Corresponding Author Yuntao Lu Department of Neurosurgery, Nanfang Hospital, Southern Medical University, 1838 North Guangzhou Ave, Guangzhou 510515, China Email: lllu2000yun@gmail.com
Junhua Ye and Qinguo Huang contributed equally to this study as co-first authors.
• Received: June 15, 2024 • Revised: August 3, 2024 • Accepted: August 13, 2024
This is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Recent studies indicate that 3 morphological types of atlanto-occipital joint (AOJ) exist in the craniovertebral junction and are associated with type II basilar invagination (BI) and atlanto-occipital instability. However, the actual biomechanical effects remain unclear. This study aims to investigate biomechanical differences among AOJ types I, II, and III, and provide further evidence of atlanto-occipital instability in type II BI.
Methods
Models of bilateral AOJ containing various AOJ types were created, including I-I, I-II, II-II, II-III, and III-III models, with increasing AOJ dysplasia across models. Then, 1.5 Nm torque simulated cervical motions. The range of motion (ROM), ligament and joint stress, and basion-dental interval (BDI) were analyzed.
Results
The C0–1 ROM and accompanying rotational ROM increased progressively from model I-I to model III-III, with the ROM of model III-III showing increases between 27.3% and 123.8% indicating ultra-mobility and instability. In contrast, the C1–2 ROM changes were minimal. Meanwhile, the stress distribution pattern was disrupted; in particular, the C1 superior facet stress was concentrated centrally and decreased substantially across the models. The stress on the C0–1 capsule ligament decreased during cervical flexion and increased during bending and rotating loading. In addition, BDI gradually decreased across the models. Further analysis revealed that the dens showed an increase of 110.1% superiorly and 11.4% posteriorly, indicating an increased risk of spinal cord impingement.
Conclusion
Progressive AOJ incongruity critically disrupts supportive tissue loading, enabling incremental atlanto-occipital instability. AOJ dysplasia plays a key biomechanical role in the pathogenesis of type II BI.
The craniovertebral junction (CVJ) is a complex anatomical region connecting the skull base and cervical spine [1]. Proper biomechanical function of the CVJ is essential for head mobility and protection of the neurovascular structures that traverse this region. Abnormalities in the bony and ligamentous structures of the CVJ can lead to instability, which may result in pain, deformity, neurological deficits, and even death [2,3]. Basilar invagination (BI) is a common bony abnormality at CVJ, characterized by the odontoid abnormally protruding into the foramen magnum. BI can be classified into 2 types based on atlantoaxial instability: type I (I-BI) with atlantoaxial dislocation, and type II (II-BI) without atlantoaxial dislocation. Traditionally, II-BI was not thought to cause instability at the CVJ. The treatment of I-BI has been extensively studied with established protocols; however, the surgical management of II-BI remains controversial. Foramen magnum decompression and transoral odontoidectomy are the 2 primary surgical approaches [4,5]. However, foramen magnum decompression may be ineffective in patients with severe ventral compression and could potentially exacerbate the CVJ instability. Moreover, transoral or transnasal procedures carry an elevated risk of postoperative complications, including infections and aspiration. Goel et al. [6] proposed that atlantoaxial instability is also present in II-BI, and advocated for atlantoaxial fixation as a treatment. However, this approach has not gained widespread acceptance because of insufficient pathogenetic evidence of atlantoaxial instability in II-BI cases. Therefore, elucidating the biomechanics of II-BI is crucial for developing more effective treatment strategies, identifying patients at higher risk of instability, and optimizing surgical interventions.
Our recent research has suggested that atlanto-occipital joint (AOJ) dysplasia is associated with craniocervical pathologies such as Chiari malformation (CM) and II-BI. Furtherly, 3 distinct AOJ phenotypes were identified by using geometric morphometric analysis [7]. Type I AOJ consist of a healthy joint structure without malformations and is characterized by a typical ball-and-socket morphology. Type II AOJ exhibit flatter articulation, yet the ball-and-socket conformation remains identifiable. Type III AOJ display the most severe deformity, denoted by a substantially flat joint surface and a greater tilted angle (Fig. 1). Dynamic imaging has revealed AOJ hypermobility in type II and III morphologies. However, the precise biomechanical impact of these morphological changes on II-BI remains unclear, necessitating further investigation to elucidate their role in CVJ instability and inform treatment decisions.
Finite element analysis is a powerful computational technique that can provide insights into complex biomechanical behaviors that are difficult to directly observe experimentally [8]. In this study, we developed a detailed finite element model (FEM) of the CVJ based on clinical computed tomography (CT) data of normal subjects. Using such models, we aimed to validate the AOJ kinematics against in vivo data and quantify the biomechanical effects of the AOJ morphological changes. The results of this study will improve our understanding of the biomechanical pathogenesis of atlanto-occipital instability in the onset of II-BI.
MATERIALS AND METHODS
1. Development of Normal Upper Cervical Spine Model
A thin-layer (0.50 mm) CT scan of a 28-year-old patient with normal CVJ anatomy, a height of 170 cm, and a weight of 75 kg was used to obtain the morphological data of the occipital-atlantoaxial complex. The study was approved by the Institutional Review Board of Nanfang Hospital, Southern Medical University (NFEC-2022-440). Informed consent was obtained. The FEM of the occipital-atlantoaxial complex included cortical and cancellous bones. The gaps in the AOJ and lateral atlantoaxial joints were modeled as cartilage, and the corresponding thicknesses were determined by dichotomizing the gaps. The cortices of C0 (occipital bone), C1 (atlas), C2 (axis), and cartilage were modeled using 8-node brick elements. These components were treated as isotropic linear elastic materials.
