The aim of this study was to determine whether non-linear three-dimensional finite element analysis (3D-FEA) can be applied to simulate pterygomaxillary dysjunction during Le Fort I osteotomy (LFI) not involving a curved osteotome (LFI-non-COSep), and to predict potential changes in the fracture pattern associated with extending the cutting line. Computed tomography (CT) image data (100 snapshots) after LFI were converted to 3D-CT images. 3D-FEA models were built using preoperative CT matrix data and used to simulate pterygomaxillary dysjunction. The pterygomaxillary dysjunction patterns predicted by the 3D-FEA models of pterygomaxillary dysjunction were classified into three categories and compared to the pterygomaxillary dysjunction patterns observed in the postoperative 3D-CT images. Extension of the cutting line was also simulated using the 3D-FEA models to predict the risk and position of pterygoid process fracture. The rate of agreement between the predicted pterygomaxillary dysjunction patterns and those observed in the postoperative 3D-CT images was 87.0% ( κ coefficient 0.79). The predicted incidence of pterygoid process fracture was higher for cutting lines that extended to the pterygomaxillary junction than for conventional cutting lines (odds ratio 4.75; P < 0.0001). 3D-FEA can be used to predict pterygomaxillary dysjunction patterns during LFI-non-COSep and provides useful information for selecting safer procedures during LFI-non-COSep.
The Le Fort I osteotomy (LFI) has become a routine procedure in orthognathic surgery. Although LFI is considered a safe surgical technique, many complications have been reported. Axhausen performed the first pterygomaxillary dysjunction to achieve complete mobilization of the maxilla during the LFI procedure. Since then, most surgeons have used a curved osteotome, which is introduced into the pterygomaxillary junction and blindly tapped until complete pterygomaxillary separation is achieved (LFI-COSep). This LFI-COSep procedure is associated with several complications, including pterygoid process fractures and severe haemorrhagic injury of the vessels around the posterior maxilla. Most often, haemorrhage arises from the branches of the maxillary artery, which runs into the pterygopalatine fossa and includes branches of the posterior, superior, alveolar, infraorbital, greater palatine, lesser palatine, ascending pharyngeal, Vidian, and sphenopalatine arteries. Serious complications such as nerve damage, especially to cranial nerves II, III, and VI, can also occur after pterygomaxillary dysjunction. Thus, pterygomaxillary dysjunction is a critical step during LFI.
In 1991, Precious et al. reported that pterygomaxillary separation can be achieved safely and easily by leverage alone, without the use of an osteotome (LFI-non-COSep), using Tessier spreaders and digital manipulation for maxillary mobilization. While this improvement in the surgical technique has led to a decrease in the number of complications observed, various complications persist. As few clinical studies have evaluated the potential surgical risk factors leading to an unfavourable pterygomaxillary dysjunction in LFI-non-COSep, a suitable evaluation method is required to ensure safer pterygomaxillary separation. Further studies regarding the patterns of pterygomaxillary dysjunction and frequency of pterygoid process fracture are warranted in order to assess the influence of such factors.
For clinical application, a surgical simulation method should essentially be capable of predicting fracture sites based on a comprehensive understanding of the mechanisms that underlie complications. Clinical and quantitative techniques to predict pterygoid process fracture may be limited because of the complexities inherent to the pterygomaxillary area, such as the thin cortical bone composition of the maxillary tuberosity and the presence of an impacted wisdom tooth. This limitation can be addressed by computed tomography (CT)-based three-dimensional finite element analysis (3D-FEA), a numerical method for solving partial derivatives, used to simulate the behaviour of solid bodies according to certain boundary conditions. 3D-FEA of quantitative CT data can predict bone strength by assessing properties related to geometry, architecture, mineralization, and heterogeneous mechanics. While some studies have suggested that fracture load and site can be predicted using CT-based non-linear 3D-FEA, none have focused on pterygoid process fracture sites.
Thus, it is expected that 3D-FEA can predict pterygomaxillary dysjunction patterns during LFI-non-COSep; however, it appears that no study on this subject has been published. The present study aimed to establish a non-linear 3D-FEA-based model for predicting pterygoid process strength and potential fractures sites, as well as to evaluate the accuracy of 3D-FEA predictions against postoperative pterygomaxillary dysjunction patterns observed in LFI-non-COSep patients.
