Impact of the lower third molar presence and position on the fragility of mandibular angle and condyle: A Three-dimensional finite element study.

Journal of Cranio-Maxillo-Facial Surgery xxx (2015) 1e9

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Impact of the lower third molar presence and position on the fragility of mandibular angle and condyle: A Three-dimensional finite element study Svetlana Antic a, b, Arso M. Vukicevic c, d, Marko Milasinovic c, d, Igor Saveljic c, d, Gordana Jovicic c, Nenad Filipovic c, d, Zoran Rakocevic a, b, Marija Djuric b, * a

Center for Radiological Diagnostics, School of Dentistry, University of Belgrade, Rankeova 6, Serbia Laborotory for Anthropology, Institute of Anatomy, School of Medicine, University of Belgrade, Dr Subotica 4/2, 11000 Belgrade, Serbia Faculty of Engineering, University of Kragujevac, Sestre Janjic 6, 34000 Kragujevac, Serbia d Bioengineering Research and Development Center Kragujevac, Prvoslava Stojanovica 6, 34000 Kragujevac, Serbia b c

a r t i c l e i n f o

a b s t r a c t

Article history: Paper received 4 September 2014 Accepted 23 March 2015 Available online xxx

The aim of the present study was to investigate the influences of the presence and position of a lower third molar (M3) on the fragility of mandibular angle and condyle, using finite element analysis. From computed tomographic scans of a human mandible with normally erupted M3, two additional virtual models were generated: a mandibular model with partially impacted M3 and a model without M3. Two cases of impact were considered: a frontal and a lateral blow. The results are based on the chromatic analysis of the distributed von Mises and principal stresses, and calculation of their failure indices. In the frontal blow, the angle region showed the highest stress in the case with partially impacted M3, and the condylar region in the case without M3. Compressive stresses were dominant but caused no failure. Tensile stresses were recorded in the retromolar areas, but caused failure only in the case with partially impacted M3. In the lateral blow, the stress concentrated at the point of impact, in the ipsilateral and contralateral angle and condylar regions. The highest stresses were recorded in the case with partially impacted M3. Tensile stresses caused the failure on the ipsilateral side, whereas compressive stresses on the contralateral side. © 2015 European Association for Cranio-Maxillo-Facial Surgery. Published by Elsevier Ltd. All rights reserved.

Keywords: Lower third molar Mandible Fracture Finite element Biomechanics

1. Introduction Although the lower jaw is the largest and the strongest bone of the facial skeleton, it is very frequently fractured. According to the epidemiological surveys, mandibular fractures are the most, or one of the most frequent facial bone injuries (Shaikh and Worrall, 2002; Van den Bergh et al., 2012; Naveen Shankar et al., 2012; Van Hout et al., 2013). They account for 15.5% up to 59% of all facial fractures, depending on the studied population (Van Hoof et al.,1977; * Corresponding author. Laboratory for Antropology, Institute of Anatomy, School of Medicine University of Belgrade - Dr Subotica 4/2 11000 Belgrade, Serbia. Tel./ fax: þ381 11 2686 172. E-mail addresses: [email protected] (S. Antic), [email protected] (A.M. Vukicevic), [email protected] (M. Milasinovic), [email protected] (I. Saveljic), [email protected] (G. Jovicic), fi[email protected] (N. Filipovic), [email protected] (Z. Rakocevic), [email protected] (M. Djuric).

Brook and Wood, 1983; Ellis et al., 1985; Scherer et al., 1989; Zix et al., 2011). It is familiar, in clinical practice, that the pattern of mandibular fracture is related to many factors such as the force properties (direction, intensity, location of the point of impact), biomechanical properties of the mandible and its position during the injury, overlying soft tissue, and present teeth. Epidemiological data have suggested that the lower third molar (M3), especially if it is impacted or partially impacted, makes the mandibular angle region weaker, and decreases its resistance to fracture (Schwimmer et al.,1983; Safdar and Meechan, 1995; Tevepaugh and Dodson, 1995; Lee and Dodson, 2000; Hanson et al., 2004). Since experiments on human mandibles are restricted, an experimental study was conducted on monkey mandibles and revealed a 30% decreased resistance to fracture of the mandibular

http://dx.doi.org/10.1016/j.jcms.2015.03.025 1010-5182/© 2015 European Association for Cranio-Maxillo-Facial Surgery. Published by Elsevier Ltd. All rights reserved.

