2 lateral displacement and C1–2 rotation.
Using FEM, we simulated the pathological, supraphysi-
ological C1–2 movement that can be found in conditions
such as EDS and evaluated its mechanical impact on the
spinal cord.
Finite Element Model Testing
Two different anatomical conditions were simulated,
including lateral displacement of C1 on C2 (2.5 and 5.0
mm) and rotation of C1 on C2 (25° and 50°). When simu-
lating C1-on-C2 motion, boundary constraints were ap-
plied to the model to mimic physiological motion. The
degrees of freedom for C2 were minimal, while C1 was
allowed to laterally translate and rotate upon C2. In mod-
eling rotation, a moment boundary was applied at the axis
of rotation line that centered around the dens (Fig. 2A and
B). The caudal aspect of the spinal cord was constrained in
degrees of freedom while the cranial aspect was allowed
Methods
Study Materials
A cervical MR image from an 18-year-old healthy vol-
TABLE 1. Components of the discretization process of the upper cervical spine with Young’s modulus and Poisson’s
ratio reported for each component
Material (element type)
Anatomy
Young’s Modulus (MPa) Poisson’s Ratio Thickness (mm)
Linear elastic (cubic)
Linear elastic (cubic)
Linear elastic (tetrahedron)
Linear elastic (cubic)
Linear elastic
Gray matter
White matter
0.277
0.656
14.8
0.45
0.45
0.48
0.45
0.45
0.28
0.3
—
—
—
—
—
—
0.3
Subarachnoid space (CSF)
Dura mater
31.5
Epidural space
31.5
Linear elastic
Cortical bone
15000
100
Linear (2D shell elements)
Dentate ligaments
2
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Patel et al.
FIG. 2. A: Inferior view of C2 (green arrow) with degree of freedom constraints defined by dotted circles. B: Moment boundary
applied to the axis of rotation (arrows) through the dens for C1–2 rotation. C: Sliding contact settings between C1 and C2 and the
epidural space. Figure is available in color online only.
to move. VMS (in MPa), an aggregate calculation to de-
termine yield criteria, was calculated for each voxel and
graphically presented in a contour map. This calculation
was performed individually for both gray and white mat-
ter throughout the lower brainstem and spinal cord. The
maximum values were utilized to compare the mechani-
cal impact of different anatomical scenarios. The force
transfer path began with movement of C1 and C2 with
sliding contact between the osseous structures and the
epidural space (Fig. 2C). The sliding contact coefficient of
friction was defined as 0.1. The force was then transferred
from the epidural space to the dura mater, then to the sur-
rounding CSF and dentate ligaments, and finally to gray
and white matter.
contour map revealed a trend toward higher VMS values
in the anterior aspect of the gray and white matter of the
spinal cord in both the 2.5- and 5-mm translation models
(Fig. 3). During 2.5 mm of C1-on-C2 lateral translation,
the spinal cord was also noted to be laterally displaced by
approximately 2.5 mm. Similarly, in 5 mm of C1-on-C2
lateral translation, the spinal cord was laterally displaced
by approximately 5 mm (Fig. 4).
Rotation
In the FEA performed for 25° of C1-on-C2 rotation,
the maximum VMS for gray and white matter was 0.052
and 0.123 MPa. In the 50° rotation model, the maximum
VMS for gray and white matter was 0.113 and 0.264 MPa
(Table 2). Similar to the lateral translation model, the con-
tour map revealed a trend toward higher VMS values in
the anterior aspect of the gray and white matter of the spi-
nal cord for both the 25° and 50° rotation models (Fig.
5). In the 25° rotation model, the posterior aspect of the
Principles of FEA Modeling
FEA of the spine uses a discretization process of re-
ducing a continuous anatomical system into discrete parts
of bones, ligaments, and neural structures. The 3D repre-
sentation is often built from CT or MR imaging and rep-
resented as geometric shapes. The material properties of
the discrete components are assigned. The stiffness of the
tissue can either be interpreted from CT or MR imaging
or be based on existing literature. Once the model is devel-
oped, unique loading conditions are applied to the system
to evaluate the clinically relevant biomechanical param-
eters such as stress and strain on the brainstem, intradiscal
TABLE 2. Minimum, maximum, and average VMS for each clinical
condition simulated
VMS (MPa)
Clinical Condition
Min
Max
Average
6,11,12
pressure, or segmental rotation.
