Assessment of the Biomechanical Performance of 5 Plating Techniques in Fixation of Mandibular Subcondylar Fracture Using Finite Element Analysis

Accepted Manuscript Assessment of the biomechanical performance of five plating techniques in fixation of mandibular subcondylar fracture using finite element analysis Mhd Ayham Darwich, Mhd Hassan Albogha, Adnan Abdelmajeed, Khaldoun Darwich PII:

S0278-2391(15)01558-X

DOI:

10.1016/j.joms.2015.11.021

Reference:

YJOMS 57045

To appear in:

Journal of Oral and Maxillofacial Surgery

Received Date: 25 September 2015 Revised Date:

19 November 2015

Accepted Date: 19 November 2015

Please cite this article as: Darwich MA, Albogha MH, Abdelmajeed A, Darwich K, Assessment of the biomechanical performance of five plating techniques in fixation of mandibular subcondylar fracture using finite element analysis, Journal of Oral and Maxillofacial Surgery (2015), doi: 10.1016/ j.joms.2015.11.021. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Assessment of the biomechanical performance of five plating techniques in fixation of mandibular subcondylar fracture using finite element analysis Mhd Ayham Darwicha, Mhd Hassan Alboghab,*, Adnan Abdelmajeedc, Khaldoun Darwichd a

Lecturer, Faculty of Biomedical Engineering, Al Andalus University for Medical Sciences, Syria

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Visiting assistant professor, Section of Orthodontics and Dentofacial Orthopedics, Faculty of Dental Science, Kyushu University, Japan

Lecturer, Faculty of Biomedical Engineering, Al Andalus University for Medical Sciences, Syria

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Deparment of oral and Maxillofacial Surgery, Faculty of Dental Medicine, Damascus University, Damascus, Syria

* Corresponding author

3-1-1 Maidashi Higashi-ku Fukuoka, Japan 812-8582

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Tel: +81-80-2697-4108

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Mhd Hassan Albogha

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E-mail: [email protected]

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Assessment of the biomechanical performance of five

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plating techniques in fixation of mandibular subcondylar

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fracture using finite element analysis

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Abstract

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Objective: The aim of this study was to compare performances of five plating techniques

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for fixation of unilateral mandibular subcondylar fracture.

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Methods: Five titanium plating techniques for fixation of condylar fracture were analyzed

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using the finite element method. The modeled techniques were: 1) straight plate, 2) two

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parallel straight plates, 3) two angulated straight plates, 4) a trapezoidal plate, and 5) a

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square plate. Three-dimensional models were generated using patient-specific geometry

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for the mandible obtained from the computerized tomography image of a healthy living

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man. Plates were designed and combined with the mandible and analyzed under a 500 N

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load.

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Results: The single straight plate had the most inferior performance; it presented the

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maximum displacement and strain in cortical bone. The trapezoidal plate induced the least

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amount of strain in cortical bone and was best at resisting displacement.

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Conclusion: We recommend use of the trapezoidal plate for fixation of subcondylar

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fracture.

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Keywords: Condyle fracture; open reduction; rigid fixation; osteosynthesis; finite element

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analysis

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INTRODUCTION

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There is accumulating evidence that open reduction and internal fixation (ORIF) would be

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the treatment of choice for mandibular condyle fractures.1–3 Important factors that play

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roles in the success or failure of ORIF are the design and material of plates utilized to

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deliver rigid fixation of fractured condyles. Biodegradable plates seem to be not

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functionally stable, while titanium plates are recommended for ORIF.4 An issue that

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remains controversial is identifying the best design and configuration of titanium plates to

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maximize the fixation stability.5

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There is evidence that one plate would not be sufficiently stable; therefore, two plates are

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required to achieve stable fixation.6–9 Furthermore, arrangement of the two plates has

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frequently been assumed to provide more favorable performance when they were not

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parallel7, although some authors reported that the opposite is true 10. Recently, frame-like

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plates (square and trapezoid) were introduced and found to provide better stability than

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two straight plates.11,12 However, some authors disagree.4 Therefore, further investigation

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must examine the mechanical performance and efficacy of various plating techniques.

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Finite element analysis (FEA) is a numerical technique that simulates the mechanical

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behaviors of loaded constructions. The technique has been frequently employed in

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biomechanical studies to solve mechanical problems related to bone tissue and has

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proved beneficial in predicting bone mechanical response.13 In this technique, a three

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dimensional model of the construction is discretized into finite number of the elements,

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resulting in three dimensional mesh. The mechanical problem is defined by applying loads

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and constraints to the mesh and then is solved using the appropriate mechanical theory.

