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. 2020 Oct 8;15(10):e0240352. doi: 10.1371/journal.pone.0240352

Biomechanical evaluation of unilateral subcondylar fracture of the mandible on the varying materials: A finite element analysis

Bryan Taekyung Jung 1, Won Hyeon Kim 2,3, Byungho Park 4, Jong-Ho Lee 3,5, Bongju Kim 3,*, Jee-Ho Lee 4,*
Editor: Essam Al-Moraissi6
PMCID: PMC7544122  PMID: 33031474

Abstract

Fixation materials used in the surgical treatment of subcondylar fractures contribute to successful clinical outcomes. In this study, we simulated the mechanical properties of four fixation materials [titanium (Ti), magnesium alloy (Mg alloy), poly-L-lactic acid (PLLA), and hydroxyapatite/poly-L-lactide (HA-PLLA)] in a finite-element analysis model of subcondylar fracture. Two four-hole plates were fixed on the anterior and posterior surfaces of the subcondyle of the mandible. In the simulation model of a subcondylar fracture, we evaluated the stress distribution and mechanical deformation of fixation materials. The stress distribution conspicuously appeared on the condylar neck of the non-fractured side and the center of the anterior plate for all materials. More stress distribution to the biologic component appeared with HA-PLLA than with Ti or Mg alloy, but its effects were less prominent than that of PLLA. The largest deformation was observed with PLLA, followed by HA-PLLA, Mg alloy, and Ti. The results of the present study imply the clinical potential of the HA-PLLA fixation material for open reduction of subcondylar fractures.

Introduction

Subcondylar fractures commonly occur at the sigmoid notch of the mandible. Although surgical approaches for open reduction risk facial nerve injury, they present superior results to and fewer complications than closed reduction [1] through a feasible visual field for accurate reduction with internal fixation devices such as mini-plates and screws [2]. However, the subcondyle in particular requires a very difficult surgical approach with limited surgical access due to the presence of the facial nerve. Therefore, surgeons’ experience and fixation materials should be carefully considered for a successful clinical outcome. Fixation materials require mechanical strength as well as biocompatibility. Recently, with the development of biomaterials for the surgical treatment of mandible fractures, composites of unsintered hydroxyapatite particles and poly-L-lactide (u-HA/PLLA) have been used for open reduction, which have led to reliable clinical outcomes in mandibular body fractures [3].

However, few studies to date have reported on HA-PLLA fixation. A previous study [4] simulated a finite-element analysis (FEA) model for open reduction internal fixation of mandibular angle fractures using four different materials to reduce the prevalence of postoperative complications: titanium (Ti), magnesium alloy (Mg alloy), biodegradable polymers such as poly-L-lactic acid (PLLA), and hydroxyapatite/poly-L-lactide (HA-PLLA). The study showed the potential clinical application of HA-PLLA for mandibular angle fractures. Extending the results from the previous study, the assessment of HA-PLLA fixation for unilateral subcondylar fracture may increase the availability of the materials in craniofacial surgery. In the present study, we used FEA to simulate a repaired unilateral subcondylar fracture and calculated the peak von Mises stress (PVMS) and deformation of mini-plates and screws of four materials: Ti, Mg alloy, PLLA, and HA-PLLA.

Materials and methods

Modeling of subcondylar fracture and implant system for GFEA

A mandibular bone model from a previous study was used [5]. The model consists of cortical and cancellous bones, and the thickness of the cortical bone was set to 3 mm, as described in previous literature [6, 7]. Subsequently, the subcondylar fracture was designed to run along a line obliquely connecting the sigmoid notch to the masseter tuberosity using the FEA program (ABAQUS CAE2016; Dassault Systèmes, Vélizy-Villacoublay, France). The screw and mini-plate models were constructed using a computer-aided design program (SolidWorks 2016, SolidWorks; Waltham, MA, USA). The thickness of the mini-plate was 1.0 mm, and the length and diameter of the screw were 6.0 mm and 2.0 mm, respectively (Fig 1).

Fig 1. Dimensions of the implant systems.

Fig 1

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(a) mini-plate, (b) screw.

The subcondylar fracture of the FEA model showed no gap between the fracture lines, assuming bone reduction (Fig 2). Two mini-plates were placed in a triangular shape on the anterior and posterior borders of the condylar neck (Fig 2). The anterior mini-plate was fixed along the coronoid notch, and the posterior mini-plate was fixed along the condylar neck (Fig 2). In our study, four types of models were considered using the material properties of Ti, Mg alloy, PLLA, and HA-PLLA, respectively. The mini-plate and screw for each type were applied with the same material properties. The bone and implant parts were assembled through the FEA program. The implant system and bone models applied were homogeneous, isotropic, and linearly elastic, according to the elastic modulus and Poisson’s ratio. The mechanical properties of the bone and implant systems used were applied by referring to the literature, as presented in Table 1 [8].

Fig 2. Unilateral subcondylar fracture model of the mandible.

Fig 2

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The two four-hole plates and screws are positioned at the right subcondyle while masticatory loading is applied to the non-fractured left first molar.

Table 1. Mechanical properties of implants and bones in finite-element analysis.

Types Elastic Modulus (MPa) Poisson’s Ratio
Titanium 96,000 0.36
Magnesium alloy 45,000 0.29
PLLA (biodegradable)a 3,150 0.46
HA-PLLAb 9,701 0.317
Cortical bone 15,000 0.33
Cancellous bone 1,500 0.3
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aPoly-L-lactic acid

bHydroxyapatite particle/poly-L-lactide

Before applying the loading and boundary conditions, the cortical and cancellous bones, the mini-plate, and the screw were created using mesh generation software (Altair Hyperworks v17.0, Altair Engineering; Troy, MI, USA). The number of elements and nodes in the bone models was set to 997,961 and 207,605 for cortical bone, and 483,548 and 96,868 for cancellous bone, respectively. In the implant system, the elements and nodes were set as 172,732 and 36,089 for the screw, and 119,198 and 26,433 for the mini-plate, respectively.