The transverse ligament is a low-elastic tissue that is notably tough and articulated with odontoid processes. Therefore, it was modeled with 8-node brick elements and attached to C1. This is consistent with previous models from similar studies [9]. All other ligaments such as the alar ligament (AL), apical ligament (APL), anterior atlanto-occipital membrane, posterior atlanto-occipital membrane (PAOM), tectorial membrane (TM), anterior longitudinal ligament (ALL), ligamentum flavum (LF), and capsular ligaments (CLs) were modeled using tension-only spring elements [7]. The attachment sites and ligament orientations were obtained from literature [10,11].
Six sliding articulations were incorporated into the model: the bilateral AOJ, the bilateral atlantoaxial joints, the atlantodental joint, and the transverse ligament-odontoid process articulation. All joint surfaces were subjected to face-to-face contact at a frictional coefficient of 0.1 to simulate sliding between joint surfaces [11]. Finally, a 3-dimensional nonlinear FEM of the occipital-atlantoaxial complex was created (Fig. 2A). The model consisted of 590,057 elements and 140,674 nodes. All material properties were derived from literature [12,13] and are tabulated in Table 1. After accurate mesh preparation was facilitated by the Altair HyperMesh software, nonlinear analysis was performed using the OptiStruct solver (Hyperworks, Altair, Troy, MI, USA).
2. Development of the Variant AOJ Models
In a prior investigation, a comprehensive study pertaining to the inherent morphological variation of the AOJ was conducted, proving a correlation with CM and II-BI [7]. To effectively classify the biomechanism of several variant AOJs, 6 pivotal parameters were considered: the length and height of the condyle and superior portion of the atlas lateral mass, and the depth and curvature of the AOJ. The CT data from a cohort of 185 adults (80 control subjects, 63 individuals with pure CM, and 42 individuals with CM and II-BI), was analyzed. The outcomes for the 6 parameters are tabulated in Table 2. The normal model (denoted as model I-I) was subsequently modified using the HyperWorks software’s morphing technique to account for morphological variations in both the condyle and C1 lateral mass. Consequently, the 6 variables encapsulating the AOJ were adjusted to simulate the conditions of types II-AOJ and III-AOJ. Following the morphing of C0 and C1, the corresponding articular cartilage between C0 and C1 underwent adaptive alterations (Fig. 2B).
We successfully developed models representing bilateral type II AOJs (model II-II), which accounted for 29.2% of all clinical cases, and bilateral type III AOJs (model III-III), which accounted for 18.3% of cases. It is worth noting that bilateral AOJ dysplasia may exhibit asynchronous characteristics, potentially manifesting as a type II AOJ on one side, while the contralateral AOJ remains normal (2.7% of cases) or even as a contralateral IIIAOJ (6.5% of cases). To represent clinical scenarios of asymmetric AOJ pathology, we consistently modeled the right AOJ as more severe than the left AOJ. Model I-II had a type I left AOJ and type II right AOJ and model II-III had a type II left AOJ and type III right AOJ. This ensured that the right AOJ was more affected than the left AOJ in representing asymmetry. Finally, 4 variant models, namely I-II (right worse than left), IIII, II-III (right worse than left), and III-III were established. The AOJ morphological abnormalities were progressively worsened (Fig. 2C). By developing these models of bilateral AOJ with distribution ratios matching clinical cases outlined in Table 3, we demonstrated their ability to simulate the spectrum of observed AOJ variations.
3. Loading and Boundary Conditions
In FEMs, all nodal points of the lower end plate region of the C2 vertebra were fixed with 6 degrees of freedom. A pure moment of 1.5 Nm was loaded along 3 planes on an RBE2 element dependent on the foramen magnum of the occipital bone. Cervical movements such as flexion, extension, bending left, bending right, rotating left, and rotating right were simulated.
4. Postprocessing and Quantitative Analyses
The model results were further examined using HyperView (HyperWorks, Altair) for quantitative measurements. Range of motion (ROM) for each motion segment was calculated using the Relative Angle tool. For solid element components such as the bone and transverse ligament, the stress results were averaged over the entire structure. The ligaments modeled using spring elements had stress data averaged across the bundles of springs representing each ligament. Basion-dental interval (BDI) measurements were performed using the minimal distance and incremental distance tools. The clivus-axial angle (CXA) was measured by the open-source software 3D Slicer (ver. 5.2.2). The pB-C2 line was measured by exporting the iso surface of FEM, and measured in HyperMesh.
RESULTS
1. Model Validation
The ROM results from our intact model (I-I AOJ) were compared with those of previous in vitro experiments and computational studies. Atlantoaxial joint mobility showed good agreement with the biomechanical data reported by Panjabi et al. [14,15] and Meng et al. [16] (Fig. 3A–F). Additionally, the axial tension force-displacement behavior of our intact model closely aligned with the experimental tensile characterization by Yliniemi et al. [17], as illustrated in Fig. 3G. The structural stiffness of model I-I was 113 N/mm in terms of axial tension. Based on the above comparative analyses, we deemed our FEM to be valid for simulating complex CVJ mechanics.
2. ROMs of Variant Models
By changing the morphological parameters of the occipital tubercle and annular isthmus joint, different upper cervical spine variant models were established, including models of I-II, II-II, II-III, and III-III AOJs. Under flexion and extension, left and right lateral bending, and left and right axial rotation loads, the ROM of different models at the C0–1 segment showed that, compared with model I-I, model I-II showed little change across loading conditions. Model II-II showed increases of 7.5% in flexion, 10.7% in extension, 17.7% in left bending, 10.9% in right bending, 31.5% in left rotation, and 46.8% in right rotation. Model II-III showed greater increases of 15.1% in flexion, 12.2% in extension, 24.9% in left bending, 60.9% in right bending, 54.1% in left rotation, and 98.5% in right rotation. Finally, model III-III showed the most substantial increases of 27.3% in flexion, 35.2% in extension, 85.4% in left bending, 78.8% in right bending, 72.9% in left rotation, and 123.8% in right rotation. Fig. 4A illustrates the results for each of the models. In summary, the C0–1 ROM increased progressively as the AOJ models changed from I-I to III-III, with the most pronounced increases observed in model III-III. This indicates that AOJs become increasingly unstable as AOJ morphological abnormalities worsen.
