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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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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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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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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 compr