Loading and boundary conditions for masticatory motion

The rotation and movement of the two mandibular condyles were completely constrained in all directions, as reported in previous studies [9, 10]. The surfaces of the screw and bones, mini-plate and screw, and cortical and cancellous bones were applied using the tie contact condition. The tie contact condition assumed that the interfaces between the cortical and cancellous bones were fully unified or that the bone and implant systems were fully merged. The interfaces between the upper and lower sides of the fracture were assumed to be in a sliding state with a friction coefficient of 0.5 [11]. Masticatory loading was applied to the left first molar with a single node, and the loading range was set from 132–1,000 N. Starting at a load of 200 N, the load was increased at intervals of 100 N until reaching 1,000 N (Fig 2). Maximum stress distributions (MPa) and deformation (mm) were measured for the screws and mini-plates. In the cortical and cancellous bones, the maximum stress and tensile stress distributions were measured. The deformation of the implants and the distance of the fracture gap were measured for every load step ranging from 132 N to 1,000 N.

Our study used the FEA method to construct different models according to design factors and measured stress distribution and displacement for comparative analysis between various models. The FEA model for medical device analysis performs comparative analysis by changing specific designs or material properties except for the same components, such as cortical and cancellous bones [12–15]. Therefore, our study compared single values for each material and did not use statistical analysis.

Results

Tensile stress of the bones and the PVMS of the mini-plate and screw systems with four different materials

The maximal and minimal tensile stresses of the cortical and cancellous bones are shown in Tables 2 and 3 for four different materials. In the Ti system at 132 N of masticatory loading, the maximal and minimal tensile stress of cortical bone were 202.1 MPa and -24.8 MPa, respectively, and those of cancellous bone were 5.76 MPa and -0.83 MPa, respectively. The maximal and minimal tensile stresses of cortical bone in the Mg alloy system were 206.3 MPa and -31.4 MPa, respectively, and those of cancellous bone were 6.69 MPa and -0.67 MPa, respectively. The maximal and minimal tensile stresses of cortical bone in the PLLA system were 144.5 MPa and -27.1 MPa, respectively, and those of cancellous bone were 4.77 MPa and -0.16 MPa, respectively. The maximal and minimal tensile stresses of cortical bone in the HA-PLLA system were 158.1 MPa and -34.2 MPa, respectively, and those of cancellous bone were 4.77 MPa and -0.16 MPa, respectively.

Table 2. Maximal and minimal tensile stresses (MPa) of cortical bone by four different materials at various masticatory loadings on subcondylar fracture.

Masticatory loading Titanium Magnesium alloy PLLA HA-PLLA
Maxa Minb Maxa Minb Maxa Minb Maxa Minb
132 N 202.1 -24.8 206.3 -31.4 144.5 -27.1 158.1 -34.2
200 N 304.2 -37.4 310.1 -47.6 216.3 -41.5 235.9 -51.9
300 N 451.7 -55.9 459.7 -71.5 319.0 -63.1 346.3 -78.1
400 N 596.3 -74.4 605.6 -95.4 418.3 -85.0 451.9 -104.4
500 N 738.0 -92.8 748.1 -119.5 514.3 -107.2 553.2 -130.7
600 N 876.8 -111.2 887.1 -143.6 607.1 -129.5 650.4 -157.0
700 N 1012.8 -129.5 1022.8 -167.8 696.9 -151.9 743.7 -183.3
800 N 1146.1 -147.7 1155.3 -192.0 783.9 -174.2 833.3 -209.4
900 N 1276.7 -165.8 1284.5 -216.2 868.0 -196.3 919.5 -235.3
1,000 N 1404.7 -183.9 1410.7 -240.5 949.5 -218.4 1002.5 -261.0
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aMaximal tensile stress

bMinimal tensile stress

HA-PLLA, hydroxyapatite/poly-L-lactide; PLLA, poly-L-lactic acid.

Table 3. Maximal and minimal tensile stresses (MPa) of cancellous bone by four different materials at various masticatory loadings on subcondylar fracture.

Masticatory loading Titanium Magnesium alloy PLLA HA-PLLA
Maxa Minb Maxa Minb Maxa Minb Maxa Minb
132 N 5.76 -0.83 6.69 -0.67 4.77 -0.16 6.32 -0.46
200 N 8.68 -1.25 10.06 -1.02 7.16 -0.23 9.45 -0.68
300 N 12.90 -1.86 14.91 -1.51 10.61 -0.35 13.90 -1.01
400 N 17.03 -2.46 19.64 -2.01 13.96 -0.46 18.15 -1.31
500 N 21.07 -3.06 24.25 -2.49 17.24 -0.56 22.23 -1.61
600 N 25.02 -3.64 28.73 -2.97 20.43 -0.66 26.12 -1.89
700 N 28.89 -4.22 33.08 -3.44 23.55 -0.74 29.85 -2.15
800 N 32.67 -4.79 37.33 -3.90 26.59 -0.81 33.43 -2.41
900 N 36.37 -5.35 41.46 -4.36 29.56 -0.86 36.84 -2.64
1,000 N 39.99 -5.91 45.49 -4.81 32.45 -0.92 40.10 -2.87
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aMaximal tensile stress

bMinimal tensile stress

HA-PLLA, hydroxyapatite/poly-L-lactide; PLLA, poly-L-lactic acid.