For the C1–2 segment, changes in the ROMs in the different models remained within a narrow fluctuation range (Fig. 4B). The C1–2 ROM remained relatively stable across AOJ models.
3. Facet Joint Stress
The stress distribution of the C1 and C2 superior articular facets showed very little difference between subtypes (Figs. 5A and 6A). However, we still observed that the C1 superior facet stresses were concentrated centrally and reduced posterolaterally as articular changes intensified. This was most evident during bending and rotation. The facet stress was calculated from the average von Mises stress on the superior articular surface of the vertebrae. Compared with model I-I, the average C1 facet stress in variant models decreased substantially in multiple loading conditions, especially model III-III in extension (-42.1%), bending left (-31.4%), bending right (-37.6%), rotating left (-26.8%), and rotating right (-48.4%). This result is illustrated in Fig. 5B. For the average C2 facet stress, no significant changes were observed (Fig. 6B).
4. Ligament Stress
Under different loading conditions, the stress distribution of the transverse ligament was essentially the same and the maximum stresses were observed at the attachment of the ligament (Fig. 7A). The average von Mises stress at the transverse ligament showed a slight increase across models in cervical flexion; however, no obvious changes were observed in the other conditions (Fig. 7B). We also measured the average stress for the other ligaments mimicked by spring elements. The results are displayed in Fig. 8. These results indicate that cervical spine activities are accomplished by the involvement of several different sets of ligaments. Most ligaments differed slightly, such as the ALL, C1–2 CL, LF, and PAOM. The AL, APL, and TM showed a continuous decrease with worsening AOJ morphological abnormalities under all loading conditions. The C0–1 CL decreased slightly during flexion and increased during bending left, bending right, rotating left, and rotating right.
5. Dynamic Changes of CXA
The CXA measures the angle between the dorsal clivus and the dorsal C2 line. It assesses the degree of ventral brainstem compression and craniocervical kyphosis. The CXA value of all models in the neutral position was 167.3°. Furthermore, we evaluated the dynamic alterations in CXA during cervical flexion and extension. The CXA progressively decreased during flexion and increased during extension from model I-I to model III-III (Fig. 9A). In particular, the CXA changed more significantly during flexion: compared to model I-I, model III-III showed most obvious changes (4.9% decrease).
6. Relative Movement of the Odontoid Process
The pB-C2 line measures the distance between the posterior edge of the basion (anterior margin of the foramen magnum) and the posterosuperior aspect of the C2 vertebral body. A longer pB-C2 line indicates greater ventral canal encroachment. The pB-C2 value of all models in the neutral position was 4.0 mm, which was increased during flexion, and decreased during extension. The degree of variation in pB-C2 between models was small (Fig. 9B).
The BDI progressively decreased during cervical flexion and extension from model I-I to model III-III (Fig. 9C). This indicates a closer approximation of the basion and dens, along with more severe AOJ abnormalities. Specifically, the minimum BDI distance decreased by 28.6% in flexion and 28.5% in extension when comparing model III-III to model I-I.
To investigate the directional alterations in the BDI, we conducted additional measurements of the incremental distance of the BDI. Results showed that the dens displayed upward (Z-direction) and posterior (Y-direction) motions under flexion loading (Fig. 9D and E). The upward movement increased by 110.1% from model I-I to model III-III during flexion. The posterior movement initially increased by 11.4% from model I-I to model II-II, before decreasing in model III-III.
These quantitative results demonstrate the tendency of progressively increasing upward and posterior dens motion under flexion as the AOJ morphology becomes more dysplastic. This suggests an elevated risk of spinal cord compression from the dens as AOJ abnormalities worsen, particularly during flexion.
7. Accompanying Rotational Motion of AOJ
The C0–1 rotational ROM progressively increased from model I-I to model III-III across loading conditions, as illustrated in Fig. 9F. The increases were most pronounced in model II-III during flexion (340.0% increase) and extension (131.0% increase). Model III-III exhibited the largest C0–1 rotational increases during bending. At C1–2, the rotational mobility was largely similar between models, except that model II-III exhibited greater motion during left (44.3% increase) and right (27.5% increase) bending versus model I-I (Fig. 9G).
DISCUSSION
The surgical management of II-BI has always been controversial, as no universally accepted treatment approach has been established. In particular, it is still uncertain whether these patients actually suffer from CVJ instability. Goldstein and Anderson [18] proposed that the diagnosis of CVJ instability is a combination of clinical and radiographic findings, including myelopathy, and BI. However, this method lacks precision in determining the stability of CVJ. Goel et al. [6] suggested atlantoaxial instability is also present in II-BI but provided no definitive imaging evidence. Our previous study identified AOJ dysplasia, and classified AOJ into 3 types. In the present study, we used finite element analysis to develop detailed models for further investigating the biomechanical effects of different AOJ types on CVJ instability. Specifically, the models incorporated both symmetric and asymmetric bilateral AOJ abnormalities to better mimic clinical scenarios.
Firstly, our results show that the C0–1 ROM substantially increased from model I-I to the severely dysplastic model III-III under all loading conditions tested, with increases between 27.3% and 123.8% compared with model I-I. These data indicate that the AOJ becomes increasingly unstable and hypermobile as articular congruency is lost, which is in agreement with prior imaging studies revealing AOJ instability in this cohort [19,20]. These findings suggest that CVJ instability does indeed exist in patients with II-BI, specifically in AOJ rather than the atlantoaxial joint. Compared with models I-II and II-II, models II-III (flexion, bending right, and rotating left) and III-III (all conditions) showed a more pronounced increase in mobility (Fig. 4). This implies that III-AOJ is the most unstable, and surgical C0–1 stabilization may be required to halt progression in II-BI patients with III-AOJ. This emphasizes the need to identify the morphological type of AOJ and to determine the stability of the AOJ when treating II-BI.
