Introduction
This study aimed to simulate the different positions of the hyrax appliance expander screw and evaluate tooth displacement and the stress distribution standard on the periodontal ligament using the finite element method.
Methods
Part of the maxilla with anchorage teeth, periodontal ligament, midpalatal suture, and the hyrax appliance was modeled, and finite element method models were created to simulate 6 different screw positions. There were 2 vertical positions at distances of 20 mm and 15 mm from the occlusal plane. Another position was anteroposterior, the center of the screw placed between and equidistant from the mesial face of the first molar and the distal face of the first premolar, aligned to the center of the crown of the first molar, with the anterior edge of the screw aligned to the distal face of the first molar. A 1 mm activation of the expander screw was simulated. The displacement (total, vertical, and buccolingual) and the stress distribution on the periodontal ligament of supporting teeth in each model were registered.
Results
The model simulating the expander screw in a more occlusal and anterior position presented higher displacement values and higher stress concentration, followed by the model with the screw in a more posterior but same vertical position. With the exception of the first premolar, the teeth presented cervical-apical displacement in the vestibular face and apical-cervical displacement in palatal faces. This displacement is compatible with the vestibular inclination associated with the activation of the expander screw. The first premolar presented an atypical tendency for the mesial and lingual displacement of the vestibular surface and counterclockwise rotation.
Conclusions
The supporting teeth presented a tendency for vestibular crown displacement and lingual root displacement associated with compression areas in the vestibular-cervical region and tensile strength in the linguoapical region. Placing the expander screw in a more occlusal and anterior position generated more mechanical stress transfer, resulting in greater dental displacement.
Highlights
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Variations of the expander screw interfered in the supporting teeth’ displacement.
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The first premolar presented atypical mesiolingual displacement of the crown.
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The anteroinferior position of the screw resulted in larger movement of the teeth.
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Dental displacement is inversely proportional to the extension of the expander legs.
Rapid maxillary expansion (RME) is the recommended treatment to correct the transversal maxillary deficiency associated with crossbite in patients undergoing bone growth. RME is a procedure that separates the midpalatal suture (MPS) and expands the maxilla transversally through lateral force applied on the maxillary teeth and maxillary bones using expanders. During RME, the expected result is the sideward expansion of both maxillary segments. , However, even though the strength applied on the maxillary bones is high, this procedure is not merely orthopedic, at it causes undesirable dental inclination of the teeth supporting the expander. , , , This fact harms the stability and the prognosis, which restricts the orthopedic results of the treatment. ,
During the activation of the expanders, the higher the undesirable dental movement, the shorter the bone expansion obtained because the excessive vestibular dental inclination causes the clinical limit of RME to be achieved early. When the palatal cusps of the maxillary teeth and the vestibular cusps of the mandibular teeth touch, the MPS opening is reduced. , , Although the orthopedic changes obtained with the RME may present some degree of recurrence, dental movement is the most unstable change in this procedure. , Its restriction is related to a lower degree of recurrence after correcting posterior crossbite. , ,
One of the devices used to perform RME is the hyrax expander screw, which has a side expander transversal to the MPS. When activated, this expander forces the maxilla segments laterally. , Laboratory production allows changes in the palate along with both the height and anteroposterior axes. Such changes may interfere clinically in distributing orthopedic forces generated by the expander and in dental effects during use, influencing the efficiency and the stability of RME. ,
The finite element method (FEM) is a computer method applied to biomechanics that is used to determine stress and deformation in structures submitted to different mechanical loads. , In orthodontics, the FEM has been used to analyze the tendency of movement and tension distribution on teeth and craniofacial bones during mechanic orthodontic simulations, such as RME. , ,
A FEM study conducted by Fernandes et al described a standard of tension and deformation distribution on maxillary bone structures after placing the expander screw into 6 different positions during maxillary expansion. Only the impact on bone structures was analyzed. The possibility of dental movement during the process was ignored.
The objective of this study was to simulate the different vertical and anteroposterior positions of the hyrax appliance expander screw and to evaluate using the FEM tooth displacement and stress distribution on the periodontal ligament.