In each of the four different materials, the stress concentration phenomena of the cortical and cancellous bones were the same in the left mandibular condylar neck (Fig 3a, 3d, 3g and 3j). The conspicuous stress concentration appeared at the left condylar neck in the PLLA compared to other materials (Fig 3g). The tensile stress distribution of the cortical bone was highest for the Mg alloy, followed by Ti, HA-PLLA, and PLLA. The stress distribution was similar between Ti and Mg alloy and between HA-PLLA and PLLA (Tables 2 and 3). On the other hand, the tensile stress distribution of cancellous bone was highest for the Mg alloy, followed by HA-PLLA, Ti, and PLLA. The stress distribution of the screw hole in the bones was higher in the anterior screw hole than in the posterior hole. Facing the fracture line, the contact area of the screw hole experienced compressive stress, and tensile stress occurred on the opposite side (Fig 3a, 3d, 3g and 3j).

Fig 3. Distribution of stress in the subcondylar fracture model according to material.

Fig 3

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Left column, stress on mandibular bones; middle column, stress on the mini-plates; right column, stress on the screws. HA-PLLA, hydroxyapatite/poly-L-lactide; PLLA, poly-L-lactic acid.

In the Ti system, the PVMS values of the mini-plate and screw were 457.81 MPa and 369.78 MPa, respectively (Table 4). In the Mg alloy system, the PVMS values of the mini-plate and screw were 358.87 MPa and 292.76 MPa, respectively (Table 4). The stress concentration was shown at the upper second screw hole of the anterior plate (Fig 3b and 3e) and the necks of all screws, which was especially conspicuous at the upper second screw (Fig 3c and 3f). In the PLLA system, the PVMS values of the mini-plate and screw were 104.34 MPa and 103.53 MPa, respectively (Table 4). The stress distribution on the implant system was similar to that on the Ti and Mg alloy systems (Fig 3h and 3i). The pattern of stress distribution on the screw was similar to that in the Ti and Mg alloy systems, but with lower intensity (Fig 3i). The PVMS values of the mini-plate and screw in the HA-PLLA system were 189.17 MPa and 167.53 MPa, respectively (Table 4). The results were remarkably lower than those for either the Ti or Mg alloy systems but higher than those for PLLA (Fig 3l). The stress distribution at the plates was similar to that in the other groups (Fig 3k), and the pattern of PVMS was similar to that of PLLA at the screw (Fig 3l).

Table 4. Peak von Mises stresses of different fixation systems with 132 N of masticatory loading on subcondylar fracture.

Types Titanium Magnesium alloy PLLA HA-PLLA
Plate 457.81 358.87 104.34 189.17
Screw 369.78 292.76 103.53 167.53
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HA-PLLA, hydroxyapatite/poly-L-lactide; PLLA, poly-L-lactic acid.

Deformation of materials during masticatory loading

The deformation of the mini-plates and screws with the PLLA material was higher than that of Ti, Mg alloy, or HA-PLLA. The largest deformations of the implant systems were in the order of PLLA, HA-PLLA, Mg alloy, and Ti. The deformation in all materials did not exceed 0.4 mm (Table 5 and Fig 4).

Table 5. Deformation (mm) of implant systems (mini-plate and screw) under loading conditions according to the four different materials.

Masticatory loading (N) Titanium Magnesium alloy PLLA HA-PLLA
Screw Plate Screw Plate Screw Plate Screw Plate
132 0.017 0.017 0.018 0.022 0.050 0.061 0.034 0.036
200 0.023 0.026 0.027 0.033 0.075 0.091 0.051 0.054
300 0.033 0.038 0.041 0.049 0.112 0.132 0.076 0.080
400 0.042 0.051 0.054 0.065 0.149 0.172* 0.100 0.106
500 0.051 0.063 0.067 0.080 0.187* 0.209* 0.124 0.131
600 0.060 0.075 0.079 0.095 0.224* 0.246* 0.147 0.157*
700 0.068 0.087 0.092 0.110 0.261* 0.282* 0.170* 0.183*
800 0.076 0.098 0.104 0.124 0.299* 0.319* 0.193* 0.208*
900 0.083 0.110 0.116 0.138 0.336* 0.355* 0.216* 0.232*
1,000 0.090 0.121 0.128 0.152* 0.374* 0.391* 0.235* 0.257*
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*Fixation deformation > 0.15 mm. HA-PLLA, hydroxyapatite/poly-L-lactide; PLLA, poly-L-lactic acid.

Fig 4. Deformation of fixation materials upon masticatory loading in the subcondylar fracture simulation.

Fig 4

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The fixation systems by all four materials showed linearly increasing deformation trends from 200 N to 1,000 N. HA-PLLA, hydroxyapatite/poly-L-lactide; PLLA, poly-L-lactic acid.

Ti and Mg alloy fixations displayed a deformation trend that was relatively linear as masticatory loading increased. In addition, the deformation of PLLA and HA-PLLA both showed a linearly increasing trend. The slope increased at 200 N in all materials (Fig 4).

Distance of the fracture gap during masticatory loading

The largest gap distance of the fracture site was observed for PLLA, followed by HA-PLLA, Mg alloy, and Ti (Table 6 and Fig 5). The distance of the fracture gap between bones increased linearly with respect to increased masticatory loading regardless of material.

Table 6. Gap distance (mm) between fracture surfaces under loading conditions according to four different materials.

Masticatory loading (N) Titanium Magnesium alloy PLLA HA-PLLA
132 0.054 0.074 0.200 0.145
200 0.082 0.111 0.299 0.218
300 0.121 0.165 0.443 0.322
400 0.160 0.217 0.582 0.423
500 0.198 0.268 0.717 0.522
600 0.235 0.318 0.848 0.618
700 0.271 0.367 0.976 0.712
800 0.306 0.415 1.100 0.803
900 0.341 0.466 1.221 0.892
1,000 0.375 0.507 1.339 0.979
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HA-PLLA, hydroxyapatite/poly-L-lactide; PLLA, poly-L-lactic acid.

Fig 5. Gap distance of two fragment parts upon masticatory loading in the subcondylar fracture simulation.

Fig 5

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Regardless of material, the gap distance showed an increasing trend. HA-PLLA, hydroxyapatite/poly-L-lactide; PLLA, poly-L-lactic acid.

