The aim of the present study was to develop a plate to treat mandibular angle fractures using the finite element method and mechanical testing.
A three-dimensional model of a fractured mandible was generated using Rhinoceros 4.0 software. The models were exported to ANSYS®, in which a static application of displacement (3 mm) was performed in the first molar region. Three groups were assessed according to the method of internal fixation (2 mm system): two non-locking plates; two locking plates and a new design locking plate. The computational model was transferred to an
A balanced distribution of stress was associated with the new plate design. This plate modified the mechanical behavior of the fractured region, with less displacement between the fractured segments. In the mechanical test, the group with two locking plates exhibited greater resistance to the 3 mm displacement, with a statistically significant difference when compared with the new plate group (ANOVA, P = 0.016).
The new plate exhibited a more balanced distribution of stress. However, the group with two locking plates exhibited greater mechanical resistance.
Fractures of the mandibular angle are the most problematic in the facial region due to the high frequency of complications after treatment. These complications mainly involve infections and non-union [
The plates employed should ensure functional, mechanical, and morphological rehabilitation [
The results of biomechanical studies do not always correspond to clinical outcomes and consequently, biomechanics are not the only factor to be considered when treating fractures [
The aim of the present study was to propose and analyse a three-dimensional finite element analysis (FEA) model to simulate the behaviour of a fractured mandible with a lost base segment, after reduction with osteosynthesis plates, in order to assess the displacement and stress fields. The results were used to support the design and development of a new osteosynthesis plate and to compare the mechanical behaviour of this plate with others in terms of the stabilization of fractured segments.
The computer model of the mandible was constructed using Rhinoceros 4.0 software (McNeel North America, Seattle, WA) and was based on a previous three-dimensional model of a mandible taken from a data bank. The data bank model was created using images from the Multislice Helical Computed Tomography of human jaws (volunteers), with a cutting thickness of 1 mm [
The mandibular fracture was fixed by three techniques of internal fixation: in Group I, one 4-hole 2 mm superior border plate was fixed with four screws with a 2 mm outer thread diameter (OTD) and a length of 6 mm, while one 6-hole 2 mm inferior border plate was fixed with six 2 mm OTD, 12 mm long screws; in Group II, one 4-hole 2 mm locking superior border plate was fixed with four 2 mm OTD, 6 mm long locking screws, while one 6-hole 2 mm locking inferior border plate was fixed with six 2 mm OTD, 12 mm long locking screws; in Group III, one newly designed 8-hole 2 mm locking plate was fixed with eight 2 mm OTD, 6 mm long locking screws.
Each plate and screw needed to be in perfect contact with the bone. An attempt was made to place the plates according to standard clinical practice. Screws connecting the plates to the mandible were modelled without threads, with a diameter of 2 mm and a length that was appropriate for monocortical penetration (6 mm) on the superior border and bicortical penetration (12 mm) on the inferior border.
The geometry was imported to the Ansys® 14.0.1. 2.0 Framework (ANSYS® Inc., Houston, USA) to pre-process the finite element model. All of the materials were considered to be homogenous, isotropic and linear elastic [
Properties of materials used in simulation at Ansys®
Young's modulus |
Poisson's ratio | |
---|---|---|
624.42 | 0.28 | |
1.138 x 105 | 0.34 | |
1.16 x 105 | 0.34 |
The elements of the meshes used in the present study were quadratic tetrahedrons, generated with the following configurations: 1) mandibular ramus adjacent to the mandibular fracture, with a mean of 1 mm for the edge of each geometric element in the cortical bone and 2 mm for the edge of the trabecular bone; 2) body of mandible and the left mandible side with a mean edge of 2 mm for each geometric element; 3) plates and screws with a mean edge of 0.3 mm for each geometric element. The mean number of nodes and elements was 775,000 and 488,000, respectively.
The mandible was constrained for all axes in the region of the temporomandibular joint and the coronoid process on both sides. A displacement of 3 mm was applied to a point on the alveolar ridge, near the middle of the occlusal face of the first molar. The contact conditions between fractured segments were frictionless. The interaction between the plates and the heads of the conventional screws was considered frictionless. For the locking group, a perfectly glued (bonded) contact was applied. The interaction between the screws and the mandible was perfectly bonded.
Mechanical static structural analysis was carried out. In addition, the displacement at a specific point above the fracture line and the reaction load at the point of displacement were assessed. All stress values were given in Megapascals (MPa) and the reaction load was given in Newtons (N). A colour scale with stress values was used to qualitatively assess the stress distribution in plates and screws.
In the mechanical test a total of 15 synthetic polyurethane mandibles (Nacional Ossos, São Paulo, Brazil) were used in this investigation. One polyurethane mandible was sectioned at the right side angle, to simulate a fracture with a triangular defect in the base, using a diamond disc mounted on a hand piece. Subsequently, this model was sent to the factory for replication. The segment contained an isosceles triangle with the following dimensions: length of the side - 15 mm; length of the inferior border defect - 10 mm. Mandibles were randomly separated into three groups according to the fixation technique used, as described in the FEA model. The plates and screws were fabricated by Tóride®. Each group contained 5 polyurethane mandibles.
Right side lateral view of the polyurethane mandible, fixed according to Group III.