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Here we used the finite element modeling technique to compare the rigidity of fixation,

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safety of bone, and integrity of plates between five fixation techniques for mandibular

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subcondylar fracture. Trapezoidal plates appear to provide the best mechanical

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performance in finite element models, manifesting as pronounced rigid fixation, less strain

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in bone, and good integrity of the plates’ materials of construction.

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MATERIALS AND METHODS

1 Generation of 3D models

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A CT image of a healthy living man was used to generate a 3D surface model of a

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mandible (stereolethography format) in 3DSlicer (www.slicer.org). The left mandibular

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condyle was cut at the base to simulate condylar base fracture; hereafter subcondylar

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fracture.14 Three-dimensional models for 5 plating techniques were designed: one straight

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plate, two straight plates in a parallel arrangement, two straight plates with a non-parallel

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arrangement, a trapezoidal plate, and a square-shaped plate; hereafter referred to as

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Techniques 1 to 5, respectively. All plates were of 1 mm thickness and fixed using screws

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of 8 mm length and 2 mm diameter. Plates were merged with the mandible in 5 models

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representing the five techniques, and each was analyzed using the finite element method

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in ANSYS v14 (ANSYS Inc., Canonsburg, PA, USA).

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Finite element analyses

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The models were discretized using tetrahedral elements, and shell elements 2 mm thick

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were added to simulate cortical bone. All materials were considered homogeneous and

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isotropic and their properties were assigned according to previous literature 15–17. Cortical

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bone was assigned 14 GPa for the elastic modulus (E) and 0.3 for the Poisson ratio (ν).

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Cancellous bone properties were assigned 1500 MPa (E) and 0.3 (ν). Titanium alloy

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properties (E = 114 GPa; ν = 0.34) were assigned to plates. A frictionless point-to-point

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gap contact element was used at the bone-titanium interface at the plate and the bone-

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bone interface at the fracture. The contact element was solved using penalty formulation.

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Condyle movement was constrained in all directions, and a load of 500 N was applied to

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the occlusal surfaces of the posterior teeth to simulate the maximum clenching condition.18

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This loading regimen exerts a posteriorly oriented bending moment on the mandible the

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same direction as the bending moment generated under muscular forces.19 The models

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were solved using linear elasticity theory, and each model consisted of roughly 50,000

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elements and 22,000 nodes.

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Post-processing results

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Peak displacement in each model was calculated as a measurement of the rigidity of

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fixation technique, where less displacement was indicative of more rigidity.

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Recent studies have shown that maximum principal strain (MaxPN) is a good indicator of

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mechanical behavior in bone when assessed using finite element modeling.20,21 We

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calculated MaxPN for the elements in cortical and cancellous bone when it exceeded 0.3%,

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the peak MaxPN found in the model of a normal mandible, without fracture, under the

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same conditions.

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Peak von Mises stresses were calculated to predict yielding in the fixation units (plates and

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screws).

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Statistical analysis

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Correlations between mandible displacement and other parameters (i.e., strain in cortical

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and cancellous bone or stress in fixation units) were found to identify rigidity for each

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plating technique. Correlations with p < 0.05 were significant.

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RESULTS

1 Rigidity of fixation

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The five plating techniques models showed different ranges of displacements (Fig. 1A),

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but the trapezoidal plate (Technique 4) was clearly superior. Its peak displacement was

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very close to that seen in the normal mandible model (Fig.1B, 1217 vs. 1162 µm,

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respectively). On the other hand, the single straight plate (Technique 1) showed the

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greatest peak displacement, reaching as much as twice that in the normal mandible model.

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At the fracture line area, all techniques, except Technique 4, yielded micro-motion in the

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range of 100 to 200 µm (Fig. 1C). Only Technique 4 yielded micro-motion less than 100

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µm at the fracture line area.

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Strain in bone

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The normal mandible model predicted a high concentration of strain at the base of the

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condyle neck, a zone where the subcondylar fracture likely onsets under excessive

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nonfunctional loads (Fig. 2). The plating techniques presented distributions of strain more

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extensive than that seen in the normal mandible model (Fig. 2). This extensive distribution

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is remarkable in Technique 1, where strains extended as far as the anterior border of the

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ramus. The least strain distribution was seen in Technique 4, which showed a pattern very

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similar to that seen in the normal mandible, except for focal concentrations of strain around

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the screws.