Lateral translation
2.5 mm
Results
Gray matter
White matter
5 mm
0
0.041
0.097
0.014
0.023
Two types of C1–2 motion were considered: lateral
translation and rotation. Lateral translation movement was
subdivided into 2.5 mm (physiological range of motion)
and 5.0 mm (supraphysiological range of motion). Rota-
tion was subdivided into 25° (physiological range of mo-
tion) and 50° (supraphysiological range of motion).
0.001
Gray matter
White matter
Rotation
0.001
0.002
0.069
0.162
0.028
0.048
25°
Lateral Translation
Gray matter
White matter
50°
0.001
0.001
0.052
0.123
0.016
0.029
In the FEA performed for 2.5-mm lateral translation of
C1 on C2, maximum VMS for gray and white matter was
0.041 and 0.097 MPa, respectively. In the 5-mm transla-
tion model, the maximum VMS for gray and white mat-
ter was 0.069 and 0.162 MPa, respectively (Table 2). The
Gray matter
White matter
0.002
0.003
0.113
0.034
0.063
0.264
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Patel et al.
FIG. 3. FEA modeling 2.5 and 5.0 mm of C1-on-C2 lateral translation. Distribution of VMS throughout the gray and white matter is
reported and axial distribution of the VMS is represented. Figure is available in color online only.
spinal cord was noted to undergo up to approximately 4
mm of lateral displacement in the direction of the rotation,
while the anterior midline aspect of the cord remained un-
changed. Similarly, in the 50° model, the posterior aspect
of the spinal cord was noted to undergo approximately 7.7
mm of lateral displacement, while the anterior midline re-
mained in its neutral location. The rotation of C1 on C2
around the axis of the dens resulted in similar rotation and
displacement of the spinal cord around an axis in the an-
terior midline (Fig. 6).
Using diagnostic criteria for Fielding type 1 AAI,
25° of rotation of C1 on C2 is considered within normal
physiological conditions, while 50° of rotation is consid-
19
ered a pathological state. Additionally, 2.5 mm of lateral
translation was considered as a potentially normal physi-
ological finding, while 5 mm of translation was consid-
19–21
ered pathological.
As expected, the FEA found higher
values of VMS all throughout the gray and white matter
of the C1–2 junction during 50° of rotation when com-
pared with the maximum VMS during 25° rotation. Simi-
larly, the maximum VMS during 5 mm of lateral trans-
lation was higher than the maximum during 2.5 mm of
movement. The maximum discrete values of VMS dur-
ing both 5 mm of lateral movement and 50° of rotation
are consistent with values of pathological stress that are
Discussion
Our study aimed to provide insight into the mechanical
impact of supraphysiological movement within atlantoax-
ial segments on the spinal cord. Using a healthy volunteer
to generate a finite element model, we tested normal and
supraphysiological movement in C1–2 lateral translation
and rotation. Although we aimed to better understand the
pathophysiology of spinal cord injury in patients with liga-
mentous laxity and hypermobility, we used a healthy vol-
unteer to generate the CAD because the osseous structures
of a patient with EDS are similar to the osseous structures
in a healthy volunteer. In this model, the Young’s modulus
of the ligaments was estimated to have little influence on
the mechanical impact exerted by the osseous structures
found in settings of severe spinal cord compression and
7,11,18
patients with myelopathy.
Evaluating the distribution
of stress throughout the white and gray matter of the spi-
nal cord revealed a trend toward increased VMS values in
the anterior horn of the gray matter, anterior corticospinal
tract, and anterior spinothalamic tract. Given the location
of stress in the upper spinal cord, the expected symptoms
were similar to those of CMS such as upper- and lower-
extremity weakness, autonomic dysfunction, numbness,
swallowing difficulties, and imbalance. With higher stress
values in the anterior spinal cord, there may be a predilec-
tion for motor symptoms. During 50° of C1–2 rotation,
there was approximately 7.7 mm of displacement noted
in the posterior aspect of the spinal cord, while the ante-
rior aspect remained relatively in its neutral position (Fig.
6). This finding correlated with increased VMS values in
11,14
on the spinal cord, thus normative values were utilized.
The simulated hypermobility within a healthy spine was
an acceptable method to evaluate the mechanical impact
of supraphysiological lateral translation and rotation on
the spinal cord.
4
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Patel et al.
the anterior aspect of the spinal cord as the inability to
displace during rotational movement resulted in increased
torsional stress.