In addition, we also find that morphological changes in the AOJ have relatively minimal biomechanical impacts on the distal structures of the atlantoaxial joint complex, including ROMs of the C1–2 segment, stress on the C2 superior facet joints, and loading of the transverse ligament, CL, LF, and ALLs. However, progressive AOJ morphological abnormalities elicit substantial alterations in localized kinematics and tissue mechanics within the joint. The concentrated and decreased stresses borne by the C1 superior facet joints signify that the bony articulations can no longer adequately dissipate loads, which may be aberrantly transferred elsewhere or manifest as instability. This redistribution of stress can seriously undermine the overall congruency and stability of the CVJ. Similarly, the reductions in ligament stresses, particularly those of the AL, APL, and TM, indicate that these stabilizing soft tissue structures are becoming progressively insufficient to constrain the excess motions enabled by deteriorating AOJ congruency. Notably, these findings enhance our understanding of the multifaceted nature of CVJ instability, particularly in cases without obvious congenital ligamentous disorders. While ligamentous laxity undoubtedly plays a crucial role in congenital conditions such as Down syndrome or Marfan syndrome. Our research, based on a clinical cohort that excluded these congenital disorders, reveals significant variations in AOJ development and morphology [7]. This suggests that altered joint morphology may be an initiating factor for IIBI in these cases. Combined with this finite element analysis, our finding complements the traditional view of ligament injury/failure as a primary factor in CVJ instability, offering a more comprehensive perspective on the biomechanical factors contributing to these complex conditions.
In the literature, the CXA and pB-C2 line are commonly used to assess CVJ instability and act as criteria for adding fusion to CVJ [21,22]. Our result showed that the CXA decreased more severely during cervical flexion in model III-III, further revealing CVJ instability, and potential risk of spinal cord compression. However, changes of pB-C2 among models were very slight. The possible cause is that CVJ instability due to changes in joint morphology is complex: in addition to increased ROMs of the cervical spine, it also accompanied by an increase in rotational motion (Fig. 9F), which may affect the bB-C2 results. To investigate the direction of motion of the odontoid, we further investigated in detail the BDI. Results showed that the minimal BDI decreased with worsening AOJ morphology, with reductions of 31.5% in flexion and 35.3% in extension for model III-III compared with model I-I. Importantly, during flexion, upward (Zdirection) and posterior (Y-direction) movements of the odontoid process were observed and showed increasing trends across models. This dynamic assessment of the odontoid process movement provides a more comprehensive understanding of potential spinal cord compression risks compared to the static pB-C2 line measurement. It suggests that the risk of ventral compression of the spinal cord progressively increases with worsening AOJ morphology. Upward and posterior movements of the odontoid process also suggest the loss of critical spatial relationships that normally prevent brainstem compression. Together, these biomechanical changes provide compelling evidence that AOJ dysmorphology and the resultant instability may be major mechanical contributors to pathological processes such as BI. Furthermore, the results showed that the rotational ROM at the C0–1 joint gradually increased from the normal model I-I to the severely dysplastic model III-III, also indicating progressively greater joint instability. The increased AOJ rotational mobility may be consistent with torticollis or the “cock-robin” posture observed clinically in patients with BI [23-26]. Biomechanical alterations that cause excessive AOJ rotation likely contribute to the symptomatic tilting posture associated with craniocervical misalignment.
These biomechanical insights have important implications for clinical practice. Screening for AOJ dysplasia may help identify patients at risk of instability and associated pathologies, such as BI, before a neurological deficit occurs [9,27]. Conservative treatment may be inadequate for this cohort, as bracing cannot alter bony morphology. Surgical C0–1 stabilization may be required to halt progression [28-30]. As reported in a previous study [20], patients with CM and II-BI treated with atlantoaxial distraction and occipitocervical fusion showed significant postoperative reductions in syringomyelia and tonsillar herniation along with excellent functional recovery. Zhang et al. [31] also reported similar technique for treating II-BI, and achieved satisfactory reduction of BI and clinical results were achieved. These findings suggest that timely surgical realignment and stabilization of the CVJ are critical for optimal clinical outcomes. However, optimal practices for surgical correction remain debated, and future modeling studies should examine the biomechanical ramifications of various constructs. Overall, this work elucidates the need to recognize AOJ dysplasia as a potential precursor to instability and that preservation of AOJ integrity is paramount when surgically correcting craniocervical pathologies.
This computational study had several limitations that merit further discussion. The FEM involved important simplifications that limit direct extrapolation to complex clinical scenarios. For instance, ligamentous structures and their attachments were modeled as normal, whereas ligamentous laxity or degeneration may influence joint stability in many patients [32-34]. Additionally, long-term consequences, such as ligament creep, bony remodeling, and osteoarthritis, were not analyzed in these acute simulations. Capturing such chronic effects requires complex time-dependent algorithms and loadings that can better approximate lifelong mechanical alteration [35-37]. Nevertheless, within the inherent constraints of finite element modeling, this study provides valuable novel insights into AOJ-mediated CVJ instability.
CONCLUSION
AOJ dysplasia may cause craniocervical instability and contribute to the pathological conditions of II-BI, which was thought to occur without instability. We simulated AOJ dysplasia using FEMs and found stepwise biomechanical alterations with worsening morphology. These results provide computational evidence that abnormalities in the AOJ may directly precipitate alanto-occipital instabilities.