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von Mises stress in plates

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All plates presented peak von Mises stresses well below 300 MPa (Fig. 3), far less than

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the yield strength of the titanium, which is 880 MPa 17. Although Technique 5 showed the

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lowest von Mises stresses, it did not help improve the rigidity of fixation when compared

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with the other techniques (Fig. 4C).

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Correlation between rigidity and cortical bone strain

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Peak displacement was significantly correlated to the MaxPN in cortical bone (Fig. 4A, P

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<0.05). Technique 1 showed the greatest predicted displacement (2475 µm) and cortical

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bone strain (0.9%) among the models. On the other hand, the one showing the lowest

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predicted displacement (Technique 4, 1610 µm) also expected the least cortical bone

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strain (0.4%). The other parameters (cancellous bone strain and plates’ stress) did not

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show significant correlations to displacement (Fig. 4B-C).

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DISCUSSION

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The base of the condyle is subject to heavy physiological forces 22,23; this phenomena was

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confirmed in our study, where high strain concentrations were present in this area of the

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condyle neck. Therefore, when a fracture is present in the condyle, an adequately rigid

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fixation technique is necessary to secure complete and correct healing. We found that

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various designs and arrangements of plates used for fixation of condyle fractures

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presented significant differences in terms of rigidity and safety of bone.

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There is already a consensus that the one straight plate is not suitable as a condylar

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fracture fixation technique8,9,24,25, but we chose to add this technique to the current study to

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serve as a reference to the other investigated techniques. The one straight plate technique

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not only presented the greatest displacement among our models, but also resulted in

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extensive bone strain contours. On the other hand, the two straight plates technique

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presented slightly better performance for the non-parallel arrangement compared with the

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parallel one. Aquilina et al.10 reported that parallel arrangement had better performance,

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but their conclusion was based on very small difference in displacement (20 microns) that

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may be clinically insignificant.

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An initial means to increase rigidity of fixation might be to increase the number of plates

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and screws, assuming that two plates and 8 screws would be more rigid than a frame-like

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plate and 4 screws. However, our models show that this is not true. The fixation

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techniques showed small differences in stress but significant differences in displacement.

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This finding may imply that rigidity of fixation might be related to a factor other than the

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rigidity of the fixation material itself.

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We found a significant correlation between displacement and strain in cortical bone. A

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similar relationship was found in a previous study on fixation techniques for sagittal split

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ramus osteotomy of the mandible.26 It can be inferred that the fixation technique that

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increases strains in cortical bone is likely to provide less rigid fixation. From this

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perspective, increasing the number of plates or screws not only fails to improve rigidity of

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fixation, but also impairs bone safety and jeopardizes the success of fixation. Impaired

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bone safety might be attributed to the increased number of screws used in the fixation

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technique, which results in more bone removed and replaced with screws, thereby

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weakening the cortical bone. The trapezoidal plate seems to overcome this pitfall. The

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frame shape of the plate seems to provide adequate rigidity, and the relatively small

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number of screws (only 4) minimally affects the rigidity of cortical bone.

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Meyer et al. 12,27 studied compression and tension strain lines in the mandible and

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proposed that osteosynthesis should follow certain ideal lines on the mandible to achieve

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maximum rigid fixation. Adopting this concept, Meyer et al.11 introduced the trapezoidal

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plate as the best design for fixation of subcondylar fracture because it disturbed the bone

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strain lines the least. They attributed its ideal performance to the harmony between its

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lateral arms and the strain lines in the mandible. We found that the lateral arms of

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trapezoidal plate were perpendicular to the contours of displacement and the two bases of

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the plate were parallel to displacement contours. This finding agrees with the principle

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introduced by Meyer et al. that the plates should follow specific lines on the mandible

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surface, and the trapezoidal plate seems to be the best plate to fulfill this principle. De

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Jesus et al.28 indicated that trapezoidal plates and two non-parallel straight plates have

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almost the same amount of displacement. However, another research group 4,29 reported

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results that seemed to negate the claim that the trapezoidal plate performance could be

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better or similar to the two straight plates technique . However, their mechanical tests

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using animal models were different from the real physiological forces. They tested

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displacement of the condyle during anterio-posterior or medio-lateral loading on the

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condyle, but they did not test the displacement under vertical loading, which is the most

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prominent force that acts to displace the fragments of the mandible during mastication.