The gap distance became wider as the masticatory loading increased regardless of material (Fig 6). In all materials, contact between the posterior fracture surfaces occurred as masticatory loading increased from 132 N (Fig 5).

Fig 6. Gap distance of fixation materials upon masticatory loading in the subcondylar fracture simulation.

Fig 6

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HA-PLLA, hydroxyapatite/poly-L-lactide; PLLA, poly-L-lactic acid.

Discussion

Ti mini-plates and screws are the standard fixation material for facial bone trauma, with many supportive results from previous studies [16]. Ti is a desirable material because of its mechanical strength and higher biocompatibility compared to other metallic materials, such as vitallium [17, 18]. Despite these advantages, Ti fixation occasionally fails due to postoperative inflammation and thermal hypersensitivity [19, 20]. Therefore, the demand from surgeons for biodegradable materials has increased because they are expected to achieve adequate stability for bony union while still resorbing in a timely fashion [16]. A previous study assessed the stability of unilateral mandibular angle fracture reduction using four different materials [4], which showed that HA-PLLA fixation could be a reasonable alternative. Extending this idea to the subcondylar region, we simulated stress and deformation of a unilateral subcondylar fracture with fixation by various materials using FEA. For the positioning of the screws and the plate, previous studies demonstrated better stability using the double mini-plate fixation technique than a single-plate fixation technique for mandibular condylar fractures [21–23]. In the subcondylar area, the anterior part of the condylar process experiences tensile strains, while the posterior border experiences compressive strains [24, 25]. Ideally, two mini-plates should be placed in a triangular manner where one is applied at the posterior border of the condylar neck and the second is applied along the anterior border [24, 25]. At least two screws should be engaged on each fracture side to stabilize the fixation until it heals completely against rotation [26]. Therefore, in the FEA model of this study, the anterior four-hole mini-plate was fixed superiorly and inferiorly along the coronoid notch, while the posterior four-hole mini-plate was placed along the condylar neck and ramus. We kept anatomical conditions consistent with those of a previous study. For the mini-plate and screw design, we maintained consistency with unified concepts regardless of material in accordance with previous studies [4, 6, 7].

We assumed a force of 132 N at 1 week after surgery, 300 N at 6 weeks after surgery, and 700 N in the mastication loading of healthy adults based on previous studies [4, 10, 27]. According to these analyses, we noticed that the non-fractured side experienced more masticatory force than the fractured side during the healing period. Similar to the previous unilateral angular fracture study, we increased the masticatory loading from 132 N to 1000 N in increments of 100 N at the first molar on the non-fractured side. The upper value of the simulation in this study far exceeds the masticatory loading force of 700 N reported by Ferrario et al. [28] because our goal was to measure stress distributions and deformations of various fixation materials under extreme conditions.

In the FEA model of the mandible, stress was distributed on the condylar neck of the non-fractured side and was more conspicuous in the biodegradable PLLA and HA-PLLA models rather than the metal Ti and Mg alloy groups (Fig 3a, 3d, 3g, and 3j).

The PVMS values of the mini-plates and screw with the Ti and Mg alloy materials were over 1.5 times that of the maximal tensile stress of the cortical bone. The PVMS values of the mini-plate and screw with HA-PLLA were slightly greater than the maximal tensile stress of the cortical bone, whereas they were smaller than the maximal tensile stress of the cortical bone with PLLA (Tables 2–4). This means that metal materials, such as Ti and Mg alloy, maintained stress at the fixation components rather than transferring it to the biologic components. HA-PLLA showed relatively less stress distribution on the non-fractured side of the condyle compared to PLLA, although the biodegradable materials tended to inflict more stress than the metal materials on the biological components. Major stress was concentrated at the upper second screw hole and the center of the anterior plate, whereas less stress distribution appeared at the posterior plate regardless of the material used (Fig 3b, 3e, 3h, and 3k). The neck of the upper second screw of the anterior plate showed prominent stress concentration in all materials (Fig 3c, 3f, 3i, and 3l). These phenomena are consistent with the findings of Throckmorton and Meyer in that tensile strength was present on the anterior surface of the condyle with compressive strength on the posterior surface of the condyle [25, 26]. According to these results, modification of the anterior plate and screw design should be considered to improve clinical outcomes, which would reinforce the central part of the plate and necks of the screws.

Plates tend to experience more deformation than screws under controlled conditions. The largest deformation appeared with PLLA, followed by HA-PLLA, Mg alloy, and Ti (Fig 4). A material with a high stress value was apt to experience lower deformation (Tables 4 and 5). In our study, masticatory loading on the left side of the mandible was assumed to be from 132 N to 1000 N after surgery with increases of 100-N increments. Søballe suggested that the bone gap should be maintained within 0.15 mm to ensure good clinical outcomes during the healing period [28]. Ti presented the highest PVMS resistance and consequently had the least deformation among the four materials. Even at 1000 N (an extreme force), the displacement did not exceed 0.15 mm. The Mg alloy maintained deformation within 0.15 mm until 900 N of masticatory loading was applied. HA-PLLA exceeded 0.15 mm of deformation at 600 N. The maximum deformation of HA-PLLA was 0.157 mm at 600 N. However, PLLA showed less than 0.15 mm of deformation under 300 N (Table 5). The masticatory force of healthy adults was assumed to be 700 N [27] in the FEA model; thus, Ti and the Mg alloy could withstand normal masticatory function, although theoretically, even immediately after surgery. PLLA and HA-PLLA could maintain approximately 0.15 mm of physiologic discrepancy to 300 N, which is the masticatory force at 6 weeks after surgery [29].