NOTES
Conflict of Interest
The authors have nothing to disclose.
Funding/Support
This work was supported by the General Programs from the National Natural Science Foundation of China (81972355 and 82373398 to Y.T.L.), Medical Scientific Research Foundation of Guangdong Province (A2023409 to Q.G.H.), the National Natural Science Foundation of Guangdong Province (2019B151502048 to Y.T.L), Shantou Medical Health Science and Technology Plan (220518116490852 to Q.G.H.), the National Key Clinical Specialty Project, and the Clinical Research Program of Nanfang Hospital, Southern medical University (2021CR018 to Y.T.L), and National High Level Hospital Clinical Research Funding (2022-PUMCHD-004 to Y.T.L).
Computed tomography (CT) images and geometric reconstruction of the occipital condyle and atlas lateral masses. (A) Type I atlanto-occipital joint (I-AOJ): Normal, ideal morphology of the atlanto-occipital joint exhibiting a well-defined ball-andsocket configuration (a and b). The occipital condyles display a spherical, protuberant shape resembling a ball (c). The superior articular surface of the atlas lateral mass exhibits distinct anterior and posterior protuberances (red dotted lines) separated by a pronounced concave depression (yellow dotted line) (d). This concave surface articulates seamlessly with the spherical occipital condyles, forming a classic ball-and-socket joint. The tilt angle of the C1 facet is within the expected normal range for this joint type (e: red lines). (B) Type II atlanto-occipital joint (II-AOJ): A transitional morphology between the normal ball-and-socket joint (type I) and severely deformed joint (type III). While still exhibiting some features of a ball-and-socket configuration, type II displays mild deviations from the typical anatomy (a´ and b´). The occipital condyle appears slightly smaller or flatter than that in type I, deviating slightly from the ideal spherical shape (c´). The superior articular surface of the atlas lateral mass is mildly flattened, with the anterior and posterior protuberances being less pronounced than in type I (d´). However, these protuberances are still discernible, and the overall concave shape is maintained, albeit shallower. The tilt angle of the C1 facet remains within the normal range, similar to that of type I (e´). (C) Type III atlanto-occipital joint (III-AOJ): Severe deformity, deviating significantly from the normal ball-and-socket joint morphology (a˝ and b˝). The occipital condyle appears flattened and dysmorphic, rather than spherical (c˝). The superior articular surface of the atlas lateral mass is markedly flattened, lacking the distinct anterior and posterior protuberances seen in types I and II (d˝). The posterior protuberance is particularly diminished or absent. While the overall size of the C1 lateral mass is reduced, the most prominent feature is an exaggerated tilt angle of the C1 facet compared with types I and II (e˝). The severe flattening of the articulating surfaces in both C0 and C1 coupled with the increased tilt angle result in the loss of the typical ball-and-socket configuration.
Fig. 2.
The 3-dimensional finite element model of normal and variant models. (A) Normal model of C0–2 segments. Images showing various structures (i): Frontal view of the complete model, which was consist of occiput (C0), atlas (C1), and axis (C2); (ii) Coronal sectional view showing ligament structure: The transverse ligament (TL) was constructed by 8-node brick elements and attach to C1. Other ligaments were modeled with tension-only spring elements, such as alar ligament (AL), apical ligament (APL), tectorial membrane (TM) and capsular ligaments (CL); (iii): Sagittal sectional view: The White arrows show the measurements of minimal and incremental basion-dental interval (BDI). The yellow lines show the anterior atlanto-occipital membrane (AAOM), posterior atlanto-occipital membrane (PAOM), anterior longitudinal ligament (ALL) and LF. A Cartesian coordinate system was used with the x-axis oriented horizontally to the left, y-axis horizontally posteriorly, and z-axis vertically upward. (B) Illustrations of progressive atlanto-occipital joint (AOJ) dysplasia within our finite element models. The left panel illustrates the morphological differences among the 3 AOJs. The grid lines form the borders of type I AOJ (I-AOJ), the blue translucent area is type II AOJ (II-AOJ), and the yellow area is type III AOJ (III-AOJ). The right panel shows the formation of I-AOJ (red dotted line), II-AOJ (black dotted line), and III-AOJ (orange dotted line) by different C0, C1, and cartilage assemblies. Quantitative computed tomography measurements guided systematic alterations in key dimensions of the articular surface of C0–1 to simulate moderate (type II) and severe (type III) AOJ abnormalities, while the portion away from the articular surface remained unchanged. Specifically, the anterior and posterior protrusions of the C1 superior articular surface were displaced downward to decrease the depth of the articular surface, and the C0 occipital condyle surface was displaced upward to decrease its height, creating a type II AOJ. The anterior and posterior protrusions of the C1 superior articulation were further downwardly displaced and posteriorly displaced even further to ensure a greater angle of inclination. The C0 occipital condyle was further upwardly displaced and decreased in circumference to create a type III AOJ. (C) Images of the finite element models and their components. The left panel shows the models of the symmetric AOJ, and the right panel shows the asymmetric models. The red dotted portion is I-AOJ, the black dotted portion is II-AOJ, and the orange dotted portion is III-AOJ.
Fig. 3.
Intact model validation. (A–F) Comparison of the range of motion of the intact model with experimental data by Panjabi et al. [14,15] and computational studies by Meng et al. [16] (G) Model tensile response compared with the force-displacement response of the upper cervical spine (occiput–C2) of a 56-year-old specimen and 61-year-old specimen by Yliniemi et al. [17]
Fig. 4.
Comparison of the range of motion at the C0–1 and C1–2 segments across models.
Fig. 5.
(A) Stress distribution of the C1 superior articular facet under different loads in the 5 models (top view). (B) Average von Mises stress of the C1 superior articular facet.
Fig. 6.