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Therefore, their findings may not be comparable to those by Meyer et al.11,12

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Interesting characteristics of trapezoidal plates are its relatively small size and the need for

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only four screws to fix it. These characteristics has apparent clinical advantages. The neck

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of condyle has small dimensions and there is small room to place many screws without

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weakening the bone. Using small plates as the trapezoidal plate in combination with

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transoral endoscopic open reduction may reduce the surgical complications that may be

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encountered when much more of the fracture area need to be stripped to place two

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straight plates with eight screws.30,31

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CONCLUSION

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Rigidity of fixation seems to depend primarily on the design and arrangement of plates and

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the way these attributes affect strains in cortical bone. We recommend the use of

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trapezoidal plates for fixation of subcondylar fractures because these plates, in models,

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produced the least amount of strain and therefore the most stable fixation.

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REFERENCES

1 2 1.

Kyzas P a., Saeed A, Tabbenor O: The treatment of mandibular condyle fractures: A meta-analysis. J Craniomaxillofac Surg 40: e438, 2012.

2.

Vesnaver A, Ahčan U, Rozman J: Evaluation of surgical treatment in mandibular condyle fractures. J Craniomaxillofac Surg 40: 647, 2012.

3.

Shiju M, Rastogi S, Gupta P, Kukreja S, Thomas R, Bhugra AK, Parvatha Reddy M, Choudhury R: Fractures of the mandibular condyle – Open versus closed – A treatment dilemma. J Craniomaxillofac Surg 43: 448, 2015.

4.

Pilling E, Eckelt U, Loukota R, Schneider K, Stadlinger B: Comparative evaluation of ten different condylar base fracture osteosynthesis techniques. Br J Oral Maxillofac Surg 48: 527, 2010.

5.

Omezli M, Dayi E: Review of biomechanical experimental studies on different plating techniques of mandibular condyle fractures. Ann Maxillofac Surg 1: 48, 2011.

6.

Choi BH, Kim KN, Kim HJ, Kim MK: Evaluation of condylar neck fracture plating techniques. J Craniomaxillofac Surg 27: 109, 1999.

7.

Wagner A, Krach W, Schicho K, Undt G, Ploder O, Ewers R: A 3-dimensional finiteelement analysis investigating the biomechanical behavior of the mandible and plate osteosynthesis in cases of fractures of the condylar process. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 94: 678, 2002.

RI PT

3 4

6 7

SC

5

9 10 11

M AN U

8

12 13 14 15

20 21

EP

19

22 23 24 25 26 27 28 29 30

8.

AC C

17 18

TE D

16

Tominaga K, Habu M, Khanal A, Mimori Y, Yoshioka I, Fukuda J: Biomechanical Evaluation of Different Types of Rigid Internal Fixation Techniques for Subcondylar Fractures. J Oral Maxillofac Surg 64: 1510, 2006.

31

11

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1 2 3

9.

Parascandolo S, Spinzia A, Parascandolo S, Piombino P, Califano L: Two load sharing plates fixation in mandibular condylar fractures: Biomechanical basis. J Craniomaxillofac Surg 38: 385, 2010.

10.

Aquilina P, Chamoli U, Parr WCH, Clausen PD, Wroe S: Finite element analysis of three patterns of internal fixation of fractures of the mandibular condyle. Br J Oral Maxillofac Surg 51: 326, 2013.

11.

Meyer C, Martin E, Kahn JL, Zink S: Development and biomechanical testing of a new osteosynthesis plate (TCP®) designed to stabilize mandibular condyle fractures. J Craniomaxillofac Surg 35: 84, 2007.

12.

Meyer C, Serhir L, Boutemi P: Experimental evaluation of three osteosynthesis devices used for stabilizing condylar fractures of the mandible. J Craniomaxillofac Surg 34: 173, 2006.

13.

Cristofolini L, Schileo E, Juszczyk M, Taddei F, Martelli S, Viceconti M: Mechanical testing of bones: the positive synergy of finite-element models and in vitro experiments. Philos Trans A Math Phys Eng Sci 368: 2725, 2010.

14.

Loukota R a., Eckelt U, Bont L De, Rasse M: Subclassification of fractures of the condylar process of the mandible. Br J Oral Maxillofac Surg 43: 72, 2005.

15.

Currey J: Cortical bone. In: Black J, Hastings G, eds. Handbook of Biomaterial Properties. London, UK: Chapman Hall, 1998:3–14.

5 6 7

RI PT

4

M AN U

9 10 11

SC

8

12 13 14 15

21 22 23 24 25 26 27 28

16.

EP

20

AC C

17 18 19

TE D

16

Keaveney TM: Cancellous bone. In: Black J, Hastings G, eds. Handbook of Biomaterial Properties. London, UK: Chapman Hall, 1998:15–23.