According to the results of the FEA simulation, HA-PLLA would stabilize the physiologically open reduction of the subcondylar fracture until the formation of a primary callus is complete, whereas PLLA could not under 132 N (masticatory loading at 1 week after surgery) [6]. Although deformations in masticatory loading differed among the materials, no deformations exceeded 1.0 mm of discrepancy, which can be compensated by physical therapy using intermaxillary fixation [2]. However, by continuing to maintain a 0.15-mm physiologic gap during primary callus formation, HA-PLLA is clinically superior to PLLA as a biodegradable fixation material. When loading was applied to the left mandibular first molar, the gap between the superior and inferior fragments of the posterior part narrowed due to compressive stress. In this case, the compressive contact between the posterior surfaces acted like a splint. On the other hand, the gap on the anterior part of the fragments widened, creating a wedge-shaped opening due to tensile force (Fig 5). Therefore, a modified anterior plate may be needed as reinforcement to cope with tensile stress.

Compared to a previous study of mandibular angle fracture (0.136 mm in screws, 0.148 mm in plate) [4], deformation at 300 N of HA-PLLA did not show a conspicuous difference in the subcondylar fracture (0.076 mm in screw vs. 0.080 mm in plate). The results suggested that triangular fixation with two plates in the subcondylar fracture might achieve higher stability in mandibular angle fractures, although open reduction of the subcondyle is more mechanically unfavorable than that of the mandibular angle [2].

More stress distribution to biologic components occurred with HA-PLLA than with Ti or the Mg alloy, but this effect was lower than that of PLLA. HA-PLLA also showed less deformation than conventional PLLA for open reduction in the subcondylar fracture. Although the mechanical properties of HA-PLLA were inferior to those of metal materials, modification of the plate design reinforcing the central part of the anterior plate and a two-plate triangular fixation method might overcome its mechanical defects.

Subcondylar fracture is commonly unfavorable compared to mandibular body and angle fractures. This is because its dimensions are relatively small, upon which most of the mastication stress would be concentrated. Therefore, materials for subcondylar fracture should have appropriate mechanical strength as well as biocompatibility.

The results of the present study imply the clinical potential of HA-PLLA as a fixation material for open reduction of subcondylar fractures. However, this study is based on an FEA simulation model, which lacks actual biologic components. Therefore, further studies should investigate biomechanical tests and long-term clinical evaluations prior to widespread clinical application.

Conclusion

A material with a high stress distribution tended to experience less deformation, which reflected the results of stress distribution. The deformation in HA-PLLA at 600 N was less than 0.16 mm, implying that triangular fixation with two plates in a subcondylar fracture could be expected to have a favorable clinical outcome [2, 4, 6, 28–30].

Data Availability

All relevant data are within the paper.

Funding Statement

This research was supported by a grant from the Korea Health Technology R&D Project through Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health and Welfare, Republic of Korea (Grant number: HI15C1535) and a Grant (No. 2016-569) from the Asan Institute for Life Sciences, Asan Medical Center, Seoul, Korea. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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Decision Letter 0

Essam Al-Moraissi

23 Jun 2020

PONE-D-20-14876

Biomechanical evaluation of unilateral subcondylar fracture of the mandible on the varying materials: a finite element analysis

PLOS ONE

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Reviewer #1: Thank you for giving me this opportunity to review this in vitro research article entitled, "Biomechanical evaluation of unilateral subcondylar fracture of the mandible on the

varying materials: a finite element analysis".

I here carefully reviewed the submitted set of the manuscript and found it possibly merits of publication. However, the article needs substantial revisions in order to meet the standard of scientific publication. Therefore, I would like to propose that the article should be revised thoroughly and need further reconsideration for re-evaluation whether this study article should be appropriate for acceptance or not.

1. What is the backgrond of this in vitro study. The ORIF of mandibular condyle fractures are well documented with some proved clinical evidence so far with various surgical approaches and various hardware materials. The back ground of this study must be well discribed using appropriate and recent references. The Introduction section and the Discussion sections are to be both the level of clinical reports of undergraduates, I'm sorry but, I need to say. The authors here also need to mention the ideal lines of double buttressing of mandibular condyle fracture should be well addressed in this section.

2. In the M&M section, all the materials tested for this research should be summarized including plate thickness, screw diameter, etc. "The thickness of the mini-plate was 2.0 mm, and the length and radius of the screw were 6.0 mm and 1.0 mm, respectively." is very unclear. The authors need to carry these photos as a figure. 1.0mm screw radius means 2.0mm diameter?? The surgeons don't describe the screw system with radius!

3. "The subcondylar fracture of FEA model was constructed that a 0.5 mm gap was set to minimize the effect of shear stress caused by the bony contact" seems hardly understandable. The authors need to further discuss this issue in the Discussion section well to persuade this idea. Actually the fractured segments are honestly well reduced as "buttressing as anatomical reduction" and the fixation should be done in a clinical setting. The present idea in in vito study should be against the clinical setting completely.

4. Statistical analyses are mandatory. I've never reviewed the article without any statistical evaluation like this article, I'm afraid.

5. The discussion sections should be by far well discussed mentioning and comparing the results obtained here with those reported previously and with the clinical issues in a clinical setting. The comprehensive structures of the Discussion should be further amended. The clinical relevance should be well discribed and discussed based on the results obtained here.

Could you please let me further re-review after substantial revisions are to be done for reconsideration for suitability?

Reviewer #2: 1. Summary of the research and my overall impression:

The aim of this research is particularly relevant to the field of Craniomaxillofacial Surgery because it is related to oral fractures, more specifically to mandible condylar ones. This subject is really challenging. Sometimes, surgeons don’t choose the open access to treat these fractures either due to anatomic reasons because important structures can be found there or due to the difficulty to reduce and to fix the fractures.

It is known that the open treatment is better than the closed one because it can facilitate the return to normal activities such as mastication and occlusion as soon as possible. Besides that, some complications caused by the non-surgical treatment can be avoided.

This paper shows a study about four kinds of ORIF to treat the mandible subcondylar fractures: titanium (Ti), magnesium alloy (Mg alloy), biodegradable polymers such as poly-L-lactic acid (PLLA) and a hydroxyapatite/poly-L-lactide (HA-PLLA). It is justified by the increasing demand of re-absorbable materials to be used instead of titanium, which is the gold standard material, owing to some disadvantages.