(A) Stress distribution of the C2 superior articular facet under different loads in the 5 models (top view). (B) Average von Mises stress of the C2 superior articular facet.
Fig. 7.
(A) Stress distribution of the transverse ligament (TL) under different loads in the 5 models (posterior view). (B) Average von Mises stress of the transverse ligament.
Fig. 8.
Stress of spring ligaments used in the finite element models. AAOM, anterior atlanto-occipital membrane; AL, alar ligament; ALL, anterior longitudinal ligament; APL, apical ligament; CL, capsular ligaments; LF, ligamentum flavum; PAOM, posterior atlanto-occipital membrane; TM, tectorial membrane.
Fig. 9.
Assessment of the clivus-axial angle (CXA), pB-C2 line, basion-dental interval (BDI) and accompanying rotational motion under different cervical loading. (A) Comparison of CXA among models. The dashed line indicates the CXA value in neutral cervical position. (B) Comparison of pB-C2 line among models. The dashed line indicates the pB-C2 value in neutral cervical position. (C) minimum distance of the BDI. The BDI is measured under conditions of cervical flexion and extension. (D) Incremental distance of BDI along the Z-direction. Utilizing the Cartesian coordinate system delineated in Fig. 2, a positive alteration indicates an enlargement of the BDI in the z-axis, correlating with an upward movement of the dens. Conversely, a negative change signifies a reduction in the BDI within the negative z-axis, associated with a downward displacement of the dens. (E) Incremental distance of BDI along Y-direction. In accordance with the Cartesian coordinate system introduced in Fig. 2, an increase in BDI within the y-axis is reflected by a positive value, indicating a posterior movement of the dens. A decrease is denoted by a negative value, resulting in anterior movement of the dens. (F) Accompanying C0–1 rotational motion. (G) Accompanying C1–2 rotational motion.
Table 1.
Material properties used in the finite element models
*These data are derived from the results of a previous study,[4] which was the average value of individual parameter based on systematic morphological measurements of 165 I-AOJs.
†These data are derived from the results of a previous study,[4] which was the average value of individual parameter based on systematic morphological measurements of 125 II-AOJs. Compared with the data of I-AOJ, the condyle length, condyle middle height, the C1 lateral mass (C1LM) length, and C1LM tilt angle were similar to II-AOJ (p>0.05), but the C1LM height and C1LM curvature was slightly smaller (p<0.05).
‡These data are derived from the results of a previous study,[4] which was the average value of individual parameter based on systematic morphological measurements of 80 III-AOJs. The size of occipital condyle and C1 lateral mass in III-AOJ cases are significantly lower than those in the other 2 groups (p<0.05). And III-AOJ has the largest tilt angle and smallest curvature (p<0.05).
Table 3.
The morphological distribution of bilateral sides of alanto-occipital joint in 185 cases
Table 3.
Cohort
I-I AOJ
Mixed I-II AOJ
II-II AOJ
Mixed II-III AOJ
III-III AOJ
Control (n = 80)
80 (100)
0 (0)
0 (0)
0 (0)
0 (0)
CM (n = 63)
0 (0)
4 (6.3)
54 (85.7)
5 (7.9)
0 (0)
BI (n = 42)
0 (0)
1 (2.4)
0 (0.0)
7 (16.7)
34 (81.0)
Total
80 (43.2)
5 (2.7)
54 (29.2)
12 (6.5)
34 (18.3)
Values are presented as number (%).
AOJ, atlanto-occipital joint; CM, Chiari Malformation; BI, basilar invagination.
I-I AOJ means type I AOJ in both sides. I-II means type I AOJ in one side, but II in the other side.
REFERENCES
1. Debernardi A, D’Aliberti G, Talamonti G, et al. The craniovertebral junction area and the role of the ligaments and membranes. Neurosurgery 2011;68:291-301.
4. Tan M, Jiang X, Yi P, et al. Revision surgery of irreducible atlantoaxial dislocation: a retrospective study of 16 cases. Eur Spine J 2011;20:2187-94.
5. de Oliveira Sousa U, de Oliveira MF, Heringer LC, et al. The effect of posterior fossa decompression in adult Chiari malformation and basilar invagination: a systematic review and meta-analysis. Neurosurg Rev 2018;41:311-21.
6. Goel A, Sathe P, Shah A. Atlantoaxial fixation for basilar invagination without obvious atlantoaxial instability (group B basilar invagination): outcome analysis of 63 surgically treated cases. World Neurosurg 2017;99:164-70.
7. Huang Q, Yang X, Zheng D, et al. Exploring the pathogenesis of atlanto-occipital instability in chiari malformation with type II basilar invagination: a systematic morphological study. Neurosurgery 2023;92:837-53.
9. Wang HW, Ma LP, Yin YH, et al. Biomechanical rationale for the development of atlantoaxial instability and basilar invagination in patients with occipitalization of the atlas: a finite element analysis. World Neurosurg 2019;127:e474-79.
10. Fiester P, Rao D, Soule E, et al. Anatomic, functional, and radiographic review of the ligaments of the craniocervical junction. J Craniovertebr Junction Spine 2021;12:4-9.
11. Brolin K, Halldin P. Development of a finite element model of the upper cervical spine and a parameter study of ligament characteristics. Spine (Phila Pa 1976) 2004;29:376-85.
12. Zhang B, Liu H, Cai X, et al. Biomechanical comparison of modified TARP technique versus modified goel technique for the treatment of basilar invagination: a finite element analysis. Spine (Phila Pa 1976) 2016;41:E459-66.
13. Zhao G, Song M, Duan W, et al. Biomechanical investigation of intra-articular cage and cantilever technique in the treatment of congenital basilar invagination combined with atlantoaxial dislocation: a finite element analysis. Med Biol Eng Comput 2022;60:2189-99.