Please cite this article in press as: Antic S, et al., Impact of the lower third molar presence and position on the fragility of mandibular angle and condyle: A Three-dimensional finite element study, Journal of Cranio-Maxillo-Facial Surgery (2015), http://dx.doi.org/10.1016/ j.jcms.2015.03.025

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S. Antic et al. / Journal of Cranio-Maxillo-Facial Surgery xxx (2015) 1e9

angle region in cases with the present lower third molar (Reitzik et al., 1978). This was explained as a replacement of the bone tissue with another harbour tissue that did not contribute to the strength of the angle. However, clinical data suggested a decreased incidence of condylar fractures in cases with present M3, concluding that when the fragility of the angle increases, the condyle is spared. Numerous epidemiological studies have analysed the impact of different positions and eruption status of the M3 on the risk for mandibular angle and condylar fracture (Iida et al., 2005; Zhu et al., 2005; Inaoka et al., 2009; Patil, 2012), but the results of these studies displayed a lack of consistency. Because of the limitations in performing experiments on humans, investigations have concentrated on finite element analysis (FEA), a computational method for predicting the biomechanical response of complex structures submitted to loading, based on assessing the distribution of the stress. This methodology has been used for describing the biomechanical behaviour of the mandible in trauma situations (Gallas Torreira and Fernandez, 2004; Tang et al., 2012; Lei et al., 2012), such as the influence of M3 on mandibular response to simulated traumatic force (Takada et al., 2006; Bezerra et al., 2013; Antic et al., in press). In the study by Takada et al., 2006 FEA showed significant differences in stress distribution between computer models of mandibular angle with and without present partially impacted M3. Bezerra et al. (2013) evaluated the distribution of stress in the angle and condylar region, but described mandibular models without and with fully erupted M3 (unilaterally and bilaterally), while the unerupted M3 is considered to be more of a contributor to the angle weakness. An FEA study conducted by Antic et al., in press compared only the cases with and without unerupted M3, but gave no information about the influence of the M3 position on the mandibular angle and condylar fragility. In cited FEA studies, mandibular bone material was assumed as homogeneous, linearly elastic, and isotropic, whereas it has been experimentally confirmed that the cortical mandibular tissue has anisotropic material properties (in the forms of transverse isotropy and orthotropy) depending on osteonal orientation (Nomura et al., 2003; Bonnet et al., 2009). In orthotropy, elastic properties are symmetrical with respect to the three orthogonal planes; elastic moduli differ among each of the three orthogonal axes (x, y z), but are the same along any one axis. Transverse isotropy is similar to orthotropy, except that within one of the orthogonal planes, elastic moduli are the same in all directions (Chung and Dechow, 2011). Schwartz-Dabney and Deschow (2003) gave a detailed presentation of macromechanical properties of the mandibular cortex, divided into the 31 zones on the facial and on the lingual side. Obtained experimental data indicated orthotropic material properties and revealed that the maximal rigidity significantly varies along the facial and lingual cortex. Apicella et al. (2010) proved the importance of adopting the cortical bone orthotropicity and thickness for the reliability of mandible numerical models, especially in sensible regions that include, inter alia, facial side of the condylar neck, and retromolar area. Furthermore, previous studies were based on calculating the effective von Mises stress, despite experimental data regarding different actions of tensile and compressive stresses on fracture development mechanism. It has been reported that bone fails and fractures more often under tension than under compression (Franklyn and Field, 2013), so the separation of these stresses is needed for obtaining more precise results. The aim of our study was to investigate the influence of the presence and eruption status of the M3 on the fragility of the mandibular angle and condyle by using FEA. Assuming the realistic geometry and material characteristics with respect to the bone orthotropicity, we analysed the distribution of stress that indicates