The methodology is especially interesting, based on other studies that have been published in high impact factor journals.

2. Discussion of specific areas for improvement

Abstract:

In order to be better understood by the readers of the journal, it would be interesting to follow the acronyms with the complete name of the materials. For example ti: titanium.

I suggest removing this sentence: “Deformation of HA-PLLA was approximately 0.15 mm upon 300 N of masticatory loading”. It is hard to understand in this section and it is well explained in the results section.

Introduction:

Line 10: “Subcondylar fractures can be treated conservatively or surgically”.

What does “conservatively” mean? The best term may be “non-surgically”, as we can have a conservative surgery, for example, depending on our care during the procedure.

Materials and methods:

In Figure 1, the posterior plate does not seem to be completely attached to the bone. I would like you to confirm this and try to explain it better.

The second screws (considering the superior to inferior) are closer to the fracture line than the ideal. On the anterior plate, this screw seems to be in the fracture line. Depending on the direction of the perforation to install this screw, I think that the fracture can be “open”. Maybe, this fact can be considered a bias.

I don’t think it can influence the results, but I think that you can try to reinstall this plate, virtually.

I suggest you provide more information about the masticatory load that was applied. Why did you choose this load? Isn´t it too high? I would like to see other papers that justify this choice.

Results:

In Figure 2: “middle column, stress on fixations (mini-plates and screws) but we can just see the plates, without screws”.

I think that you need to change this caption due to the fact that the screws are not there, just the plates.

Do you have information about the bone? If so, you can insert main maximum tension and minimum tension to increase the amount of information and to make this article even more relevant.

**********

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Reviewer #1: No

Reviewer #2: Yes: Ricardo Augusto Conci

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PLoS One. 2020 Oct 8;15(10):e0240352. doi: 10.1371/journal.pone.0240352.r002

Author response to Decision Letter 0

12 Aug 2020

#Reviewer1

Comments and suggestions

Thank you for giving me this opportunity to review this in vitro research article entitled, "Biomechanical evaluation of unilateral subcondylar fracture of the mandible on the varying materials: a finite element analysis".

I here carefully reviewed the submitted set of the manuscript and found it possibly merits of publication. However, the article needs substantial revisions in order to meet the standard of scientific publication. Therefore, I would like to propose that the article should be revised thoroughly and need further reconsideration for re-evaluation whether this study article should be appropriate for acceptance or not.

1. What is the backgrond of this in vitro study. The ORIF of mandibular condyle fractures are well documented with some proved clinical evidence so far with various surgical approaches and various hardware materials. The back ground of this study must be well discribed using appropriate and recent references. The Introduction section and the Discussion sections are to be both the level of clinical reports of undergraduates, I'm sorry but, I need to say. The authors here also need to mention the ideal lines of double buttressing of mandibular condyle fracture should be well addressed in this section.

Response: Two paragraphs were re-written in ‘Introduction’ section as reviewer remarked. In ‘Discussion’ section, the ‘Ideal lines of double buttressing of mandibular condyle’ has been already described with some references. (Line 227-243)

- Line 32-45 : The subcondylar fracture commonly occurred at the sigmoid notch of mandible. Although, surgical approaches for open reduction risk facial nerve injury, it presented superior results to and fewer complications than closed reduction [1], for which present feasible visual field for accurate reduction with internal fixation devices such as mini-plates and screws [2]. However, the subcondyle, in particular, is a very difficult to be surgically approached that only present limited surgical access due to the presence of facial nerve. Therefore, surgeons’ experience and the fixation materials should be carefully considered for a successful clinical outcome. For the fixation materials, that requires mechanical strength as well as biocompatibility. Recently, with development of biomaterials for surgical treatment of mandible fractures, composites of unsintered hydroxyapatite particles and poly-l-lactide (u-HA/PLLA) has been used for open reduction, which reported reliable clinical outcome in mandibular body fracture [3,4].

However, Limited studies to date have reported on HA-PLLA fixation.

2. In the M&M section, all the materials tested for this research should be summarized including plate thickness, screw diameter, etc. "The thickness of the mini-plate was 2.0 mm, and the length and radius of the screw were 6.0 mm and 1.0 mm, respectively." is very unclear. The authors need to carry these photos as a figure. 1.0mm screw radius means 2.0mm diameter?? The surgeons don't describe the screw system with radius!

Response: As suggested, we have added Fig 1 and revised this sentence.

- Line 74-76 : The thickness of the mini-plate was 1.0 mm, and the length and diameter of the screw were 6.0 mm and 2.0 mm, respectively (Fig 1).

3. "The subcondylar fracture of FEA model was constructed that a 0.5 mm gap was set to minimize the effect of shear stress caused by the bony contact" seems hardly understandable. The authors need to further discuss this issue in the Discussion section well to persuade this idea. Actually the fractured segments are honestly well reduced as "buttressing as anatomical reduction" and the fixation should be done in a clinical setting. The present idea in in vito study should be against the clinical setting completely.

Response: Thank you for your comments. We made a new model without fracture gap, assuming bone reduction. Also, we re-analysis new model without fracture gap

4. Statistical analyses are mandatory. I've never reviewed the article without any statistical evaluation like this article, I'm afraid.

Response: Thank you for your suggestion. We have revised the Materials & methods section as below. In general, FEA constructs a single model and the data is extracted, so there is only one number of data. Therefore, statistical analysis was not performed in this study, and the data were compared based on the single data values.

- Line 119-125 : Our study used the finite element method to construct different models according to design factor and measure stress distribution and displacement for comparative analysis between various models. The finite element model for medical device analysis performs comparative analysis by changing specific designs or material properties except the same components such as cortical and cancellous bones [13-17]. Therefore, our study compared the single value for each material and did not use statistical analysis.