Material and methods
A computer-aided design model from the Renato Archer Information Technology Center, Campinas, São Paulo, Brazil, was employed. It included the maxilla, the skull base (with the zygomatic, nasal, sphenoid, and frontal bones), the central incisor, the lateral incisor, the canine and the first premolar (U4), the second premolars (U5), the first molar (U6), the second molars (U7), the periodontal ligament, and a bone-suture unit representing the MPS. The dental crowns contact and transfer the force to each other. The model was created (Rhinoceros 4.0; McNeel North America, Seattle, Wash) from computerized tomography images (GE Lightspeed Pro 16; GE Healthcare, Chicago, Ill) taken from an adult, without any evident facial asymmetry, with all the permanent teeth emerged, with the exception of the third molars, and without any dental restoration or congenital or acquired craniofacial alterations. The use of these images was approved by the ethics research committee of the University of São Paulo (no. 97/06).
The anatomic model of part of the maxilla, teeth, periodontal ligament, and MPS was imported into the software program FEMAP (version 10.1.1; Siemens PLM Software, Plano, Tex), incorporating the single-body hyrax appliance, composed of 1 expander screw and 3 wire segments of 0.036-in diameter that joined the screw to the U4 and U6 and the teeth to each other (from U4 to U7), resulting in a geometric model with a tetrahedral mesh ( Fig 1 ).
The geometric model was subjected to mathematical analysis (Ansys 17.2; Ansys, Inc, Canonsburg, Pa), using a bone thickness of 2 mm and bar elements with elastic properties to represent the MPS. A horizontal movement restriction was imposed on the body of the device to simulate soldering to the orthodontic bands connected to the U4 and U6. The model structures were determined with specific properties ( Table I ), and the simulated materials had elastic, isotropic, and uniform characteristics.
| Material | Poisson coefficient | Young’s modulus (MPa) |
|---|---|---|
| Cortical bone | 0.3 | 13,700 |
| Trabecular bone | 0.3 | 1370 |
| Teeth | 0.3 | 20,000 |
| Periodontal ligament | 0.49 | 0.69 |
| Hyrax expander | 0.33 | 200,000 |
| Midpalatal suture | 0.49 | 1 |
Six distinct positions of the expander screw were simulated in FEM models. Three of them were anteroposterior, and 2 of them were vertical. In all the simulations, the expander screw was placed in the transversal center of the palate, perpendicular to the MPS and parallel to the occlusal plane.
In anteroposterior position 1, the center of the screw was positioned equidistant to the mesial face of U6 and the distal face of U4. In anteroposterior position 2, the center of the screw was aligned to the center of the U6 crown. In anterior position 3, the anterior edge of the expander was aligned to the distal face of U6. Vertically, the expander screw was positioned 20 mm (vertical position 1) and 15 mm (vertical position 2) from the occlusal plane. Table II and Figure 2 show the positions of all 6 models.
| Vertical variation | ||
|---|---|---|
| Anteroposterior variation | Vertical position 1 | Vertical position 2 |
| Anteroposterior position 1 | Model 1 (M1) | Model 4 (M4) |
| Anteroposterior position 2 | Model 2 (M2) | Model 5 (M5) |
| Anteroposterior position 3 | Model 3 (M3) | Model 6 (M6) |
A condition for the outline of the maxillary bone was set for both stress distribution and displacement analysis to restrict vertical, anteroposterior, and transverse movements in the model. A bar element was created for each node on the edge of the face in the MPS and perpendicular to it, simulating the MPS during the RME. The activation of the hyrax appliance was achieved only by the enforced displacement toward maxillary expansion.
In the MPS region, symmetry was required as a condition, and the loading was recreated symmetrically on the opposite side to obtain equivalent results for both sides. For each model, a transversal displacement of 0.5 mm in the center of the screw was simulated. Because of its symmetry, it was the same as 1 mm of activation of the hyrax expander.
Results
After simulating the opening of the expander screw, tooth displacement was analyzed as a whole and separately on vertical and buccolingual axes.
The total tooth displacement in each model after opening the screw was evaluated from an axial point of view, represented in Figure 3 . The M1, M2, and M3 models presented a similar maximum total displacement of approximately 0.2 mm. However, such displacements occurred in different areas. On the M1 model, there was a distolingual displacement in U6, U5, and the vestibular area of U4. In M2, the entire U6 crown presented displacement. A few areas in U4 and U5 also presented short displacement. In M3, only the vestibular and mesial faces of U4 and the distolingual face of U6 presented displacement.