fracture of the mandibular angle and condyle, after the simulation of frontal and lateral blow. We also estimated the influence of compressive and tensile stresses on fracture development, by calculating appropriate failure indices. 2. Material and methods 2.1. Geometry A human male mandible, aged between 30 and 40 years, with present M3, was selected from the collection of the Laboratory for Anthropology, Faculty of Medicine, University of Belgrade. The mandible was imaged with diagnostic computed tomography (CT) (Siemens Somatom Sensation 16) in transversal planes, in slices of 0.75-mm thickness. Reconstruction of 3D model from the CT scans (Fig. 1a) was performed through a several steps by using Mimics software, version 10 (Materialize, Leuven, Belgium). The first step was obtaining the mask of cortical bone. Next, the mask of trabecular bone of the mandible was created; and finally, the mask of teeth was created. By using Mimics STL þ module, all masks were converted into the stereolithography (STL) format. The REMESH module attached to Mimics was used to reduce the number and to fix the quality of the triangles that were not appropriate for the finite element analysis. From CT scans of a human mandible with normally erupted M3, two additional virtual models were generated: a model with partially impacted M3 and a model without M3 (Fig 1b). For the generation of the last two mandibular models, an adequate positioning and removal of the lower third molar (M3) was realized by converting the pixels of the M3 from initial tooth structure mask to the masks of cortical and medullary bone, in each CT slice, with respect to the anatomic structure. The models were designed as symmetrical, concluding that the contralateral side is based on the mirror imaging to avoid the effect of possible different situations on the result. Model 1 represents the human mandible with completely erupted M3 in vertical position. Model 2 represents the human mandible with partially impacted M3 in mesioangular position. Model 3 represents the human mandible without M3. The STL files of all three developed models were imported into CATIA V5 softmes, Velizy-Villacoublay, France) ware, version R20 (Dassault Syste and converted into the NURBS surfaces using Digitized Shape Editor and Quick Surface Reconstruction modules. Obtained solid models were exported to ANSYS software, version 14.5.7 (SASI, Canonsburg, PA, USA) for producing finite element mesh and structural analysis. 2.2. Meshing and material characteristics Facial and lingual cortical bone of the mandible was divided into the 31 anatomical zones, as it was previously suggested in the literature (Schwartz-Dabney and Deschow, 2003). The zones of cortical bone were generated by grouping areas with similar values of Young's modulus of elasticity (adopted from literature) and thickness measured directly from the models (Fig. 1d and e). Young's modulus (E) and Poisson's ratio (n) are experimentally estimated characteristics of the materials that determine its mechanical behaviour. Young's modulus is a measure of the stiffness of an elastic material which, over Hooke's Law “s ¼ Eε”, describes the ratio between stress “s” (force per unit area) and strain “ε” during the elastic deformation. Poisson's ratio is the fraction of expansion divided by the fraction of compression, for small values of these changes (Pruitt and Chakravartula, 2011). By using an ANSYS Meshing module, the models were discretized into the very dense tetrahedron volume mesh. The number of finite elements for Model 1, Model 2, and Model 3 was 1.706.616, 1.726.999, and 1.673.931, respectively.



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Fig. 1. Generation of the three mandibular models: a,b; Boundary conditions, muscle support, and simulation of the frontal and lateral blow: c; Defining the zones of orthotropicity: 31 zones of cortical bone were generated by grouping areas with similar values of Young's (adopted from literature) module and thickness measured directly from the models: d,e.

