It has been suggested that unerupted lower third molars (M3) increase the fragility of the mandibular angle and simultaneously decrease the risk of condylar fracture. However, it is unknown whether this applies regardless of the direction and point of impact of the traumatic force. The aim of this study was to investigate the impact of an unerupted M3 on the fragility of the angle and condyle in terms of a force acting from different directions and affecting different regions of the mandible. Computed tomography scans of a human mandible and finite element methodology were used to obtain two three-dimensional models: a model with, and the other without an unerupted M3. A force of 2000 N was applied to three different regions of the models: the symphysis, ipsilateral body, and contralateral body, respectively. When the force was applied to the mandibular body, the results revealed increased angle fragility in cases with unerupted M3. When the force was applied to the symphysis, the condyle region showed higher fragility, irrespective of the presence of an unerupted M3. In summary, fragility of the angle and condyle regions depends on the presence of an unerupted M3 and on the direction and point of impact of the force.
The association of unerupted lower third molars (M3) and angle fractures of the lower jaw has been the subject of many recent epidemiological studies. It is suggested that the presence of the M3, especially in cases where it is impacted or partially impacted and angulated, increases the risk of fracture in the region of the mandibular angle two- to four-fold. Nevertheless, previous studies have shown that when the M3 is not present, the fracture is more likely to occur in the region of the mandibular condyle. This suggests that the presence of the M3 might prevent condylar fracture.
Takada et al. used a finite element analysis (FEA) method to analyse the distribution of stress during the simulation of traumatic force in the region of the mandibular angle, and compared two cases: with half-impacted M3 and without M3. They found differences in the distribution of stress, and also in average and maximum values of stress. However, that study showed the stress distribution only in the case where force acted in the region of the ipsilateral mandibular body. The FEA study of Bezerra et al. showed that erupted M3 weaken the angle region after a blow simulated to the chin region.
The aim of this study was to evaluate the influence of the unerupted M3 on the distribution of stress and fragility in the regions of the mandibular angle and condyle, in three standard trauma situations: a simulated blow to the region of the symphysis, the ipsilateral body, and the contralateral body. Further, we sought to determine the pattern of biomechanical behaviour in each case.
Materials and methods
The mandible of a middle-aged male with partially impacted M3 was imaged with diagnostic computed tomography (CT) (SOMATOM Sensation 16; Siemens) in transversal planes, with slices of 0.75 mm in thickness. The slices obtained were used for the creation of the following computer models of the mandible: (1) A model of the human mandible without M3. In this model, M3 was removed by computer manipulations; the pixels of the M3 were converted from initial tooth structure mask to cortical and medullar bone masks on each CT slice, with respect to the anatomic structure. (2) A model of the human mandible with partially impacted M3 in the mesioangular position.
Symmetrical models based on the left side were created by mirror-imaging in order to avoid the possible influence of differences in the sides on the distribution of stress.
These models were studied using FEA methodology, a numerical method that is widely used in biomedical sciences and engineering as a tool for providing an accurate prediction of the mechanical response of complex structures when submitted to loading. This method is based on subdivision of the complex geometry into smaller elements of finite dimensions, which, when combined, form the mesh model of the analysed structure.
As a first step, we used Mimics visualisation software (version 10.1; Materialise, Leuven, Belgium) for three-dimensional (3D) reconstruction of the CT images ( Fig. 1 ). Based on image density thresholding, three different masks were obtained: a cortical mask, a trabecular mask, and a mask for all teeth. Using the Mimics STL+ module, cortical bone, trabecular bone, and teeth were converted into stereolithography files. To reduce triangles and fix the quality of the triangles that were not appropriate for the FEA, we used the REMESH module attached to Mimics. TetGen was then used to create a 3D mesh. Four-node tetrahedral elements were used as the final element, where each node had three degrees of freedom: translation in the nodal x , y , and z directions. The average size of elements from each group was used, as follows: 0.5 mm for cortical bone, 1.0 mm for trabecular bone, and 2.0 mm for teeth. Non-linear FEA was performed using PAKC (BioIRC-Bioengineerng Research and Development Center, Kragujevac, Serbia) software.
Linear and homogeneous material behaviours were assumed for mandibular bone and teeth. The Young modulus and Poisson ratio values, based on Lotti et al., are given in Table 1 .
|Material||Elastic modulus (GPa)||Poisson ratio|
Figure 2 shows the 3D mandible model with boundary conditions and loadings, where actions of traumatic forces in three different directions and points of action were simulated using the FEA method.
A blunt trauma with a magnitude of 2000 N was applied perpendicularly to the frontal plane (in the region of symphysis) and laterally (in the region of the mandibular body) on a circular area of 1 cm in diameter. The results were evaluated qualitatively using a colour scale by assessing the distribution of von Mises equivalent stress along the mandible as a response to the loading condition, and quantitatively by calculating the average and the maximum stress in the regions of interest. The von Mises stress scores were calculated automatically by the software.
|Model||Region of the acting force||von Mises stress in the region of the angle (MPa)||von Mises stress in the region of the condyle (MPa)|
Mandible without M3
Mandible with partially impacted M3