14. Panjabi M, Dvorak J, Crisco J 3rd, et al. Flexion, extension, and lateral bending of the upper cervical spine in response to alar ligament transections. J Spinal Disord 1991;4:157-67.
16. Meng Cl, Yang S, Zheng HH, et al. Validation of a finite element model of C0-C1-C2. In: 2010 2nd International Conference on Information Engineering and Computer Science; 2010 Dec 25-26; Wuhan, China. IEEE; 2010:1-6.
17. Yliniemi EM, Pellettiere JA, Doczy EJ, et al. Dynamic tensile failure mechanics of the musculoskeletal neck using a cadaver model. J Biomech Eng 2009;131:051001.
19. Wang S, Huang Z, Xu R, et al. Chiari malformations type I without basilar invagination in adults: morphometric and volumetric analysis. World Neurosurg 2020;143:e640-7.
20. Zhou Q, Song C, Huang Q, et al. Evaluating craniovertebral stability in Chiari malformation coexisting with type II basilar invagination: an observational study based on kinematic computed tomography and its clinical application. World Neurosurg 2022;164:e724-40.
22. Grabb PA, Mapstone TB, Oakes WJ. Ventral brain stem compression in pediatric and young adult patients with Chiari I malformations. Neurosurgery 1999;44:520-7. discussion 527-8.
24. Samartzis D, Shen FH, Herman J, et al. Atlantoaxial rotatory fixation in the setting of associated congenital malformations: a modified classification system. Spine (Phila Pa 1976) 2010;35:E119-27.
28. Bollo RJ, Riva-Cambrin J, Brockmeyer MM, et al. Complex Chiari malformations in children: an analysis of preoperative risk factors for occipitocervical fusion. J Neurosurg Pediatr 2012;10:134-41.
29. Peng X, Chen L, Wan Y, et al. Treatment of primary basilar invagination by cervical traction and posterior instrumented reduction together with occipitocervical fusion. Spine (Phila Pa 1976) 2011;36:1528-31.
30. Sawin PD, Menezes AH. Basilar invagination in osteogenesis imperfecta and related osteochondrodysplasias: medical and surgical management. J Neurosurg 1997;86:950-60.
31. Zhang B, Qi M, Xin Z, et al. Intra-articular distraction versus decompression to treat basilar invagination without atlantoaxial dislocation: a retrospective cohort study of 54 patients. Neurospine 2023;20:498-506.
32. Lasswell TL, Cronin DS, Medley JB, et al. Incorporating ligament laxity in a finite element model for the upper cervical spine. Spine J 2017;17:1755-64.
33. Wang HH, Wang K, Deng Z, et al. Effects of facet joint degeneration on stress alterations in cervical spine C5-C6: a finite element analysis. Math Biosci Eng 2019;16:7447-57.
34. Masni A, Tanaka M. Biomechanical investigation on the influence of the regional material degeneration of an intervertebral disc in a lower lumbar spinal unit: a finite element study. Comput Biol Med 2018;98:26-38.
35. LeVeau BF, Bernhardt DB. Developmental biomechanics. Effect of forces on the growth, development, and maintenance of the human body. Phys Ther 1984;64:1874-82.
36. Ashrafi M, Ghalichi F, Mirzakouchaki B, et al. Numerical simulation of hydro-mechanical coupling of periodontal ligament. Proc Inst Mech Eng H 2020;234:171-8.
Biomechanical Study of Atlanto-occipital Instability in Type II Basilar Invagination: A Finite Element Analysis
Fig. 1. Computed tomography (CT) images and geometric reconstruction of the occipital condyle and atlas lateral masses. (A) Type I atlanto-occipital joint (I-AOJ): Normal, ideal morphology of the atlanto-occipital joint exhibiting a well-defined ball-andsocket configuration (a and b). The occipital condyles display a spherical, protuberant shape resembling a ball (c). The superior articular surface of the atlas lateral mass exhibits distinct anterior and posterior protuberances (red dotted lines) separated by a pronounced concave depression (yellow dotted line) (d). This concave surface articulates seamlessly with the spherical occipital condyles, forming a classic ball-and-socket joint. The tilt angle of the C1 facet is within the expected normal range for this joint type (e: red lines). (B) Type II atlanto-occipital joint (II-AOJ): A transitional morphology between the normal ball-and-socket joint (type I) and severely deformed joint (type III). While still exhibiting some features of a ball-and-socket configuration, type II displays mild deviations from the typical anatomy (a´ and b´). The occipital condyle appears slightly smaller or flatter than that in type I, deviating slightly from the ideal spherical shape (c´). The superior articular surface of the atlas lateral mass is mildly flattened, with the anterior and posterior protuberances being less pronounced than in type I (d´). However, these protuberances are still discernible, and the overall concave shape is maintained, albeit shallower. The tilt angle of the C1 facet remains within the normal range, similar to that of type I (e´). (C) Type III atlanto-occipital joint (III-AOJ): Severe deformity, deviating significantly from the normal ball-and-socket joint morphology (a˝ and b˝). The occipital condyle appears flattened and dysmorphic, rather than spherical (c˝). The superior articular surface of the atlas lateral mass is markedly flattened, lacking the distinct anterior and posterior protuberances seen in types I and II (d˝). The posterior protuberance is particularly diminished or absent. While the overall size of the C1 lateral mass is reduced, the most prominent feature is an exaggerated tilt angle of the C1 facet compared with types I and II (e˝). The severe flattening of the articulating surfaces in both C0 and C1 coupled with the increased tilt angle result in the loss of the typical ball-and-socket configuration.
