Introduction
Uprighting mesially tipped molars is often a necessary step before implant placement. However, the orthodontic treatment can be lengthy and discourage patients from choosing implant prostheses. Periodontally accelerated osteogenic orthodontics is reported to facilitate molar movements. This study aimed to evaluate the biomechanical effects of various corticotomy and osteotomy approaches on the uprighting of a mesially tipped mandibular second molar in a 3-dimensional finite element analysis model.
Methods
The initial tooth displacement and periodontal ligament (PDL) strain in 9 finite element analysis models with various corticotomy and osteotomy simulations were compared under 3 intended tooth movement scenarios: distal crown tipping, mesial root movement with restraints, and mesial root movement without restraints.
Results
Corticotomy or osteotomy approaches altered the tooth displacement and the PDL strain in all 3 intended molar uprighting scenarios. The 2 most extensive surgical approaches, the combined mesial and distal osteotomy with horizontal corticotomy and the circumferential corticotomy at root apex level, resulted in increased tooth movement but had a distinct impact on PDL strain.
Conclusions
It was revealed that different combinations of corticotomy and osteotomy had a biomechanical impact on orthodontic molar uprighting movements.
Highlights
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The impact of corticotomy and osteotomy on molar uprighting was studied.
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Twenty-seven molar uprighting movement scenarios were studied with finite element analysis.
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Corticotomy or osteotomy has altered the periodontal ligament strain during molar uprighting.
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The results may contribute to an optimal treatment protocol for molar uprighting.
Molars facing a mesial edentulous space are likely to tip mesially over a long time. , Tipped molars can cause occlusal and periodontal problems such as overeruption of opposing teeth and angular loss of an alveolar bone level. It is a common situation among adult patients seeking comprehensive or limited orthodontic treatment before bridge or implant restoration for the premature loss of permanent molars. It is often necessary to upright the tipped molar orthodontically to develop proper edentulous span and root angles for the dental prosthesis. However, conventional or miniscrew-assisted orthodontic treatment to upright a severely tipped molar can be time-consuming, especially at the mandibular posterior region with thick cortical bones. The lengthy treatment time might discourage patients from accepting the adjunctive orthodontic or restorative plan.
Periodontally accelerated osteogenic orthodontics were reported to facilitate orthodontic movement for uprighting tipped molars or intruding elongated molars. In these limited data, the authors believed that the treatment time was significantly reduced. In a recent clinical case report, 2 severely inclined second molars were uprighted with different selective osteotomy-assisted orthodontic treatment as part of the implant site development. It was revealed that the selective osteotomy facilitated the distal tipping movement of a mandibular molar with reduced treatment time. The biological effects of the corticotomy are believed to be associated with the regional acceleratory phenomenon (RAP), , which is the local and transitory demineralization and remineralization in the alveolar bone during the wound healing period. The mechanical effect of the surgical interruption on the continuity of the alveolar bone and the en-bloc movement of the bone segment is another theory of the accelerated tooth movement , that has not been well studied.
Finite element analysis (FEA) is a numeric technique for simulating a mechanical process in a physical system, such as in an orthodontic tooth movement model. It is a valid study method to analyze the immediate tooth movement and the deformation in the dentoalveolar structures under certain mechanical loadings without using animal or clinical samples. , FEA models have been applied to study the mechanical effect of corticotomy- and osteotomy-assisted canine retraction and molar uprighting. It was revealed in these studies that the simulated surgical alternation of the alveolar bone structure can affect the immediate tooth movement and periodontal ligament (PDL) deformation.
Therefore, this pilot study is designed to evaluate the immediate mechanical effects of various corticotomy and osteotomy approaches on the uprighting of a mesially tipped mandibular molar in a 3-dimensional (3D) FEA model. Clinically there are 2 ways to achieve molar uprighting: distal crown movement and mesial root movement. The distal crown movement can be achieved with an uprighting spring delivering distal tipping and intrusion force. The mesial root movement can be achieved with a moment built in the spring, with or without the wire cinched distal to the molar bracket. In this study, 3 mechanical settings were designed for these intended tooth movement scenarios: distal crown tipping, mesial root movement with restraint, and mesial root movement without restraint (a fixed pivoting point for the moment, mimicking the effect of the distally cinched wire). The immediate mechanical effects on tooth movement and the PDL deformation of the force systems under the 9 simulated surgical interventions of corticotomy and osteotomy were studied. Although the biological effects of the RAP cannot be replicated in this FEA model, a better understanding of the mechanical effects of various surgical interventions on orthodontic tooth movement may provide insights for developing future study models or clinical protocols that maximize the biological benefits of the RAP effect.
