Biomechanical Analysis of Atlantoaxial Dorsal Fixation Using Finite Element Models

Background: Atlantoaxial instability can cause spinal cord compression with clinical signs ranging from cervical pain to tetraplegia and death. Although a variety of dorsal xation techniques have been described, some of them have been related to the fracture of the dorsal arch of the atlas, leading to surgical failure. We hypothesized that the shape of the dorsal arch of the atlas and types of implants might affect these bone fractures. Thus, the objective of this study was to analyze bone stresses through simulations of the dorsal xation using nite element models. Results: The width between wires and the length of the bone did not affect the maximum stress on the bone. The maximum bone stress increased as the bone got thinner and the angle of the notch got steeper. The bone with band implant had lower maximum bone stress than that with wire implants. When using wire implants, wires applied beyond the notch of the dorsal arch reduced the maximum bone stress more than wires positioned within it. Conclusions: The fracture of the dorsal arch of the atlas was related to the shape of the bone and types of implant applied. Band implant can effectively reduce the fracture of the dorsal arch compared to wire implant in atlantoaxial dorsal xation. When considering wire implant, it is recommended to apply wires beyond the notch of the atlas.

with continuous advancement of computer technology [12]. Although FEMs have been widely used in human spine biomechanics to analyze fractures, injuries, and surgical techniques, only a few studies have used FEMs in canine spine biomechanics known to adapt human material properties [13][14][15][16][17][18][19][20][21]. To the author's knowledge, there are very few biomechanical studies for the fracture of the dorsal arch of the atlas in atlantoaxial dorsal xation. Based on our clinical experience that proper positioning of the implant could reduce fracture of the dorsal arch in atlantoaxial dorsal xation, we hypothesized that the shape of the dorsal arch of the atlas and types of implants might affect the fracture. Thus, the objective of this study was to analyze bone stresses through simulations of the dorsal xation using FEMs so that we could nd a way to reduce bone fracture.  16.061 MPa, and 26.287 MPa, respectively. As the force increased from 20 N to 80 N, the difference in the maximum bone stress between model 6.1 and model 6.4 (20.671 MPa) increased much more than that between model 6.3 and model 6.4 (2.351 MPa). Under the force of 80 N, the maximum bone stresses in models 6.1 and 6.2 were relatively closer to the bone yield stress than those in models 6.3 and 6.4 ( Fig. 1 and Fig. 2).

Discussion
Models for biomechanical study such as in vitro, in vivo, and nite element models have greatly improved our understanding of biomechanics and medicine [22]. FEMs can evaluate internal response such as stress-related information which is di cult to obtain in in vivo and in vitro models [23,24]. Stress analysis is important to understand the fracture mechanism. Thus, FEMs have been widely used for studies on bone fractures [13,14,25,26]. We modeled the arch-shaped bone re ecting characteristics of the dorsal arch of the canine atlas and analyzed the behavior of the spinal bone fracture in atlantoaxial dorsal xation using FEMs. In patients with atlantoaxial instability, ligamentous lesions such as disruption of atlantoaxial ligaments, osseous lesions such as dens fracture, or a combination of them cause distraction of atlantoaxial joint related to atlantoaxial subluxation [27,28]. Thus, we applied tension forces to implants for simulations of atlantoaxial dorsal xation which handles the distraction force. When giving tension forces to implants applied, the maximum bone stress increased as bone got thinner and the oblique angle got steeper. Considering the shape of the dorsal arch of the canine atlas which has the thin notch with steep oblique angle, the bone will get greater maximum stress if the implant is applied to this notch during dorsal xation. In the arch-shaped bone based on atlas, the maximum bone stress was actually higher and closer to bone yield stress when applying wires within the notch compared to that when positioning them laterally beyond the notch. In addition, as tension force to implant increased, difference in the maximum bone stress between the bone with wires applied within the notch and the bone with them positioned beyond the notch also increased. Thus, the bone with wires positioned beyond the notch is less vulnerable to bone fracture than the bone with wires applied within it.
One clinical study on dorsal stabilization for dogs with AAI has reported that the fracture of the dorsal arch is reduced with the use of band implant due to an increased contact surface between the bone and the implant, leading to better repartition of forces [6]. If the bone is at and platy, band implant can reduce the maximum bone stress effectively compared to wire implants. However, the dorsal arch of the canine atlas has protrusions that can prevent band implant from reducing the maximum bone stress as the decreased contact surface can lead to higher concentration of the stress. In our study, the reduction of the maximum bone stress by band implant in arch-shaped bone (1.157 MPa) is less than that in the platy bone (10.193 MPa) under 20 N of the force. In addition, when the tension force to implants increased from 20 N to 80 N, the difference in the maximum bone stress between the bone with wires positioned beyond the notch and the bone with band implant was increased by only 2.351 MPa while that between the bone with wires applied within the notch and the bone with band implant was increased by 20.671 MPa. Taken together, although band implant can reduce the maximum bone stress and the risk of bone fracture compared to wire implants, wire implants can also decrease the risk of bone fracture if wires are applied beyond the notch. Several limitations of our models exist. There was no consideration for individual or breed variation during the modeling of the dorsal arch. However, characteristics re ected in our arch-shaped bone model can be applied to dorsal arches of most toy breed dogs. In performing the study, material properties for human were used in this study due to the lack of those for canine. No signi cant issue has been reported in studies on canine spine using human material properties [19], but further studies are needed to set proper material properties for a more realistic behavior of canine bone model and to validate FEMs in canine study. Although spine response is nonlinear, linear analysis related to distraction force was conducted in this study. It is because linear models could make analysis simpler and have been successfully used to understand bone fractures in previous studies [14,25,29]. In addition to distraction force, other forces such as exion, extension, shear force, lateral bending, and axial rotation are also possible in atlantoaxial joint and should be further considered.

