Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 October 2018 doi:10.20944/preprints201810.0676.v1 1 Type of the Paper (Article) 2 Finite Element Analysis of Adolescent Mandible 3 Fracture Occurring during Accidents 4 Jarosław Żmudzki 1,*, Karolina Panek 2, Grzegorz Chladek 1, Marcin Adamiak 1 and Paul Lipinski 5 3,* 6 1 Faculty of Mechanical Engineering, Institute of Engineering Materials and Biomaterials, Silesian University 7 of Technology, ul. Konarskiego 18a, 44-100 Gliwice, Poland; [email protected] (G.C.); (M.A.) 8 2 Graduate student of materials engineering, Faculty of Mechanical Engineering, Institute of Engineering 9 Materials and Biomaterials, Silesian University of Technology, ul. Konarskiego 18a, 44-100 Gliwice, 10 [email protected] 11 3 LEM3, Université de Lorraine, Ecole Nationale d’Ingénieurs de Metz, 1 route d'Ars Laquenexy, BP 65820, 57 12 078 Metz Cedex 03, France 13 14 * Correspondence: [email protected] (J.Ż); Tel.: +48-32-237-2907; [email protected] 15 (P.L); Tel.: +33 (0)3-72-74-86-46 16 17 18 Featured Application: Authors are encouraged to provide a concise description of the specific 19 application or a potential application of the work. This section is not mandatory. 20 Abstract: The paper aims in assessing risks of mandible fractures consequent to impacts or sport 21 accidents. The role of the structural stiffness of mandible, related to disocclusion state, is evaluated 22 through numerical simulations using the finite element method (FEM). It has been assumed that 23 the quasi-static stress field, due to distributed forces developed during accidents, could explain the 24 common types of mandibular fractures. Geometric model of adolescent mandible was built, upon 25 the basis of medical imaging, in CAD software with distinction between cortical layer and inner 26 spongy bone. The finite element model of disoccluded mandible was next created. Mandibular 27 condyles were supposed jammed in the maxillary fossae. The total force of 700 N, simulating an 28 impact on mandible, has been sequentially applied in three distinct areas: centrally, at canine zone 29 and at the mandibular angle. Clinically most frequent fractures of mandible were recognized 30 through the analysis of maximal principal stress and maximal principal strain fields. Mandibular 31 fracture during accidents can be analyzed at satisfactory level using linear quasi-static FE models 32 for designing protections in sport and transport. The proposed approach can be improved by 33 introducing more realistic interactions between condylar processes and fossae. 34 Keywords: mandible fracture, disocclusion state, finite element analysis, critical blow force 35 36 1. Introduction 37 Injuries in the stomatognathic system, as a consequence of traffic or sports accidents, attained 38 the status of the main public health problem [1]. Following a literature review the authors find that 39 from 76 to 93% of patients who experienced facial wounds suffered mandibular fractures [2,3]. They 40 are mainly located in the condylar neck, in the symphysis and parasymphysis but also in the body 41 and the mandibular angle [4,5]. 42 Studies of tissues under impact forces are essential for research improving safety solutions 43 [6–12]. There are numerous finite element quasi- static analyses of biomechanics of mandible. They 44 concern the force transmission into temporo-mandibular joint (TMJ) [13–16], TMJ implants and bone 45 fixation plates [17–19], distraction osteogenesis [20,21] as also contact phenomena in dental © 2018 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 October 2018 doi:10.20944/preprints201810.0676.v1 2 of 14 46 restorations [22–24] under occlusal forces [25,26] and intra-oral forces of lips and tongue [27,28]. 47 However, numerical studies on risk of mandibular fractures are rarely presented in the literature, 48 although finite element method has been successfully applied in fracture predictions of such bones 49 like femur and tibia [29]. Realistic simulations of deceleration during accidents allow precise 50 determination of dynamic forces. However, they frequently concern greatly simplified bone 51 structures [6,30–32]. Brain injury was the topic of the works [30–32] but the mandible was 52 represented as a simplified structure with average elastic properties of cortical and cancellous bone 53 tissues. However, skull bone answer is depended on its structure and cortical bone layer thickness 54 [33–36] Force transfer to the skull in case of impact to mandible was conducted by Tuchtan et al. [37] 55 taking into account its cortical and cancellous constituents. But the risk of mandibular fracture was 56 not analyzed in this investigation. Simulation and experimental studies [38] show that prediction of 57 fracture localization is possible based on modal vibrational analysis. However, a free-support 58 condition on sponge and stiffness of alveolar processes without periodontal ligament are not 59 consistent with real mandible behavior. Also in the modeling approach developed in works [39,40] 60 the lack of periodontal tooth resiliency makes impossible the analyses of teeth fracture, for example, 61 in design of protections in sport (mouthguards). This fact affects analysis of the mandibular fractures 62 due to incorrect load transfer into bone tissue surroundings excessively stiff alveolar processes [41]. 