Patients and methods
Patient selection and study design
Fifty patients diagnosed with mandibular prognathism (20 male and 30 female), with a mean age of 25.3 years (range 16–40 years), were included in this study. All patients underwent LFI-non-COSep to create a forward displacement of the maxilla, with a simultaneous bilateral sagittal split osteotomy of the mandibular ramus. The procedures were performed in the Department of Maxillofacial Surgery of the Dental Hospital of Aichi Gakuin University. All patients underwent pre- and postoperative radiographic examinations, followed by orthodontic treatment. The maxillary third molars of all patients were removed at least 3 months before the surgery. Ethical approval for this study was obtained from the Ethics Committee of the School of Dentistry of Aichi Gakuin University, and written informed consent was obtained from all patients.
LFI-non-COSep was used in all cases. The LFI-non-COSep surgery was performed according to the method reported by Precious et al., who described the use of digital pressure alone in combination with Tessier spreaders as an alternative approach to vertical separation. In order to standardize the surgical procedures across all patients, the osteotomy of the maxilla was performed with a reciprocating saw, in a line passing (1) through the anterolateral surface, high enough not to harm the root apices of the maxillary second molar, and (2) posteriorly, through a line passing between the middle point of the posterior plane of the maxilla and the pterygomaxillary junction.
Evaluation of the patterns of pterygomaxillary dysjunction using postoperative CT
The pterygomaxillary dysjunction patterns of the LFI-non-COSep were evaluated using postoperative helical taken approximately 7 days after the surgery. The CT dataset was exported to DICOM (Digital Imaging and Communications in Medicine) format, used for reconstruction, and analysed using OsiriX (version 5.9; OsiriX Foundation, Geneva, Switzerland). Using the 3D images, the pterygomaxillary dysjunction patterns resulting from LFI-non-COSep were classified into three categories, as reported previously : dysjunction within the maxillary tuberosity, dysjunction at the pterygomaxillary junction, and dysjunction in the pterygoid process.
3D-FEA of preoperative CT images
The 3D-FEA models of the midface were constructed from the data in DICOM format using 3D-FEA software (Mechanical Finder version 6.2; Research Center of Computational Mechanics, Inc., Tokyo, Japan).
The midface bone was simulated using 1-mm linear tetrahedral elements. To allow for bone heterogeneity, the mechanical properties of each element were computed from the Hounsfield unit value. The ash density of each element was set as the average ash density of the voxels contained in one element. The physical properties of the 3D-FEA model were set as follows: Young’s modulus E (MPa) and yield strength σ γ (MPa) for the assumed isotropic tetrahedral elements were calculated from the bone density ρ (g/cm 3 ) using the equations proposed by Keyak et al. ; the Poisson ratio was set at 0.37 and the material characteristics of the bone tissue elements were determined as reported previously.
The virtual cut of the maxillary anterolateral wall was planned from the piriform aperture to the middle point between the distal surface of the maxillary second molar and the pterygomaxillary junction. Following the surgery planning, the virtual pterygomaxillary dysjunction was performed using a single load to the maxilla through the lateral ridge of the anterior nasal aperture. Next, the top of the skull was fixed in the 3D-FEA software, and the left and right nasomaxillary buttresses received a load of 150 N, applied incrementally with 5 N per step for 30 steps, using a virtual impactor ( Fig. 1 ). After simulating the pterygomaxillary dysjunction with LFI-non-COSep, von Mises stress was used to analyse the pterygomaxillary dysjunction patterns using non-linear, subject-specific 3D models. Using the analysis software, the bone tissue was demonstrated to be a brittle material when subjected to strong tensile stress. Moreover, when the force exceeded the threshold value for the maximum principal stress, set according to the maximum principal stress theory, the bone fractured. Further, the ductility of the bone material along the sides was assessed by subjecting the bone to compressive stress, and when the equivalent stress exceeded the threshold value, which was set according to the shear strain energy theory, the bone yielded. In the 3D-FEA model, which performs a non-linear analysis of the material, the fracture line evaluation was used in order to predict the site of fracture. In addition, the distribution of high stress areas was evaluated using maximum principal stress evaluation (MPSE) and equivalent stress evaluation (ESE) on the 3D-FEA model ( Fig. 2 ). It was considered that an elementary breakdown had occurred when a tension or compression line crossed one triangular or tetrahedral element, and that a fracture line was created when elementary breakdowns connected to each other forming a line in the pterygomaxillary region. The patterns of fracture obtained from the fracture line evaluation, ESE, and MPSE were classified as defined in the previous subsection.
