Introduction
Nonsurgical mandibular expansion has been increasingly performed in recent years because it can effectively expand the mandibular dental arch. However, many types of mandibular expanders have been used in previous studies. No relevant studies have compared the biomechanical responses of different designs of mandibular expansion appliances with screws. Therefore, the purpose of this study was to analyze the stress distribution and displacement of the dentoalveolar structures according to different designs of mandibular screw expanders.
Methods
Cone-beam computed tomography scans were used for 3-dimensional reconstruction of the mandibular finite element model. Four different designs of mandibular expanders, 1 removable expander (type A) and 3 fixed expanders (types B, C, and D), were added to the finite element models. Expanders were activated transversely for 0.2 mm. The initial tooth displacement and von Mises stress distribution were evaluated.
Results
All the expanders enlarged the arch dimensions. In types A and B, the stress was mainly concentrated in the region of the anterior teeth, along with greater tooth displacement, whereas in types C and D, greater stress and displacement occurred in the region of the posterior teeth. Type A showed the greatest amount of transverse displacement. Type D was more efficient in the region of the posterior teeth.
Conclusions
Types A and B should be used with great caution in the clinic because of their incompatible expansion pattern. Type D is the recommended mandibular expansion appliance because of its appropriate expansion pattern.
Highlights
- •
Designs of mandibular screw expanders can influence responses of dentoalveolar structures.
- •
The lower Schwarz expander can produce more expansion in the anterior region than in the posterior.
- •
The modified mandibular expander promotes the expansion pattern and distalizes the posterior teeth.
The decision to extract teeth in individuals with moderate crowding has always been, and will continue to be, one of the most contentious issues in orthodontics. There is no doubt that for the orthodontist, and particularly for the patient, nonextraction therapy is extremely attractive. Since the 1960s, nonextraction approaches have been gaining popularity with the introduction of expansion appliances. , Maxillary expansion is now a well-established nonextraction approach for increasing the dental arch perimeter and relieving dental crowding. , In contrast, the use of mandibular expansion is still under debate.
McNamara pointed out that one of the limiting factors in the management of tooth size–arch size problems is available space in the mandibular dental arch. Unfortunately, true orthopedic expansion of the mandibular arch is unlikely unless recently developed distraction osteogenesis techniques are used. Some researchers have observed that after maxillary expansion, there is expansion of not only the maxillary dental arch but also the mandibular dental arch, suggesting that the position of the mandibular dentition may be influenced by maxillary skeletal morphology. However, other studies have shown that the spontaneous dentoalveolar changes found in the mandibular dental arch after maxillary expansion were very small and not clinically significant. ,
Walter stated that mandibular arch width could be expanded permanently. Mandibular expansion has been increasingly performed in recent years. , , After mandibular expansion treatment, a significant increase in dental arch widths was observed, along with a significant reduction in crowding and even long-term stability.
Currently, mandibular expansion appliances with screws are widely used for greater efficiency, hygiene, and comfort and for minimal interference with speech. However, different arm shapes are used in different expanders, which may produce different outcomes. , , , To our knowledge, studies comparing the efficacy of mandibular expanders with different arm shapes are currently lacking. Therefore, the purpose of the present study was to compare the biomechanical effects of 4 different types of mandibular expanders using the 3-dimensional finite element method (FEM). The stress distribution and displacement of mandibular dentoalveolar structures were examined.
Material and methods
Finite element (FE) analysis involves dividing a complex structure into a system of nodes and elements, creating a grid or mesh. Strain and stress distributions can be assessed for each node, and the response to different loading conditions can be predicted. The overall deformation of the entire structure can be calculated by considering the individual deformations. The mandibular FE model was constructed on the basis of a cone-beam computed tomography scan (slice thickness, 0.25 mm; pixel size, 0.25 mm) of a 14-year-old girl from the Department of Stomatology at the Air Force Medical Center, People’s Liberation Army. The scan had been previously obtained for the assessment of an unerupted maxillary canine. Four different mandibular expanders were designed and modeled using computer-aided design software (SolidWorks 2014; Dassault Systems, Concord, Mass), and all components were saved and assembled. The trabecular bone, cortical bone, mucosa, teeth, periodontal ligament, and expanding appliances were considered to be linearly elastic, homogeneous, and isotropic. The material properties of the elements in all the models were based on published data ( Table I ). The thickness of the cortical bone, trabecular bone, and mucosa was 2.0 mm each, and the periodontal ligament was 0.2-mm thick. Each model was meshed automatically using SolidWorks. Table II gives the number of nodes and elements in each model. The differences between the mandibular elements of the 4 types are due to different force vectors created by the expanders.