63 Resiliency of teeth was considered by Bezerra et al. [42] The authors correlated stress concentration 64 around third molars with a high number of fractures [43]. But stresses in bone reached exaggerated 65 value of 180 MPa due to the assumed extreme level of blow force of 250 kgf. Consequently, tendency 66 to the most common fractures of condylar neck was not detectable. Fractures of adolescent mandible 67 during sports are common, despite lower blow forces involved in regards to muscle strengths and 68 body weight. During blow external forces produce stresses, whose distribution in mandible is 69 sensitive to structural stiffness of alveolar processes. In general, the modeling conditions close to real 70 life are crucial for strength analysis but from the other hand they increase computing costs [44]. In 71 this work special attention was paid to mandibular fracture prediction in teenagers. Indeed, they 72 commonly suffer teeth and jawbone injuries during sport and daily activity [45,46]. 73 The aim of this work was to analysis the risk of fracture of adolescent mandible under 74 forces associated with standard accidents. The problem was treated via the FEM simulations based 75 on quasi-static elastic bone answer to a blow on disoccluded mandible. It has been assumed that the 76 quasi-static stress field, due to distributed forces developed during accidents, could explain the 77 common types of mandibular fractures. 78 2. Materials and Methods 79 CAD software (Solidworks) with reverse engineering capability (ScanTo3D) was used for 80 reconstruction of human mandibular surfaces on the basis of an imported stereolithography triangle 81 surface (STL) file model of the 12 years-old adolescent. Thickness of cortical bone layer was 82 estimated basing on average literature data [47]. Teeth were redesigned because the 83 three-dimensional reconstruction of teeth with periodontal ligament and alveolar socket from 84 medical imaging is cumbersome and specialized software is still under development [48]. Teeth 85 roots were simplified and slightly contracted in radial direction leading to an increase of gap 86 between adjacent teeth in the mandible larger than naturally observed. This modification was 87 necessary to avoid problems in mesh generation due to small gaps between adjacent teeth and 88 chosen mean element size. Concerning the hard tissues of teeth, only dentine was taken into account. 89 Enamel was neglected because of a weak influence of this thin layer on stress field in mandible. The 90 resulting FE mesh (Ansys, Workbench) is illustrated (Fig. 1). 91 Mesh involved 558838 nodes and 381189 tetrahedral 10-node elements (Ansys, TET10). 92 Statistics of elements' quality is displayed in Fig. 2a. Poor quality elements (having Jacobean lower 93 than 0.25) are highlighted in Fig. 2b. The elastic, linear and isotropic 30 constitutive law was 94 assumed for all involved tissues. The associated mechanical properties are summarized in Table 1 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 October 2018 doi:10.20944/preprints201810.0676.v1 3 of 14 95 Figure 1. Finite element model of the mandible and cross-section view by the incisor tooth with 96 arrangement of tissues in alveolar processes taking into account periodontal ligament in cortical 97 bone socket. The force of 700 N simulating an impact in XY (occlusal) plane was subsequently 98 applied centrally (FI), at canine zone (CI) and at the mandibular angle (LI). (a) (b) 99 Figure 2. Statistics (a) and location (b) of poor quality elements (with quality parameter lower than 100 0.25). 101 To simulate impact to the mandible, a distributed horizontal force (parallel to occlusal plane 102 XY) of 700N of magnitude was applied [49]. Three load cases were simulated: Frontal Impact (FI) to 103 the mental protuberance (FY = -700N), Impact to Canine (CI) region (FX = -367,73N; FY = 595,63N) 104 and Lateral Impact (LI) to mandibular angle (FX = 700N). The blow force was distributed on the 105 relatively large areas, illustrated in Figure 1, because the study was not addressed to bone split at the 106 impact-concerned cross-sections of mandible. Fixing the appropriate components of displacement 107 vector on the condylar surfaces in contact with the temporo-mandibular discs (red area named "D" 108 in Figure1) eliminated the rigid body motion of the model. 109 Fracture risk of the mandible was evaluated using two simple criteria based on the maximal 110 principal stress and maximal principal strain values, well adapted for quasi-elastic materials such as 111 cortical bones.