5. The discussion sections should be by far well discussed mentioning and comparing the results obtained here with those reported previously and with the clinical issues in a clinical setting. The comprehensive structures of the Discussion should be further amended. The clinical relevance should be well discribed and discussed based on the results obtained here.

Response: We appreciate reviewer’s detailed remarks over discussion. In observation of stress distribution on FEA model, biodegradable materials such as PLLA, HA-PLLA has less stress distribution, which meant they would inflict more stress than the metal materials on the biologic components of mandible. These results were consistent with other previous researches of Throckmorton and Meyer’s (reference 25,26). Therefore, we suggested the modification of plate and screw design according to the stress distribution in the materials (Line 252-276).

Response: We made conclusion from discussion with relevant references (ref. 2, 4, 6, 29, 30 and 31).

- Line 323-327 : For magnitude of deformation, a material with high stress distribution tended to experience less deformation, that reflected the results of stress distribution. The deformation in HA-PLLA at 600N less than 0.16 mm implicated that triangular fixation with two plates in subcondylar fracture could be expected favorable clinical outcome.

We made additional explanation for clinical relevance in line 238 as follows.

Response: We made additional explanation for clinical relevance in Line 312 as follows.

- Line 313-316 : Subcondylar fracture is commonly unfavorable compared to mandibular body and angle fractures. Because, its dimension is relatively small and most of mastication stress would be concentrated on that. Therefore, the materials for subcondylar fracture should have appropriate mechanical strength as well as biocompatibility.

Could you please let me further re-review after substantial revisions are to be done for reconsideration for suitability?

#Reviewer2

Comments and suggestions

Summary of the research and my overall impression:

The aim of this research is particularly relevant to the field of Craniomaxillofacial Surgery because it is related to oral fractures, more specifically to mandible condylar ones. This subject is really challenging. Sometimes, surgeons don’t choose the open access to treat these fractures either due to anatomic reasons because important structures can be found there or due to the difficulty to reduce and to fix the fractures.

It is known that the open treatment is better than the closed one because it can facilitate the return to normal activities such as mastication and occlusion as soon as possible. Besides that, some complications caused by the non-surgical treatment can be avoided.

This paper shows a study about four kinds of ORIF to treat the mandible subcondylar fractures: titanium (Ti), magnesium alloy (Mg alloy), biodegradable polymers such as poly-L-lactic acid (PLLA) and a hydroxyapatite/poly-L-lactide (HA-PLLA). It is justified by the increasing demand of re-absorbable materials to be used instead of titanium, which is the gold standard material, owing to some disadvantages.

The methodology is especially interesting, based on other studies that have been published in high impact factor journals.

Abstract:

In order to be better understood by the readers of the journal, it would be interesting to follow the acronyms with the complete name of the materials. For example ti: titanium.

I suggest removing this sentence: “Deformation of HA-PLLA was approximately 0.15 mm upon 300 N of masticatory loading”. It is hard to understand in this section and it is well explained in the results section.

Response: Thank you for your suggestion. We have written Ti as titanium and removed the sentence “Deformation ~ loading.”

- Line 18-21 : Here, we simulated the mechanical properties of four fixation materials, namely, Titanium (Ti), Magnesium-alloy (Mg-alloy), poly-L-lactic acid (PLLA), and hydroxyapatite/poly-L-lactide (HA-PLLA), in a finite element analysis model of subcondylar fracture.

- Line 29 : We have removed this sentence

Introduction:

Line 10: “Subcondylar fractures can be treated conservatively or surgically”.

What does “conservatively” mean? The best term may be “non-surgically”, as we can have a conservative surgery, for example, depending on our care during the procedure.

Response: We revised the introduction section.

- Line 32-44 : The subcondylar fracture commonly occurred at the sigmoid notch of mandible. Although, surgical approaches for open reduction risk facial nerve injury, it presented superior results to and fewer complications than closed reduction [1], for which present feasible visual field for accurate reduction with internal fixation devices such as mini-plates and screws [2]. However, the subcondyle, in particular, is a very difficult to be surgically approached that only present limited surgical access due to the presence of facial nerve. Therefore, surgeons’ experience and the fixation materials should be carefully considered for a successful clinical outcome. For the fixation materials, that requires mechanical strength as well as biocompatibility. Recently, with development of biomaterials for surgical treatment of mandible fractures, composites of unsintered hydroxyapatite particles and poly-l-lactide (u-HA/PLLA) has been used for open reduction, which reported reliable clinical outcome in mandibular body fracture [3].

Materials and methods:

In Figure 1, the posterior plate does not seem to be completely attached to the bone. I would like you to confirm this and try to explain it better.

The second screws (considering the superior to inferior) are closer to the fracture line than the ideal. On the anterior plate, this screw seems to be in the fracture line. Depending on the direction of the perforation to install this screw, I think that the fracture can be “open”. Maybe, this fact can be considered a bias.

I don’t think it can influence the results, but I think that you can try to reinstall this plate, virtually.

I suggest you provide more information about the masticatory load that was applied. Why did you choose this load? Isn´t it too high? I would like to see other papers that justify this choice.

Response: Thank you for your comments. As you suggested, we have repositioned the plate position and re-performed the analysis. Please find Figure 2 and Figure 5 for the plate position.

Also, We set up occlusal forces 132N at one week and 300N at 6 weeks after surgery. One week and 6 weeks after surgery are important timing in mandible surgery, for patients would commonly start to have food intake under elastic occlusal guidance. In healthy adult, usual mastication force is 700N (that was explained Line 234-243). Clinically relevant mastication force during formation of primary bony callus in patients who had mandible surgery usually would be observed from one week to 6 weeks after surgery, though we simulated deformation of materials to extreme condition such as 1000N.

These set up based on other previous studies as below. (we’ll added these two references in revised manuscript).