Material and methods
With appropriate institutional review board approval, the 3D geometric model of a mandible was reconstructed using Amira image processing software (version 5.4; Amira, Thermo Fisher Scientific, Waltham, Mass) from an existing pretreatment cone-beam computed tomography scanning of a previous patient (Planmeca 3D Max; Planmeca, Helsinki, Finland; voxel dimensions: 0.35 × 0.35 × 0.35 mm 3 ). This patient is a healthy 46-year-old African American male with bilaterally missing first molars and mesially tipped second molars. There were no craniofacial anomalies or history of temporomandibular disorder reported from this patient. The treatment for the tipped molars was described in a previous case report. Briefly, the mandibular second molars were uprighted with selective osteotomy-assisted orthodontics in 5 months.
The 3D geometric models of the mandibular right second molar, the mandibular cortical, and trabecular bones were reconstructed through segmentation of cone-beam computed tomography images using Amira software ( Fig 1 ). The PDL surrounding this molar was generated using Geomagic Studio designing software (version 12; 3D Systems, Rock Hill, SC) with an average thickness of 0.2 mm ( Fig 1 ). The contour of a stainless-steel bracket was created at the center of the buccal surface of the molar crown using Solidworks (Solidworks 2016; Solidworks, Vélizy-Villacoublay, France) to indicate the location of the applied orthodontic force loadings ( Fig 1 ).
Volumetric meshes were generated separately for the geometric components, including the mandibular cortical and trabecular bones, the molar, and the PDL in preprocessing software Hypermesh (version 11.0; Altair Engineering, Troy, Mich). The numbers of elements and nodes for each component are listed in the Table . The whole meshed models were then imported into FEA software Abaqus (version 6.14; Abaqus, Inc, Vélizy-Villacoublay, France) for further analysis. The mandible, molar, and PDL were modeled to be an isotropic linearly elastic material. The Young’s modulus and Poisson’s ratio were based on previous studies listed in the Table .
| Geometric components | Young’s modulus (GPa) | Poisson’s ratio | Element types | Nodes (n) | Elements (n) | References |
|---|---|---|---|---|---|---|
| Cortical bone | 10.7 | 0.3 | C3D10 | 393612 | 255626 | Aversa et al (2009) |
| Trabecular bone | 0.97 | 0.3 | C3D10 | 264710 | 181355 | Aversa et al (2009) |
| Molar | 20.7 | 0.3 | C3D10 | 19895 | 13515 | Lee and Baek (2012) |
| PDL | 0.05 | 0.45 | C3D20R | 54231 | 11665 | Lin et al (2013) |
The FEA models were constrained with fixed-displacement boundary conditions along the bilateral mandibular sigmoid notches, the condylar heads, and the coronoid processes to prohibit the free movement of the mandible on force loading ( Fig 1 ). To prevent separation between geometric models, interfaces including mandibular cortical bone to trabecular bone, mandibular cortical and trabecular bones to the PDL, and the PDL to the tooth were constraint to be rigidly bonded.
Three mechanical settings were designed for these intended tooth movement scenarios: distal crown tipping, mesial root movement with restraint, and mesial root movement without restraint. For the distal crown movement, 1 N (about 102 g or 3.6 oz) of distalizing force and 0.5 N (about 51 g or 1.8 oz) of intrusion force were loaded ( Fig 2 , A ). For the mesial root movement, 5 N⋅mm (about 510 g⋅mm) of mesial root movement moment was loaded with and without a fixed pivoting point, mimicking orthodontic uprighting springs with and without cinching back at the distal end ( Fig 2 , B and C ). The forces and moments were directly loaded at the center point of the buccal crown surface. The force and moment values are the same as in a clinical case report and within the range of force and moment values described in previously published orthodontic molar uprighting studies. ,
Each type of orthodontic loadings was applied to 9 different simulated models (1 control and 8 surgical models): (a) control; (b) mesial osteotomy; (c) distal osteotomy; (d) combined mesial and distal osteotomy; (e) mesial osteotomy combined with buccal horizontal corticotomy 10 mm below cementoenamel junction (CEJ); (f) distal osteotomy combined with buccal horizontal corticotomy 10 mm below CEJ; (g) combined mesial and distal osteotomy with buccal horizontal corticotomy 10 mm below CEJ; (h) circumferential corticotomy with buccal-lingual cuts at 10 mm below CEJ; and (i) circumferential corticotomy with buccal-lingual cuts at root apex level, approximately 13 mm below CEJ.
Shear bands representing the periodontal surgical approaches were created using computer-assisted design software Solidworks. The osteotomy shear bands were all placed approximately 1 mm away from the molar root with the dimension of 2 mm wide and a depth through the cortical and trabecular bone. The corticotomy cuts were 1 mm wide and only through the cortical bone. The occlusal and buccal views and 3D models of all cutting patterns were shown in Figure 3 .