The maximum VMS of both gray and white matter
during 2.5 mm of lateral translation was noted to be less
than the maximum VMS in both gray and white matter
during 25° of rotation. Given that 25° of C1-on-C2 rota-
tion is well accepted as normal physiological motion, this
finding may suggest that 2.5 mm of lateral translation of
C1 on C2 can be an acceptable finding. Rotational move-
ment in the C1–2 segment led to overall higher maximum
VMS in both gray and white matter when compared to
displacement. This effect may be seen due to motion cou-
pling, in which rotation in the atlantoaxial joint is coupled
to lateral displacement and lateral bending, thus leading
to more strain and stress applied to the spinal cord.
Clinically, dynamic spinal cord stress and strain in an
unstable spine is associated with chronic spinal cord in-
jury and dysfunction. Repetitive shear forces due to in-
stability can induce localized mechanical axonal injury.
Both tensile and compressive stress forces can lead to in-
creased intramedullary pressure, reduced perfusion, and
22
ischemic injury in the spinal cord. Through this FEA
we found that specific anatomical movements within the
atlantoaxial segment result in distinct amounts of spinal
cord stress, with certain movements generating stress val-
ues similar to those found in patients with severe spinal
11,18
cord compression. Yang et al. evaluated the maximum
spinal cord stress associated with C4–5 stenosis in pa-
tients with cervical myelopathy. Spinal cord stress dur-
ing loading conditions at the C4–5 level in a control pa-
tient ranged from 0.00014 to 0.001 MPa, while the stress
values within a diseased myelopathic spinal cord ranged
FIG. 4. FEA evaluating the total displacement of the spinal cord during
2.5 and 5.0 mm of C1-on-C2 lateral translation. Figure is available in
color online only.
18
from 0.0194 to 0.039 MPa. Although the stress values
generated from specific models in different regions of the
spinal cord cannot be directly compared with the values
generated within this study, a trend was identified, with
higher values associated with pathological states. Simi-
larly, previous studies have shown that increased spinal
cord VMS as measured by FEA in craniocervical con-
modalities. Consequentially, identification of atlantoaxial
hypermobility or CCI is often missed on static imaging
7,11
4
ditions correlates clinically with increased disability.
modalities. As the most mobile segment of the spine, the
Henderson et al. noted within their finite element model
of craniocervical compression that clinical improve-
ment following decompression correlated with a 68%
atlantoaxial joint is prone to developing instability. Range-
of-motion studies report maximum global head rotation in
a single direction as 70°–90°, with the C1–2 segment re-
11
23–25
reduction in modeled stress values (e.g., 0.7–0.13 MPa).
sponsible for 50%–60% of the movement.
The maxi-
Within our study, we noted a 53.4% and 54.0% reduction
in VMS between 50° and 25° of rotation when compar-
ing the maximum VMS in white (0.264–0.123 MPa) and
gray matter (0.113–0.52 MPa), respectively. Similarly, the
maximum VMS in white matter and gray matter when
comparing 5 to 2.5 mm of lateral translation resulted in
a 40.1% (0.162–0.97 MPa) and 40.6% (0.162–0.041 MPa)
reduction, respectively. The relative differences between
the VMS scores of 25° of rotation and 2.5 mm of lateral
translation when compared with 50° rotation and 5 mm
of lateral translation suggest a similar relationship of non-
pathological and pathological states between these ranges
of motion.
mum rotation of C1 relative to C2 in normative settings is
23,25
reported to be between 36° and 43°.
In vivo kinematic
studies reveal coupled motion, including lateral bending
and flexion/extension of the C1–2 segment, during upright
rotation as well as lateral translation and axial rotation of
23,26
C1–2 during cervical lateral bending.
Although there
is a paucity of data regarding the normative lateral trans-
lation of C1 on C2 during maximal lateral bending, a few
studies have suggested that 1–2 mm of ipsilateral C1-on-
C2 overhang may be within normal parameters, while >
3.5 mm of translation is associated with hypermobility
20,21
and AAI.
Our investigation suggests that both 50° of
rotation and 5 mm of lateral translation are associated with
pathologic amounts of stress within the spinal cord. In the
clinical evaluation of patients with EDS and hypermobil-
ity, dynamic films revealing 50° of C1-on-C2 rotation or
Defining parameters of abnormal atlantoaxial motion
continues to be challenging due to the dynamic nature of
the underlying pathology and the static nature of imaging
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Patel et al.