The inter-method agreement between the actual pterygomaxillary dysjunction site and that predicted by the 3D-FEA simulation model was evaluated with the κ coefficient using JMP v11 software (SAS Institute, Cary, NC, USA). The values of κ were classified as follows: poor, 0 ≤ κ ≤ 0.40; fair to good, 0.41 ≤ κ ≤ 0.74; excellent, 0.75 ≤ κ ≤ 1.00.
Patterns of pterygomaxillary dysjunction in postoperative CT
In all cases, the maxillary occlusal unit was moved to the planned position without postoperative complications such as haemorrhage or nerve palsy. The most frequent separation in the area of the maxillary tuberosity and pterygoid process occurred at the pterygomaxillary junction (50 sides, 50%). The pterygoid process was fractured during the separation in 34 sides (34%) and the maxillary tuberosity was fractured in 16 sides (16%) ( Table 1 ).
|Maxillary tuberosity||Pterygomaxillary junction||Pterygoid process|
|3D-CT image analysis||16||50||34|
|Finite element analysis|
|Fracture line evaluation||21||48||31|
|Equivalent stress evaluation||21||52||27|
|Maximum principal stress evaluation||15||52||33|
Results of 3D-FEA
The 3D-FEA model analysis of the preoperative CT datasets resulted in 1,056,716 ± 205,588 tetrahedral elements in the pterygomaxillary dysjunction area, and a force of 83.4 ± 22.9 N was required for the simulated pterygomaxillary dysjunction. Markedly higher stresses in the pterygomaxillary junction were observed when the fracture line was closer to the pterygomaxillary junction. Figure 3 shows a comparison of the maximum von Mises equivalent stress value, the equivalent stress distribution, and the maximum principal stress distribution in the predicted fracture line of the 3D-FEA model.
Regarding the predicted fracture line using the 3D-FEA model, the most frequent fracture site in the pterygomaxillary area was the pterygomaxillary junction (48 sides, 48%), followed by the pterygoid process (31 sides, 31%) and the maxillary tuberosity (21 sides, 21%) ( Table 1 ). Regarding the equivalent stress distribution using the 3D-FEA model, the most frequent fracture site in the pterygomaxillary area was the pterygomaxillary junction (52 sides, 52%), followed by the pterygoid process (27 sides, 27%) and the maxillary tuberosity (21 sides, 21%). Regarding the distribution of maximum principal stress using the 3D-FEA model, the most frequent fracture site in the pterygomaxillary area was the pterygomaxillary junction (52 sides, 52%), followed by the pterygoid process (33 sides, 33%) and the maxillary tuberosity (15 sides, 15%) ( Table 1 ). High stresses were observed in the pterygomaxillary junction in all models.
Comparison between the actual pterygomaxillary dysjunction site and the pterygomaxillary dysjunction site predicted by the FEA simulation
The rate of agreement between the predicted pterygomaxillary dysjunction site and the actual pterygomaxillary dysjunction site was, by simulation, as follows: 3D-FEA, 87.0%, κ = 0.79 (excellent); ESE, 78.0%, κ = 0.64 (fair to good); MPSE, 85.0%, κ = 0.75 (excellent) ( Table 2 ).
|Concordance rate (%)||κ coefficient evaluation|
|Finite element analysis|
|Fracture line evaluation||87||0.79 (excellent)|
|Equivalent stress evaluation||78||0.64 (good)|
|Maximum principal stress evaluation||85||0.75 (excellent)|
3D-FEA prediction of pterygoid process fracture for different cuts in the maxillary lateral wall
The 3D-FEA prediction of pterygoid process fracture for the 100 sides of the 50 patients, when the cutting line of the lateral wall of the maxilla was designed to extend through the maxillary tuberosity, was assessed ( Fig. 4 ).