Fig. 2. The 3-dimensional finite element model of normal and variant models. (A) Normal model of C0–2 segments. Images showing various structures (i): Frontal view of the complete model, which was consist of occiput (C0), atlas (C1), and axis (C2); (ii) Coronal sectional view showing ligament structure: The transverse ligament (TL) was constructed by 8-node brick elements and attach to C1. Other ligaments were modeled with tension-only spring elements, such as alar ligament (AL), apical ligament (APL), tectorial membrane (TM) and capsular ligaments (CL); (iii): Sagittal sectional view: The White arrows show the measurements of minimal and incremental basion-dental interval (BDI). The yellow lines show the anterior atlanto-occipital membrane (AAOM), posterior atlanto-occipital membrane (PAOM), anterior longitudinal ligament (ALL) and LF. A Cartesian coordinate system was used with the x-axis oriented horizontally to the left, y-axis horizontally posteriorly, and z-axis vertically upward. (B) Illustrations of progressive atlanto-occipital joint (AOJ) dysplasia within our finite element models. The left panel illustrates the morphological differences among the 3 AOJs. The grid lines form the borders of type I AOJ (I-AOJ), the blue translucent area is type II AOJ (II-AOJ), and the yellow area is type III AOJ (III-AOJ). The right panel shows the formation of I-AOJ (red dotted line), II-AOJ (black dotted line), and III-AOJ (orange dotted line) by different C0, C1, and cartilage assemblies. Quantitative computed tomography measurements guided systematic alterations in key dimensions of the articular surface of C0–1 to simulate moderate (type II) and severe (type III) AOJ abnormalities, while the portion away from the articular surface remained unchanged. Specifically, the anterior and posterior protrusions of the C1 superior articular surface were displaced downward to decrease the depth of the articular surface, and the C0 occipital condyle surface was displaced upward to decrease its height, creating a type II AOJ. The anterior and posterior protrusions of the C1 superior articulation were further downwardly displaced and posteriorly displaced even further to ensure a greater angle of inclination. The C0 occipital condyle was further upwardly displaced and decreased in circumference to create a type III AOJ. (C) Images of the finite element models and their components. The left panel shows the models of the symmetric AOJ, and the right panel shows the asymmetric models. The red dotted portion is I-AOJ, the black dotted portion is II-AOJ, and the orange dotted portion is III-AOJ.
Fig. 3. Intact model validation. (A–F) Comparison of the range of motion of the intact model with experimental data by Panjabi et al. [14,15] and computational studies by Meng et al. [16] (G) Model tensile response compared with the force-displacement response of the upper cervical spine (occiput–C2) of a 56-year-old specimen and 61-year-old specimen by Yliniemi et al. [17]
Fig. 4. Comparison of the range of motion at the C0–1 and C1–2 segments across models.
Fig. 5. (A) Stress distribution of the C1 superior articular facet under different loads in the 5 models (top view). (B) Average von Mises stress of the C1 superior articular facet.
Fig. 6. (A) Stress distribution of the C2 superior articular facet under different loads in the 5 models (top view). (B) Average von Mises stress of the C2 superior articular facet.
Fig. 7. (A) Stress distribution of the transverse ligament (TL) under different loads in the 5 models (posterior view). (B) Average von Mises stress of the transverse ligament.
Fig. 8. Stress of spring ligaments used in the finite element models. AAOM, anterior atlanto-occipital membrane; AL, alar ligament; ALL, anterior longitudinal ligament; APL, apical ligament; CL, capsular ligaments; LF, ligamentum flavum; PAOM, posterior atlanto-occipital membrane; TM, tectorial membrane.
Fig. 9. Assessment of the clivus-axial angle (CXA), pB-C2 line, basion-dental interval (BDI) and accompanying rotational motion under different cervical loading. (A) Comparison of CXA among models. The dashed line indicates the CXA value in neutral cervical position. (B) Comparison of pB-C2 line among models. The dashed line indicates the pB-C2 value in neutral cervical position. (C) minimum distance of the BDI. The BDI is measured under conditions of cervical flexion and extension. (D) Incremental distance of BDI along the Z-direction. Utilizing the Cartesian coordinate system delineated in Fig. 2, a positive alteration indicates an enlargement of the BDI in the z-axis, correlating with an upward movement of the dens. Conversely, a negative change signifies a reduction in the BDI within the negative z-axis, associated with a downward displacement of the dens. (E) Incremental distance of BDI along Y-direction. In accordance with the Cartesian coordinate system introduced in Fig. 2, an increase in BDI within the y-axis is reflected by a positive value, indicating a posterior movement of the dens. A decrease is denoted by a negative value, resulting in anterior movement of the dens. (F) Accompanying C0–1 rotational motion. (G) Accompanying C1–2 rotational motion.
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Biomechanical Study of Atlanto-occipital Instability in Type II Basilar Invagination: A Finite Element Analysis
These data are derived from the results of a previous study,[4] which was the average value of individual parameter based on systematic morphological measurements of 165 I-AOJs.
These data are derived from the results of a previous study,[4] which was the average value of individual parameter based on systematic morphological measurements of 125 II-AOJs. Compared with the data of I-AOJ, the condyle length, condyle middle height, the C1 lateral mass (C1LM) length, and C1LM tilt angle were similar to II-AOJ (p>0.05), but the C1LM height and C1LM curvature was slightly smaller (p<0.05).
These data are derived from the results of a previous study,[4] which was the average value of individual parameter based on systematic morphological measurements of 80 III-AOJs. The size of occipital condyle and C1 lateral mass in III-AOJ cases are significantly lower than those in the other 2 groups (p<0.05). And III-AOJ has the largest tilt angle and smallest curvature (p<0.05).
Table 3. The morphological distribution of bilateral sides of alanto-occipital joint in 185 cases
Values are presented as number (%).
AOJ, atlanto-occipital joint; CM, Chiari Malformation; BI, basilar invagination.
I-I AOJ means type I AOJ in both sides. I-II means type I AOJ in one side, but II in the other side.
, Qinguo Huang3,4,*