FIG. 5. FEA modeling 25° and 50° of C1-on-C2 rotation. Distribution of VMS throughout the gray and white matter is reported and
axial distribution of VMS is represented. Figure is available in color online only.
5 mm of lateral translation during lateral bending may be
an indication of instability and need for stabilization. Fur-
thermore, our investigation suggests that 2.5 mm of C1-
on-C2 lateral translation leads to comparatively less stress
on the spinal cord than 25° of C1-on-C2 rotation. Given
that 25° of C1-on-C2 rotation is well defined as within nor-
mal physiological range, our investigation suggests that 2.5
mm of lateral translation should also be considered within
normal physiological range.
as a solid element with equivalent fluid properties, thus
the fluid is unable to displace under force. While there are
many intrinsic limitations to FEM of the craniocervical
spine, we believe these studies provide useful insight into
biomechanics that would be difficult to ascertain through
cadaveric studies.
CoWneclhuasveiountislized FEM to evaluate spinal cord stress in
the atlantoaxial junction during normative and pathologi-
cal ranges of motion. The FEA performed revealed signifi-
cant spinal cord stress during pathological rotation (50°)
and lateral translation (5 mm). During these movements,
there is significant stress within the anterior horn of the
gray matter, anatomically corresponding to projections of
anterior corticospinal and anterior spinothalamic tracts.
In a clinical scenario, stress within this region can be as-
sociated with symptoms similar to CMS with autonomic
dysfunction, motor weakness, numbness, and imbalance.
While FEA of the craniocervical junction requires over-
simplification of a complex anatomical region, the study
provides biomechanical insight into spinal cord stress in
C1–2 hypermobility.
Limitations of the Study
Overall, FEM of the craniocervical junction requires
simplification of the most mobile and complex anatomi-
cal region of the spine. In the absence of an intervertebral
disc, the atlantoaxial segment has a multitude of ligaments
that play an important role in limiting segmental motion.
FEA requires the simplification of such ligaments and re-
duction to linear material properties. In our study, we used
normative values for Young’s modulus despite investigat-
ing the mechanical impact of hypermobility on the spinal
cord. This was an acceptable limitation for our analysis as
the FEM can simulate hypermobile movement indepen-
dent of Young’s modulus of the ligaments. The focus of
our investigation was evaluating spinal cord stress gener-
ated by motion of the osseous structures. Furthermore,
within our model the spinal cord was designed to be fixed
caudally with no degrees of freedom and allowed to move
cranially. This fixation method can impact the results as
the ability of the spinal cord to displace can directly im-
pact the VMS measured. Additionally, CSF was modeled
Acknowledgments
No sponsor contribution to the design and conduct of the
study; collection, management, analysis, or interpretation of data;
or preparation, review, or approval of the manuscript was given by
the Ehlers-Danlos Syndrome Initiative Germany.
6
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Patel et al.
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FIG. 6. FEA evaluating the total displacement of the spinal cord during
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tion. Figure is available in color online only.
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Author Contributions
Conception and design: Patel, Greenberg, Steinmetz, Nevzati,
Spiessberger. Analysis and interpretation of data: Patel, Vorster,
Spiessberger. Drafting the article: Patel. Critically revising the
article: all authors. Reviewed submitted version of manuscript: all
authors. Approved the final version of the manuscript on behalf
of all authors: Patel. Statistical analysis: Patel. Study supervision:
Spiessberger.
25. Pang D, Li V. Atlantoaxial rotatory fixation: part 1—biome-
chanics of normal rotation at the atlantoaxial joint in chil-
dren. Neurosurgery. 2004;55(3):614-626.
26. Ishii T, Mukai Y, Hosono N, et al. Kinematics of the cervical
spine in lateral bending: in vivo three-dimensional analysis.
Spine (Phila Pa 1976). 2006;31(2):155-160.
Correspondence
Arpan A. Patel: Cleveland Clinic, Cleveland, OH. patela16@
Disclosures
ccf.org.
Dr. Steinmetz reported receiving royalties from Elsevier and
royalties/honoraria from Globus outside the submitted work. Dr.
Nevzati reported receiving grants from Deutsche Ehlers Danlos
Gesellschaft during the conduct of the study. Dr. Spiessberger
reported that this study was financially supported by a patient
advocacy group (EDS Germany, 4000 USD).
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