Material properties for each of the zones of facial and lingual cortical bone are given in Table 1, presenting the following mechanical characteristics of the orthotropic zones: elastic moduli (E), Poisson's ratios (n), and shear moduli (G) in GPa for human dentate mandible. Besides the parameters presented in Table 1, mechanical properties of bone tissue include tensile, compressive, and shear

strength. Since cortical bone has anisotropic structure, its strength significantly depends on the orientation of osteons to the direction of load (Nomura et al., 2003). Here, the values of compressive and tensile ultimate strength in the direction of osteons were sc3 ¼ 199:5 MPa and st3 ¼ 138 MPa, respectively. The strength in the plane orthogonal to the osteon axis was approximately the

Table 1 Mechanical characteristics of the orthotropic zones of facial and lingual cortical bone: Elastic moduli (E), Poisson's ratios (n) and shear moduli (G) in GPa for human dentate mandible.The numbers given in the subscript (eg. E1, n12, G12) are related to the orthotropy and indicate the directions of the three orthogonal axes: x, y, and z. 2 3 3 2 sxx sxy sxz s11 s12 s13 4 s21 s22 s23 5 or 4 syx syy syz 5 szx szy szz s31 s32 s33 Zone

E1 GPa

E2 GPa

E3 GPa

n12 ¼ n21

n13 ¼ n31

n23 ¼ n32

G12 ¼ G21 GPa

G13 ¼ G31 GPa

G23 ¼ G32 Gpa

1F 2F 3F 4F 5F 6F 7F 8F 1L 2L 3L 4L 5L 6L 7L 8L

11.51 12.98 11.35 14.15 12.55 13.60 14.00 13.20 12.78 12.46 12.65 12.65 12.64 12.70 13.25 12.65

15.38 18.03 18.05 20.15 19.27 18.10 19.55 18.00 17.31 17.69 19.40 19.20 18.02 17.35 17.25 17.75

20.00 23.22 20.10 28.15 22.40 26.10 28.55 25.95 20.98 20.31 22.60 26.55 23.02 24.55 25.50 24.50

0.20 0.22 0.15 0.27 0.19 0.26 0.27 0.26 0.21 0.19 0.20 0.21 0.26 0.25 0.24 0.21

0.41 0.428 0.48 0.34 0.46 0.37 0.325 0.37 0.45 0.46 0.445 0.39 0.32 0.34 0.32 0.40

0.33 0.32 0.34 0.27 0.32 0.28 0.325 0.265 0.34 0.35 0.32 0.297 0.26 0.235 0.25 0.30

4.57 5.10 4.70 5.15 5.10 5.10 5.20 5.05 5.08 5.07 5.05 5.02 4.80 4.75 5.20 5.05

4.98 5.65 5.10 5.80 5.55 5.50 5.75 5.55 5.65 5.39 5.45 5.40 5.10 5.50 5.40 5.15

6.57 7.67 7.25 8.05 7.70 7.60 7.65 7.45 7.25 7.25 7.75 7.20 6.85 7.40 7.10 7.30

1F(L) ¼ Symphisis (basis þ pars alveolaris); 2F(L) ¼ Body (basis þ pars alveolaris); 3F(L) ¼ Angle (inferior part); 4F(L) ¼ Angle (superior and middle part); 5F(L) ¼ Ramus (middle and frontalpart); 6F(L) ¼ Posterior ramus and a part of inferior border of the angle region; 7F(L) ¼ Coronoid process; 8F(L) ¼ Condylar process.


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same: compressive strength sc1 zsc2 ¼ 133 MPa, and tensile strength st1 zst2 ¼ 92 MPa. Shear ultimate strength in the plane of orthotropy and without the plane were s23 zs13 ¼ 79:5 MP and s12 ¼ 53 MPa, respectively. Material properties of medullary bone and teeth were assumed to be isotropic (medullar bone: Young's modulus: 1.37 GPa, Poisson's ratio 0.30; teeth: Young's modulus 18.60, Poisson's ratio 0.31) (Lotti et al., 2006; Bezerra et al., 2013). 2.3. Boundary conditions Boundary conditions, sketched in Fig. 1c, were taken from the literature (Bezerra et al., 2013). The most posterior and superior part of the mandibular condyles were fixated in all degrees of freedom (Fig. 1c, black). Movement of molars 1, 2, and 3 was constrained in the vertical direction (in order to simulate closed jaw). Since the jaw is capable of motion on all three axes, there are several muscles in place to facilitate the movement (Fig 1c, blue). Considered muscles were the temporal muscles, masseter muscles, medial and lateral pterygoid muscles, and depressor musclesdthe main muscles for closing or elevating the jaw. These muscles were modelled as springs with no resistance during compression. Spring tension stiffness values were taken from the literature: masseter muscle ¼ 16.35 N/mm, lateral pterygoid muscle ¼ 12 N/mm, medial pterygoid muscle ¼ 15 N/mm, anterior temporal muscle ¼ 14 N/ mm, posterior temporal muscle ¼ 13 N/mm, and depressor muscles ¼ 10.9 N/mm (Meyer et al., 2002; Müftüand Müftü and Müftü, 2006). Lines of action for masticatory muscles were modelled as described previously (Kober et al., 2004). A blunt trauma with a magnitude of 2000 N was applied perpendicularly to

