Abstract
It has been suggested that third molars increase mandibular fragility because they do not contribute to its strength. For ethical reasons, a human study design that would permit the elucidation of this interference is not possible. This study evaluated the impact of the presence of erupted third molars on the mandibular angle of resistance when submitted to trauma. A three-dimensional (3D) mandibular model was obtained through finite element methodology using computed tomography (CT) with the geometry and mechanical properties to reproduce a normal mandibular structure. Human mandibles with no, one or two erupted third molars were evaluated. Whenever the third molar was present there was a greater concentration of tensions around the cervical part of its alveolus. Approximated Von Mises equivalent stress of the third molar region was 107.035 MPa in the mandible with teeth and 64.6948 MPa in the mandible without teeth. In the condylar region it was 151.65 MPa when the third molar was present and 184.496 MPa when it was absent. The digital models created proved that the mandibular angle becomes more fragile in the presence of third molars. When they are absent the energy concentrates on the lateral e posterior aspect of the condylar neck.
The mandible is one of the bones most susceptible to trauma in the facial region due to its more projected position in the facial skeleton. This prevalence is influenced by factors such as sex, age, socioeconomic condition and the type of trauma. An experimental study with monkeys has shown that mandibles containing unerupted third molars fractured at approximately 60% of the force required to fracture mandibles with erupted third molars. Bezerra et al. reported a 1.94-fold higher risk of mandibular angle fractures when the third molar is present.
Force applied directly in the symphysis region in axial plane is distributed along the arch of the mandible. The condylar heads are free to rotate within the glenoid fossa, to a certain degree, thus tension develops along the lateral aspect of the condylar neck and mandibular body regions, as well as along the lingual aspect of the symphysis. This leads to a bilateral condylar fracture and a symphysis fracture, unless a fragility factor exists.
The reason for the increased prevalence of mandibular angle fractures is not well established. The presence of third molars has been suggested to contribute to an increased mandibular fragility because the mandible loses part of its bone structure to harbour tissues that do not contribute to its strength. Some authors suggest that completely unerupted teeth are more associated with mandibular fragility because they compromise the bone structure to a great extent. The effect of partially erupted teeth on the support structures of the mandibular framework (external oblique line) should also be taken into account. A review of retrospective data files indicated that the prevalence and relative risk of mandibular angle fracture are both significantly higher in subjects with fully erupted third molars than in individual lacking those teeth.
For ethical reasons, no human study design would permit the elucidation of this interference, since it would be impossible to submit experimental and control groups to injuries likely to fracture the mandible, in order to evaluate the resistance of this bone and the effect of the third molar on mandibular fractures.
Aeronautical engineering studies have allowed the development of a computational method for mechanical tests by creating virtual elements with finite dimensions and physical properties. This may be adapted to real structures, to recreate load applications and present the distribution of stresses and deformation. This methodology, called finite element analysis (FEA), is a powerful tool for computational modelling that is being widely used to predict the mechanical behaviour of complex biological structures such as bone. The accuracy of FEA to describe the biomechanical behaviour of bone specimens has been shown by different authors.
In the present study, a three-dimensional (3D) computed tomographic-based finite element reconstruction of three human mandibles with or without third molars was performed to evaluate these mechanical properties. The aim was to evaluate the impact of the presence of erupted third molars on mandibular angle stiffness when submitted to a trauma to the chin region.
Materials and methods
The ethics committee of the local institution approved the protocol for this study. Informed written consent was obtained from a 30 year old, male patient selected for the study who underwent computed tomography (CT), based on the fact that he had all the mandibular teeth, and no structural mandibular changes (osseous callus/fracture, pathologic entities, previous orthodontic treatment maxilla-mandibular discrepancy or periodontal illness).
The images were obtained by a cone beam CT, and were imported by the ScanIP software (Simpleware ® Ltd., Exeter, UK) in which the tomographic density window applicable to the object in study (2240 × 550 UH) and pixel size to be used (0.55 mm) were defined.
In order to produce the virtual structure, the 3D mesh and all the steps to perform the FEA were adapted from the procedure described by Silva et al. The mesh production began by separating the masks of the mandibular structures in order to include them in the model (discretization). These masks were obtained by digitalization of each CT slice, and a pixel-by-pixel individualization of the tissues evaluated in the study (cortical bone, marrow bone, enamel, dentin, cement, pulp, periodontal ligament), based on the tomographic density. During segmentation only bone- and teeth-related structures were kept and soft tissues were disregarded.
After the production of the final model in all slices, the software generated a 3D structure maintaining each discretized mask in position. For greater smoothness on the surface of the structure, a software tool was used to fill in small gaps and round angles. The result was a very detailed 3D mesh.
To create the three meshes to be included in this study, the initial mandibular structure (mandible 01) was submitted to a digital mask substitution. On the software interface the pixels of the third molar were changed from the initial tooth structure masks to those from cortical and medullar bone in each CT slice in accordance with an anatomic aspect. Therefore, it was possible to create a second structure without the left third molar (mandible 02), and a third one without third molars (mandible 03) ( Fig. 1 ). The remainder of the structure remained the same.
In the ScanFE ® software (Simpleware Ltd., Exeter, UK), each of the three mandibles was exported to a finite element mesh that consisted of triangular and tetrahedral elements to interconnect the nodes. The meshes were exported to the software ANSYS ® (SIMULIA, Providence, RI, USA), version 13.0, for structural analysis of the mechanical tests. The homogeneity of the structures, linear elastic deformation pattern, and the standardization of the isotropic mechanical properties were ensured for each discretized mask ( Table 1 ). The values of Young modulus and Poisson ratio were based on Lotti et al.
| Anatomic structure | Young modulus | Poisson ratio | Mandible 1 | Mandible 2 | Mandible 3 | |||
|---|---|---|---|---|---|---|---|---|
| Nodes | Elements | Nodes | Elements | Nodes | Elements | |||
| Pulp | 0.02 | 0.45 | – | 17.914 | – | 16.250 | – | 14.764 |
| Dentin | 18.60 | 0.31 | – | 174.940 | – | 149.896 | – | 141.569 |
| Cement | 18.60 | 0.31 | – | 114.618 | – | 104.475 | – | 96.478 |
| Enamel | 41.00 | 0.30 | – | 54.887 | – | 50.659 | – | 47.247 |
| Medullar bone | 1.37 | 0.30 | – | 193.168 | – | 192.120 | – | 189.685 |
| Cortical bone | 13.70 | 0.30 | – | 331.759 | – | 327.615 | – | 317.851 |
| Periodontal ligament | 0.0689 | 0.45 | – | 23.359 | – | 21.356 | – | 19.337 |
| Muscle | – | – | – | 4.307 | – | 4.812 | – | 4.966 |
| Total | – | – | 178.041 | 914.952 | 169.929 | 867.183 | 163.507 | 831.897 |
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