| Material | Young modulus, MPa | Poisson ratio |
|---|---|---|
| Cortical bone | 14,700 | 0.30 |
| Trabecular bone | 1500 | 0.30 |
| Tooth | 20,700 | 0.30 |
| Periodontal ligament | 6.89 × 10 −2 | 0.45 |
| Mucosa | 2.8 | 0.40 |
| Stainless steel | 200,000 | 0.30 |
| Resin | 2000 | 0.30 |
| Mode | Number of nodes | Number of elements |
|---|---|---|
| Type A | 604,518 | 334,069 |
| Type B | 602,033 | 331,349 |
| Type C | 609,351 | 334,689 |
| Type D | 616,281 | 338,113 |
Figure 1 shows the designs of the 4 mandibular appliances: 1 removable expander (type A) and 3 fixed expanders (types B, C, and D). Type A was designed on the basis of the removable mandibular Schwarz appliance. Type B was a conventional fixed mandibular expander. The 1.5-mm-diameter expanding arms of the expansion device extended backward along the lingual side of the clinical crowns, and the distal part of each side was soldered to the band on the first permanent molars. Type C was constructed on the basis of type B with a 1.5-mm wire soldered to the 2 arms to add the required length so that the wire could extend backward along the midroot of the posterior teeth and then return to the midcrown height of the first molars to which it was soldered. This wire continued to the canines below the midcrown level of the second and first premolars. The midroot and midcrown parts of the arm were joined in the first premolar region. Type D was similar to type C. In type D, the parts of the expansion arm between the midroot and midcrown were connected with a curved wire for rigidity. All components were saved in initial graphics exchange specification format and imported into ANSYS 16.0 software (Ansys Inc, Canonsburg, Pa).
To ensure the contact condition between the oral tissues (the teeth and lingual mucosa) and the expansion arms of the 4 types of expanders, the connections between the tissues and the extension arms were set to “No Separation.” In types B, C, and D, the connections between the expansion arm and the molar band and between the first molar and the band were both set to “Bond.” The adjacent teeth were independent of each other.
To simulate the temporomandibular joint, 2 blocks of temporal bone were made, and the space between the temporal bone and condyles was filled by a 2-mm-thick layer of articular disc. For boundary conditions for the temporomandibular joint, constraints were placed on the 2 bone blocks in all 3 axes.
The 3-dimensional coordinates were x, transverse direction; y, anteroposterior direction; and z, vertical direction. Positive values indicated outward, backward, and upward displacements on the x, y, and z planes, respectively.
The 4 expanders were activated transversely for 0.2 mm by rotating the screw one quarter of a turn. Each model was analyzed for the von Mises stress distribution and the displacement of the teeth (including canines, premolars, and first molars).
Results
Type A resulted in von Mises stresses on the bone being concentrated at the region of anterior teeth, with a maximum value of 26.54 MPa on the lingual alveolar bone of the incisors. In addition, type A generated the highest level of stress of all 4 types of expanders.
For type B, stress was mainly distributed on the bone near the bilateral canines and premolars, and the maximum value of 3.99 MPa was at the buccal alveolar crest of the first premolars.
Types C and D demonstrated similar stress distribution patterns on the bone, with stress mostly located in the regions of premolars and first molars. Moreover, the maximum stress concentrations occurred at both of the buccal alveolar crests of the second premolars, and the maximum value in type D (5.79 MPa) was larger than that in type C (1.36 MPa). Furthermore, type C produced lower von Mises stresses than the other 3 types ( Figs 2 and 3 ).
In type A, the von Mises stress distribution for the teeth was mainly at the incisors and canines, and the maximum value of 32.03 MPa was found on the lingual side of the necks of the incisors.
Type B showed stresses concentrated on the canines and premolars, with a maximum value of 72.2 MPa on the lingual side of the first premolars. In addition, type B produced a higher level of stress than the other 3 types.
In types C and D, stress was concentrated on both the middle and posterior segments of the dental arch. Furthermore, type C generated the lowest von Mises stress (25.5 MPa), and type D produced the second highest value (70.04 MPa) of all 4 types of expanders ( Fig 4 ).