the frontal plane and laterally, on a circular area 1 cm in diameter (Fig 1c, red). Force intensity of 2000 N is representative of a punch, and was used in previous FEA studies of the mandible (Takada et al., 2006; Bezerra et al., 2013; Antic et al., in press). 2.4. Structural strength analysis After performing the FEA, the effective von Mises stresses were estimated. Effective or von Mises stress is a measure of the intensity of the multiaxial stress state. If the von Mises stress exceeds the experimentally determined ultimate strength, the material ruptures at that location loads (Pruitt and Chakravartula, 2011). Since von Mises stress cannot be experimentally measured, the mentioned material characteristics (elastic moduli, E; Poisson's ratios, n; and shear moduli, G) and constitutive relations were used by FEA to numerically calculate the stress distribution over a complete structure, and thus estimate places that may rupture under the given loads. The fracture risk for each of the developed models was estimated by using the maximum principal stress criterion (MPSC) (Gross and Seelig, 2011). According to the MPSC, it is assumed that failure occurs when the maximum principal stress exceeds the tensile strength sTS or when the minimum principal stress is less than the compressive strength sCS . Therefore, the failure index (FI) was defined via principal stress s1 (maximal tensile stresses) and s3 (maximal compressive stress) as: FI ¼ sPS =sSM , where sPS is the principal stress generated in the material and sSM is the tensile or compressive strength of the material (if sPS > 0 then sSM ¼ sTS and if sPS is negative then sSM ¼ sCS ). As it may be noted, FI is the dimensionless coefficient comparable to 1; the value FI ¼ 1

Fig. 2. Chromatic distribution of von Mises equivalent stress on the three mandibular models, in the case of frontal blow (A: a) lateral aspect of the mandible; b) posterior aspect of the condyle), and lateral blow (B: a) lateral aspect of the mandible; b) internal aspect of the right mandibular angle and ramus).



corresponds to initialization of the failure (which is typically interpreted as forming of flaw) and the value of FI > 1 corresponds to failure (forming of macro-crack). 3. Results The results are based on chromatic analysis of the distribution of effective (von Mises stress), compressive, and tensile stresses, and on calculating the maximum effective stresses in the regions of interest. The influence of the M3 resulted with differences in the distribution of stress among the studied models. Fig. 2 is a chromatic presentation of the distributed von Mises stress on each of the three models, in cases with simulated frontal (2aec) and lateral blow (2def). In the frontal blow, the stress mostly concentrated at the point of impact, in the angular region that surrounds the M3, and on the posterior part of the condyle. In the angle region, the highest stress was measured at Model 2, followed by the Model 1 and Model 3. In contrast, the stress level measured in condylar region showed an opposite decreasing order among the models: Model 3 > Model 1 > Model 2. Comparison of the angle and condyle in each case revealed higher levels of stress in the angle region of the models 1 and 2, contrary to Model 3, where condyle region showed higher stress (Table 2). After simulation of the lateral blow, maximum stress concentrated at the point of impact, on the ipsilateral condylar regions of all the three models, and on the ipsilateral lingual aspects of the angle, followed by contralateral condyle and angle. In the angle region, the highest stress was measured at Model 2, followed by Model 1 and Model 3. The stress level measured at the ipsilateral condylar region showed the following decreasing order among the models: Model 2 > Model 1 > Model 3. In contrast, the contralateral condylar region showed an opposite decreasing order of stresses among the models: Model 3 > Model 1 > Model 2. Comparison of the angle and condyle in each case with lateral blow revealed the following (Table 3). On the ipsilateral side, higher stress was recorded in the condylar region of all the three models. The contralateral side showed a different distribution of stress among the models. The stress levels were higher in the angle regions of Model 1 and Model 2, but at Model 3 higher stress was recorded in the condylar region. In order to perceive the type of the stresses when submitting the models to the frontal and lateral blow, analysis of the principal