J Oral Maxillofac Surg

. 2000 Apr;58(4):370-3; discussion 373-4. doi: 10.1016/s0278-2391(00)90913-3.

Measure of bite force and occlusal contact area before and after bilateral sagittal split ramus osteotomy of the mandible using a new pressure-sensitive device: a preliminary report

K Harada 1, M Watanabe, K Ohkura, S Enomoto

J Oral Maxillofac Surg

. 2014 Feb;72(2):402.e1-13. doi: 10.1016/j.joms.2013.10.003. Epub 2013 Oct 17.

Biomechanical evaluation of magnesium-based resorbable metallic screw system in a bilateral sagittal split ramus osteotomy model using three-dimensional finite element analysis

Jin-Yong Lee 1, Jung-Woo Lee 2, Kang-Mi Pang 3, Hyoun-Ee Kim 4, Soung-Min Kim 5, Jong-Ho Lee 6

- Line 234-236 : We assumed 132 N of force at 1 week after surgery, 300 N at 6 weeks after surgery, and 700 N in the healthy adult’s mastication loading based on previous studies [4,27,28].

Results:

In Figure 2: “middle column, stress on fixations (mini-plates and screws) but we can just see the plates, without screws”.

I think that you need to change this caption due to the fact that the screws are not there, just the plates.

Do you have information about the bone? If so, you can insert main maximum tension and minimum tension to increase the amount of information and to make this article even more relevant.

Response: As suggested, we have added maximal and minimal tensile stress values and revised the middle column in Fig 3.

- Line 144-152 : The tensile stress distribution of cortical bone was highest for Mg-alloy, followed by Ti, HA-PLLA and PLLA. The stress distribution was similar between Ti and Mg-alloy and between HA-PLLA and PLLA (Table 2 and Table 3). On the other hand, the tensile stress distribution of cancellous bone was highest for Mg-alloy, followed by HA-PLLA, Ti and PLLA. The stress distribution of screw hole in the bones was higher in the anterior screw hole compared to the posterior hole. Facing the fracture line, the contact area of the screw hole was applied compressive stress, and tensile stress occurred on the opposite side (Fig 3a,d,g,j).

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Submitted filename: Reviewer 2_Point-By-Point Response.docx

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Decision Letter 1

Essam Al-Moraissi

27 Aug 2020

PONE-D-20-14876R1

Biomechanical evaluation of unilateral subcondylar fracture of the mandible on the varying materials: a finite element analysis

PLOS ONE

Dear Dr. Kim,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

==============================

ACADEMIC EDITOR: Authors should improve English language by native English speaker for the whole text of the paper before consideration of publication />==============================

Please submit your revised manuscript by Oct 11 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

  • A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

  • A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

  • An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

We look forward to receiving your revised manuscript.

Kind regards,

Essam Al-Moraissi

Academic Editor

PLOS ONE

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: (No Response)

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: No

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

Reviewer #2: N/A

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: No

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: I here carefully re-evaluated the revised set of the manuscript and found it no merits of publication. I'm sorry but I can't support this study article. Further the re-submitted article would be wrongly carried with English grammatical corrections.

Reviewer #2: Thanks for answering my questions. I think that the information now is better and you improved your paper.I appreciate it.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: Yes: Ricardo Augusto Conci

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PLoS One. 2020 Oct 8;15(10):e0240352. doi: 10.1371/journal.pone.0240352.r004

Author response to Decision Letter 1

10 Sep 2020

#Reviewer1

Comments and suggestions

Reviewer #1: I here carefully re-evaluated the revised set of the manuscript and found it no merits of publication. I'm sorry but I can't support this study article. Further the re-submitted article would be wrongly carried with English grammatical corrections.

Response: Thank you for your suggestion.

We have undergone the service by Editage (www.editage.co.kr) for English language editing. I attached the certification.

Moreover, our study examined simulations of four different fixation materials (titanium, magnesium alloy, poly-L-lactic acid [PLLA], and hydroxyapatite/poly-L-lactide [HA-PLLA]) in finite-element analysis models of subcondylar mandibular fracture.

Predicted result using computer simulation (mathmetical annalysis) was affected only by change of material’s property (Elastci Modulus, Poisson’s Ratio) under same conditions (design, fracture type, load condition etc.). therefore, repeated simulation result is always same for same material with same condition.

Reviewer #2: Thanks for answering my questions. I think that the information now is better and you improved your paper. I appreciate it.

Response: Thank you for your kind comment.

Attachment

Submitted filename: Response to Reviewers.docx

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Decision Letter 2

Essam Al-Moraissi

25 Sep 2020

Biomechanical evaluation of unilateral subcondylar fracture of the mandible on the varying materials: a finite element analysis

PONE-D-20-14876R2

Dear Dr. Kim,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Essam Al-Moraissi

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: All comments have been addressed

Reviewer #3: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #2: N/A

Reviewer #3: (No Response)

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: No

Reviewer #3: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

Reviewer #3: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: (No Response)

Reviewer #3: The design of this study is very unique and interesting.

The data is clear and the manuscript is well corrected.

It seems that there is no problem as a paper to be published.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #2: Yes: Ricardo Augusto Conci

Reviewer #3: No

Acceptance letter

Essam Al-Moraissi

29 Sep 2020

PONE-D-20-14876R2

Biomechanical evaluation of unilateral subcondylar fracture of the mandible on the varying materials: a finite element analysis

Dear Dr. Kim:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

If we can help with anything else, please email us at plosone@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Essam Al-Moraissi

Academic Editor

PLOS ONE

Associated Data

    This section collects any data citations, data availability statements, or supplementary materials included in this article.

    Supplementary Materials

    Attachment

    Submitted filename: Reviewer 2_Point-By-Point Response.docx

    Click here for additional data file. (47.7KB, docx)
    Attachment

    Submitted filename: Response to Reviewers.docx

    Click here for additional data file. (33.5KB, docx)

    Data Availability Statement

    All relevant data are within the paper.

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