Conclusion
These results showed that the fracture of the dorsal arch was highly associated with bone shapes and types of implants. Band implant reduced the maximum bone stress the most. When using wire implants, consideration for the notch of the dorsal arch is necessary to decrease the maximum stress in the bone.

Methods
Geometric and nite element modeling of bones and implants for simulations of atlantoaxial dorsal xation and nite element analyses for the bone stresses were performed using Abaqus software program (Abaqus , Version 6.10; Abaqus, Inc., Providence, RI, USA).

Geometric modeling of bones and implants
Bones used in this study were simpli ed to platy or arch-shaped structures. Arch-shaped bone was modeled based on a three-dimensional ( were modeled and applied to bones. The diameter of the wire implant was 0.8 mm. The thickness of the band implant was also 0.8 mm. Finite Element modeling 3D FEMs for simulations of dorsal xation were generated using hexahedral and pentahedral elements (Fig. 4). On average, 36,023 nodes and 28,557 elements were used in each simulation. Bones were de ned as cortical bones. Cancellous bones in the internal matrix were ignored. Implants were made of stainless steel. Material properties of bones and implants are shown in Table 1. They were assumed to be homogenous and linear isotropic. The friction coe cient value for bone-steel is 0.37 [30]. Material properties of bones were adapted from a previous study of human atlas [13] because of the lack of material de nition for canine spine. Material properties of implants were obtained from the literature on stainless steel [31,32].

Experimental design
Two studies were performed and referred to as project A and project B (Fig. 5 and Fig. 6). Project A using platy bones was carried out to explain stress-related results of project B. Project B using arch-shaped bones was implemented to simulate the clinical situation of dorsal xation.

Project B
In project B, in uences of types and positioning of implants on arch-shaped bones were investigated.
Four models (referred to as model 6) were used in project B. Wire implants were applied within notches of arch-shaped bones in models 6.1 and 6.2 and beyond the notch in model 6.3. The width between wires was 2 mm in model 6.1, 4 mm in model 6.2, and 6 mm in model 6.3. Band implant with a width of 6 mm was applied in model 6.4 (Fig. 6).

Finite element analyses
Arbitrary tension forces of 20 N were applied to implants in project A while 20 N, 40 N, and 80 N of tension forces were applied to implants in project B for simulations of the dorsal xation. The maximum bone stresses under these forces did not exceed the yield stress of cortical bone. Considering our bone elastic modulus (10 GPa), the bone yield stress in this study was 66.  Tables   Due to technical limitations, table 1   Project B (model 6) using arch-shaped bones designed based on types and positioning of implants. Wire implants were applied within notches of arch-shaped bones in models 6.1 and 6.2. They were applied beyond the notch in model 6.3. The band implant was applied in model 6.4 Supplementary Files This is a list of supplementary les associated with this preprint. Click to download. Table1.JPG