Table 2 Maximum von Mises equivalent stress measured in the regions of mandibular angle and condyle in the case of frontal blow. Model 1 Region of the mandible von Mises stress (Mpa)

Model 2

Model 3

Angle

Condyle

Angle

Condyle

Angle

Condyle

109.65

79.69

114.13

78.5

77.3

93.5

Table 3 Maximum von Mises equivalent stress measured in the regions of ipsilateral and contralateral angle and condyle in the case of lateral blow. Region of the mandible

Von Mises stress (Mpa) Model 1

Model 2

Model 3

Ipsilateral angle Ipsilateral condyle Contralateral angle Contralateral condyle

456.8 579.16 451.45 448.79

483.06 632.05 458.37 447.51

437.67 511.93 413.1 473.12

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stresses with calculation of the failure indices FI ðs1 Þ i FI ðs3 Þ on all three mandibular models was performed. This form of analysis is presented on Figs. 3 and 4. Fig. 3 shows the chromatic presentation of the principal stresses,s1 ; s3 and failure indices FI ðs1 Þ and FI ðs3 Þ of the three mandibular models in the case of a frontal blow, and Fig. 4 in the case of a lateral blow. In the case of a frontal blow, compressive stress (s3 ) was the highest at the point of impact, in the region of the angle, and on the posterior aspect of the condyle, bilaterally, but without failure in all three models (Fig. 3A, B). Tensile stress (s1 ) was detected in the angle region superiorly to the zone of compression, in the retromolar area, and on the lingual aspect of the symphysis. Failure ðFI ðs1 Þ > 1Þ occurred only in the retromolar area of Model 2 (Fig. 3C, D). In the case of a lateral blow, compressive stresses were the highest and caused the failure at the point of impact, on the lingual side of ipsilateral condyle, facial side of contralateral condyle and in the contralateral angle region. The failure index FI ðs3 Þ was the highest at Model 2, followed by Model 1 and Model 3 (Fig 4A, B). Dominant critical zones of tensile stresses (s1 ), with the failure, were the ipsilateral condyle and ipsilateral angle region, distally to the M3. The failure index FI ðs1 Þ was the highest at Model 2, followed by Model 1 and Model 3 (Fig. 4C, D). 4. Discussion The angle and the condyle are frequently fractured regions of the mandible. Depending on the studied population, angle fractures comprise approximately 12%e32% of all mandibular fractures and condylar 19.9%e43% (Dongas and Hall, 2002; Zix et al., 2011; Chrcanovic et al., 2012; Jung et al., 2014). As possible influential factors, the characteristics of trauma, bone tissue quality, and type of dental impaction were suggested. Given the discordant clinical data and limitations of experimental studies on human mandibles, the present study was based on numerical simulations and virtual models obtained by the use of FEA as an applied methodology. In order to obtain the most realistic models, the geometric shape of the mandible was obtained from CT scans, including the modelling of masticatory muscles with respect to their anatomic insertion and position. Material properties were reproduced with great similarity to the human mandible, with respect to the bone orthotropicity. CT scan used for creation of the models were obtained from a male, dentate mandible, aged between 30 and 40 years. In the epidemiological studies related to the mandibular trauma (Dongas and Hall, 2002; Halmos et al., 2004 Zix et al., 2011; Chrcanovic et al., 2012; Thangavelu et al., 2010; Jung et al., 2014), there are very inhomogenous samples regarding the patients' age, ranging from 15 to 80 years, with the pick between 16 and 40 years. The mandible used in the study could not represent the whole trauma patient group, but partly covers the most critical group. Analysis of the material properties of the mandibular cortical bone revealed that zones with higher values of Young's modulus of elasticity comprise predominantly the regions of the angle, condylar, and coronoid process (zones: 4F, 6F, 7F, 8F, 4L, 6L, 7L, 8L) (Table 1). This suggests that these regions are the most rigid but also the most brittle regions of the mandible, which might also be one of the factors contributing to their increased fragility. In addition, we created a new division of the mandible, based on the values of Young's modulus of elasticity, that comprises 15 zones of different rigidity symmetrically distributed on the facial and lingual cortex (Fig. 1). Clinical data suggested that the presence and the position of an M3 influenced the risk of angle and condyle fractures. In the presence of an M3, the fragility of the angle increases, whereas the