29 30 31 32

17.

Sarda S, Ginebra M, Rodriguez D, Casals J, Navarro M, Aparicio C, Manero J, Gil F, Planell J, Nilsson M, Fern√°Ndez E: Materials in dental implantology. In: Nata li A, ed. Dental Biomechanics. CRC Press, 2003:69–89.

12

ACCEPTED MANUSCRIPT

1 18.

Braun S, Bantleon HP, Hnat WP, Freudenthaler JW, Marcotte MR, Johnson BE: A study of bite force, part 1: Relationship to various physical characteristics. Angle Orthod 65: 367, 1995.

19.

Eijden TM van: Biomechanics of the mandible. Crit Rev Oral Biol Med 11: 123, 2000.

20.

Schileo E, Taddei F, Cristofolini L, Viceconti M: Subject-specific finite element models implementing a maximum principal strain criterion are able to estimate failure risk and fracture location on human femurs tested in vitro. J Biomech 41: 356, 2008.

21.

Albogha MH, Kitahara T, Todo M, Hyakutake H, Takahashi I: Maximum principal strain as a criterion for prediction of orthodontic mini-implants failure in subjectspecific finite element models. Angle Orthod: 150401112935002, 2015.

22.

Vollmer D, Meyer U, Joos U, Vègh a, Piffko J: Experimental and finite element study of a human mandible. J Craniomaxillofac Surg 28: 91, 2000.

23.

Xiangdong QI, Limin M a, Shizhen Z: The influence of the closing and opening muscle groups of jaw condyle biomechanics after mandible bilateral sagittal split ramus osteotomy. J Craniomaxillofac Surg 40: e159, 2012.

24.

Asprino L, Consani S, Moraes M De: A comparative biomechanical evaluation of mandibular condyle fracture plating techniques. J Oral Maxillofac Surg 64: 452, 2006.

RI PT

2 3 4 5 6

M AN U

8 9 10 11

SC

7

12 13 14 15

20 21 22

EP

19

23 24 25 26 27 28 29 30

25.

AC C

17 18

TE D

16

Choi B-H, Yi, DDS C-K, Yoo J-H: Clinical evaluation of 3 types of plate osteosynthesis for fixation of condylar neck fractures. J Oral Maxillofac Surg 59: 734, 2001.

31

13

ACCEPTED MANUSCRIPT

1 2 3

26.

Albougha S, Darwich K, Darwich M a., Albogha MH: Assessment of sagittal split ramus osteotomy rigid internal fixation techniques using a finite element method. Int J Oral Maxillofac Surg 44: 823, 2015.

27.

Meyer C, Kahn J-L, Boutemi P, Wilk A: Photoelastic analysis of bone deformation in the region of the mandibular condyle during mastication. J Craniomaxillofac Surg 30: 160, 2002.

28.

Jesus GP de, Vaz LG, Gabrielli MFR, Passeri L a., Oliveira T V., Noritomi PY, Jürgens P: Finite element evaluation of three methods of stable fixation of condyle base fractures. Int J Oral Maxillofac Surg 43: 1251, 2014.

29.

Lauer G, Haim D, Proff P, Richter G, Pradel W, Fanghänel J, Pilling E, Gedrange T, Mai R: Plate osteosynthesis of the mandibular condyle. Ann Anat - Anat Anzeiger 189: 412, 2007.

30.

Lauer G, Pradel W, Schneider M, Eckelt U: A New 3-Dimensional Plate for Transoral Endoscopic-Assisted Osteosynthesis of Condylar Neck Fractures. J Oral Maxillofac Surg 65: 964, 2007.

31.

Schön R, Schramm A, Gellrich N-C, Schmelzeisen R: Follow-up of condylar fractures of the mandible in 8 patients at 18 months after transoral endoscopicassisted open treatment. J Oral Maxillofac Surg 61: 49, 2003.

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Figure legends

2 Fig. 1. (A) Displacement contours in the mandible for various techniques. (B) The peak

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values of displacement for various techniques compared to peak displacement in a normal

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mandible. (C) The scale of displacement values is modified to show the displacement

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contours in the condyle neck area.

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Fig.2. Maximum principal strain contours.

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Fig.3. von Mises stress contours in fixation units.

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Fig.4. Spearman correlation test between (A) peak displacement and maximum principal

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strain in cortical bone, (B) maximum principal strain in cancellous bone, (C) and von Mises

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stress in plates. Red curves represent the 95% bivariate normal density ellipses. Narrow

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and diagonally oriented ellipse indicates significant correlation.

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