The adaptation of the titanium-based plates to the mandible was ensured by using the specific instruments offered in the manufacturer’s set. To standardize the position of the plate, acrylic jigs were made for each sub-group and adapted to the lateral aspect of the polyurethane mandibles during the fixation of the plate. The sample groups were submitted to a linear loading test in the upper and lower areas of the first molar region using the Instron 4411 (Instron Corp., Norwood, MA) servohydraulic material testing unit.
The mandibles were included in acrylic in a mechanical testing structure that was custom-made for the present study. In the testing structure, the condyle and coronoid processes were fixed on both sides while the loading was applied to the occlusal surface of the first molar on the same side of the fracture.
Instron 4411 produced linear displacement at a rate of 1 mm/min and the loading was continuously applied up to 5 mm of displacement. Load data for the reaction force (Newtons) was obtained for 1, 3 and 5 mm of displacement.
In the FEA the results were descriptive regarding displacement of fractured segment, reaction load and equivalent Von Mises Stress distribution. In the mechanical test, parametric data were expressed as mean and standard deviation (M [SD]). These values were derived and compared for statistical significance within the attachment categories and then tested using analysis of variance (one-way ANOVA). Values were considered significant at P < 0.05. Mean values were compared using Tukey´s test.
It was clear that the lower plate was placed under less stress than the upper plate in the FEA. The stress was mostly concentrated in the area of the first distal screw and around the plates that crossed the fracture line in Groups I and II. The stress distribution was similar for locking and non-locking plates in terms of sharing the load among the screws: the screws at the extremities do not share load. In the Group III, there is a more homogeneous stress distribution along the plates; however, it was more pronounced between the second and third screws of the upper area of the plate.
Von Mises Stress scale.
Equivalent Von Mises Stress distribution in plates and screws from Group I.
Equivalent Von Mises Stress distribution in plates and screws from Group II.
Equivalent Von Mises Stress distribution in plates and screws from Group III.
Displacement of geometric reference (mm) in the finite element analysis model
Axis |
|||
---|---|---|---|
X | Y | Z | |
|
0.69 | 0.51 | 1.98 |
|
0.81 | 0.59 | 1.56 |
|
0.74 | 0.28 | 1.47 |
Group II exhibited the highest value of reaction force at specific displacement points.
In the mechanical test, fixation failure was not found in the groups with a displacement of 5 mm.
Force reaction in simulation of 3 mm of displacement
Reaction force (N) | |
---|---|
|
467.35 |
|
651.67 |
|
594.41 |
Comparison of reaction force values (N) in between fixation groups
Displacement |
|||
---|---|---|---|
1 mm |
3 mm |
5 mm |
|
Mean (SD) | |||
|
44.96 (8.87) | 113.87 (14.69) | 155.58 (25.39) |
|
53.61 (9.83) | 131.93 (16.1) | 187.52 (19.93) |
|
41.82 (9.94) | 98.73 (16.9) | 145.06 (36.28) |
SD = Standard deviation.
Several plates and screws with different geometric designs have been used in the treatment of mandibular angle fractures [
The geometric configuration and boundary conditions used in the FEA of mandibular fractures are diverse. To simplify the model, the teeth were removed, and the cortical and cancellous bones were modelled in polyurethane, as described in previous studies [
In the present study, we elected to apply a displacement of 3 mm in z direction above the ipsilateral first molar area. However, the literature contains studies that used bite force in a load point [
The new plate exhibited the lowest Von Mises stress values, which could be due to the more uniform distribution of the load on the plate. In Groups I and II, the upper plate exhibited a significant concentration of stress as the upper part of new designed plate. There is less material in the new plate design (eight screws instead of ten) and this plate is thinner than the lower locking plate (1 mm instead of 1.5 mm). New bone plates can support a greater load than commercially available plates with the same amount of material. In addition, new bone plates can be manufactured with less material to support the same load [
During the fracture healing period, the premature failure of plates must be prevented. The loads transmitted through the plates should not exceed the limit of the strength of the material. Screws near the fracture site are exposed to the greatest load [
On the other hand, using more screws and increasing the length of the plates helped to distribute the stress throughout the plates and screws. Distributing the stress improves the rigidity of the system, which can also be achieved by applying a more rigid plate or a second plate [
The locking plate/screw reconstruction system used to treat mandibular fractures has the following advantages over other plating systems: these plates work as internal fixators; and they achieve stability by locking the screw to the plate [
One limitation of the present study, similar to most FEA models, was the assumption of a perfect bonding union between the bone and screws [
Trivellato et al. [
Due to the complexity of the current finite element model and mechanical test, the best form of validation can be achieved through a post-market study. In addition, the developed plate must undergo an optimization process. This could increase the efficacy of current devices while reducing their overall size and cumbersome nature.
The present study has limitations related to the study design. FEA did not incorporate teeth into the simulation. In addition, the model used was specific for a mandibular angle fracture with a segmental defect, and thus, was less generalized for all mandibular angle fractures. This new plate in relation to the osteosynthesis armamentarium will increase the costs once it can only be used for mandibular angle fractures. Finally, the present study contained the limitations inherent to all
This finite element model confirmed that two 2 mm locking plates provided more stiffness than the new plate. However, the new plate exhibited a more satisfactory distribution of stress. Furthermore, the new plate modifies the displacement pattern of fractured segments. The present study confirmed that two locking plates promote a better mechanical resistance for complex mandible fractures. Further studies using modifications of the mechanical condition should be performed to determine whether the new design is sufficiently stable to favour the healing of the mandible.
The authors report no conflicts of interest related to this study.