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Fig. 3. Chromatic distribution and appropriate failure indices of compressive (A, B) and tensile stresses (C, D) on the three mandibular models, in the case of frontal blow: a) lateral aspect of the mandible; b) posterior aspect of the condyle.



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Fig. 4. Chromatic distribution and appropriate failure indices of compressive (A, B) and tensile stresses (C, D) on the three mandibular models, in the case of lateral blow: a) lateral aspect of the mandible; b) internal aspect of the right mandibular angle and ramus.


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condylar region becomes more resistant to fracture (Iida et al., 2005; Zhu et al., 2005; Inaoka et al., 2009; Patil, 2012). Halmos et al. (2004) reported higher risk of angle fractures in cases with partially impacted M3. Thangavelu et al. also observed an association between higher incidence of angle fractures and partially impacted M3s, specifically class IIB and mesioangular position (Thangavelu et al., 2010). These data have influenced the selection criteria for the three models presented in this study. The results that we obtained confirmed clinical data of higher angular fragility in the presence of an M3, in the both cases, the frontal and lateral blows. Futhermore, in the case of a frontal blow, condylar fragility decreased with the M3, supporting clinical data. However, in the case of a lateral blow, the M3 contributed to the decreased condylar fragility only at the contralateral side. The ipsilateral condyle showed increased fragility in the presence of M3. We found that fully erupted M3contributed to the weakness of the angle, in accordance with the FEA study of Bezerra et al. (2013). Analysis of the case with partially impacted M3 confirmed clinical findings that the position of the M3 also influence the pattern of angle and condylar fractures (Bezerra et al., 2011). The von Mises stress distribution, in the case of a frontal blow, showed condyles as weak points when the M3 was absent. In contrast, with a fully erupted M3, the angle regions were more fragile than the condyles, and this fragility increased in the case of partially impacted M3. In the case of lateral blow, both the angle and condyle on the ipsilateral side showed higher fragility in comparison to the angle and condyle on the contralateral side. The ipsilateral condyle was more fragile than the ipsilateral angle, irrespective of M3, whereas on the contralateral side the condyle was more fragile than the angle only in the absence of M3. Comparison of the models based on the principal stresses and failure indices, revealed that in the frontal blow tensile stress in the retromolar region caused the failure, but only in the case with a partially impacted M3. Compressive stress did not cause a failure, but with higher force intensity, failure would probably occur at the most critical regions. In the lateral blow, the failure was caused by compressive stresses at the point of impact and contralateral side, and by tensile stresses at the ipsilateral side. Tensile stresses were more critical for the fracture when compared to the compressive stresses, because of higher failure indices. Both angle regions and the ipsilateral condyle expressed the greatest fragility in the case with partially impacted M3, whereas the contralateral condyle showed the greatest fragility in the absence of M3. However, the fracture pattern in the lateral blow might also be influenced by the surface area at the point of impact and its precise location (lateral symphysis/body/angle), which should be the subject of further investigation. In addition, with higher force intensity, especially when applied to the small surface area, the fracture will occur at the point of impact, which could also influence the pattern of mandibular angle and condylar fractures. In the case of a frontal blow, failure at the point of impact probably will not change the fracture pattern in the angle and condylar regions. In the case of a lateral blow, the failure at the point of impact will cause the indirect fracture on the contralateral side with greater probability than on the ipsilateral side. This is because a jaw fractured at the impact point acts like a lever. In the case of a frontal blow, the length of the lever arms is approximately equal. In the case of a lateral blow, a longer arm is that on the contralateral side, contributing to the higher moment of the force torque, which would cause a failure. This could be an explanation for the frequently seen fracture pattern in clinical practice: mandibular body þ contralateral condyle/angle region.

In the present study, we considered a case with a generally impacted third molar. It is familiar that cases with a third molar impacted partially through the lingual or buccal cortex of the mandible are possible. Any discontinuation of the lingual or buccal cortex might act as a weak point and contribute to the increased fragility of the angle region, so this should be the point of interest in future FEA studies. 5. Conclusions Both the presence and the position of the M3 influence the fracture pattern of the mandibular angle and condylar regions. This influence is recorded in both analysed trauma situations, namely, in the case of a frontal blow and in the case of a lateral blow. In the frontal blow, a partially impacted M3 contributes to the increased tensile stress in the retromolar region and causes an angle fracture. In the absence of an M3, the condyle becomes more fragile due to compressive stress at the posterior aspect, but fracture will occur after applying force of a higher intensity. In the lateral blow directed to the mandibular body, fracture could be expected at the ipsilateral condyle, irrespective of M3, due to increased tensile stress. However, concentrated compressive stress could cause a fracture at the point of impact, and on the contralateral side: with M3, especially partially impacted in the angle region, and without M3 in the condylar region. Conflict of interest statement None of the authors or the authors' institutions had financial or personal relationships with other people or organisations that inappropriately influence (bias) his or her actions. There are no conflicts based on personal relationships, academic competition, or intellectual passion. All authors have viewed and agreed to the submission. Acknowledgements The authors acknowledge support from the Ministry of Science of the Republic of Serbia: III45005, III41007. References Antic S, Saveljic I, Nikolic D, Jovicic G, Filipovic N, Rakocevic Z, et al: Does the presence of an unerupted lower third molar influence the risk of mandibular angle and condylar fractures? Int J Oral Maxillofac Surg, 2015 [in press] Apicella D, Aversa R, Ferro F, Ianniello D, Perillo L, Apicella A: The importance of cortical bone orthotropicity, maximum stiffness direction and thickness on the reliability of mandible numerical models. J Biomed Mater Res B Appl Biomater 93: 150e163, 2010 Bezerra TP, Studart-Soares EC, Pita-Neto IC, Costa FW, Batista SH: Do third molars weaken the mandibular angle? Med Oral Pathol Oral Cir Bucal 16: 657e663, 2011 Bezerra TP, Silva Junior FI, Scarparo HC, Costa FW, Studart-Soares EC: Do erupted third molars weaken the mandibular angle after trauma to the chin region? A 3D finite element study. Int Illofac Surg 42: 474e480, 2013 Bonnet AS, Postaire M, Lipinski P: Biomechanical study of mandible bone supporting a four-implant retained bridge: finite element analysis of the influence of bone anisotropy and foodstuff position. Med Eng Phys 31: 806e815, 2009 Brook IM, Wood N: Aetiology and incidence of facial fractures in adults. Int J Oral Surg 12: 293e298, 1983 Chrcanovic BR, Abreu MH, Freire-Maia B, Souza LN: 1,454 mandibular fractures: a 3year study in a hospital in Belo Horizonte, Brazil. J Craniomaxillofac Surg 40: 116e123, 2012 Chung DH, Dechow PC: Elastic anisotropy and of axis ultrasonic velocity distribution in human cortical bone. J Anat 218: 26e39, 2011 Dongas P, Hall GM: Mandibular fracture patterns in Tasmania, Australia. Aust Dent J 47: 131e137, 2002 Ellis 3rd E, Moos KF, el-Attar A: Ten years of mandibular fractures: an analysis of 2,137 cases. Oral Surg Oral Med Oral Pathol 59: 120e129, 1985 Franklyn M, Field B: Experimental and finite element analysis of tibial stress fractures using a rabbit model. World J Orthop 4: 267e278, 2013


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