Abstract
The surgical treatment of mandibular condyle fractures currently offers several possibilities for stable internal fixation. In this study, a finite element model evaluation was performed of three different methods for osteosynthesis of low subcondylar fractures: (1) two four-hole straight plates, (2) one seven-hole lambda plate, and (3) one four-hole trapezoidal plate. The finite element model evaluation considered a load applied to the first molar on the contralateral side to the fracture. Results showed that, although the three methods are capable of withstanding functional loading, the lambda plate displayed a more homogeneous stress distribution for both osteosynthesis material and bone and may be a better method when single-plate fixation is the option.
Condyle fractures are one of the most controversial maxillofacial injuries regarding diagnosis, classification, and treatment. One of the most used classifications considers the anatomical level of the fracture: condylar head, neck, and base.
In growing patients, these fractures may impair the growth of the craniofacial skeleton and result in mandibular deficiency, asymmetry, or ankylosis. In adult patients, condylar head and high subcondylar fractures have greater potential for functional adaptation of the condyle without restoration of the anatomy than displaced base fractures with loss of ramus height. Thus, high fractures with little bone available for fixation are usually treated non-surgically, whereas low displaced fractures are frequently treated surgically by reduction and stable internal fixation.
In the condylar region, functional loads result in compressive stress patterns along the posterior border of the ramus and tensile stress patterns along the anterior border of the ramus and in the zone situated below the sigmoid notch. Osteosynthesis of condylar fractures must properly stabilize both areas, allowing early function with minimum stress. Failure of osteosynthesis, such as plate fractures or loosening of screws has been reported, leading to a better understanding of the biomechanics of condylar osteosynthesis and of how fixation methods behave in the condylar area.
Mechanical dynamic essays have led to advances in our understanding of the stress that occurs at the condylar process and to the osteosynthesis materials applied to that area, providing information that can be used in other types of analysis. Finite element analysis is a technique by which a physical prototype can be studied by creating a precise mathematical model. It is considered an efficient method for the evaluation of the biomechanical behaviour of the mandible. Mathematical models do not allow absolute clinical inferences but can offer a detailed description of the distribution and relationship between forces and tensions within biological variability.
This study aimed to evaluate the biomechanical behaviour of three methods of plate osteosynthesis of condyle base fractures, in relation to load transferring and tension distribution over the fixation materials and bone, through finite element analysis.
Materials and methods
Construction of the mandibular model
A three-dimensional finite element model (FEM) of a human mandible without anomalies was generated from DICOM files of data collected by the Centre for Information Technology (CTI; Renato Archer Information Technology Centre, Campinas, SP, Brazil). The data were derived from a dry mandible from which computed tomography (CT) images were obtained. The software InVesalius (version 2.1; CTI, Ministry of Science and Technology, Campinas, SP, Brazil) was used for image processing and the creation of an STL model, which was later converted to CAD (computer aid-designed) geometry with the software Rhinoceros (version 4.0, Robert McNeel and Associates, Seattle, WA, USA) and exported for FEM analysis with the software ANSYS Workbench (version 14.0; Canonsburg, PA, USA). For the study, a condylar base fracture was simulated on the left side of the mandibular model. It was classified in accordance with the recommendations of the Strasbourg Osteosynthesis Research Group (SORG). According to this classification, condyle fractures are defined as diacapitular fractures (through the head of the condyle), condylar neck fractures, and condylar basis fractures.
The element type used for this FEM was ‘tetrahedral with 10 nodes’ (Tet10). A manual control was carried out, where structures close to the plates and screws had smaller element sizes so that they could better demonstrate the stress gradient.
Construction of the osteosynthesis models
Three different digital models of commercially available titanium plates were provided by the manufacturer (Synthes, Basel, Switzerland) as STL models, which followed the same processing method as described for the construction of the mandibular FEM model. Virtual screws were created according to the manufacturer’s specifications. The virtual plates and screws were used to simulate the osteosynthesis of the condylar fracture created on the mandibular model. Plate models were 1 mm thick and stabilized with 6 mm × 2 mm screws on the condyle segment and 8 mm × 2 mm screws on the mandibular ramus, following principles of functionally stable internal fixation, to control tensile and compression functional stresses that develop on the bone and osteosynthesis material. Plates and screws are made of commercially pure titanium. Screws from the particular manufacturer that provided the plate models are made of a titanium alloy (Ti–6Al–7Nb). Regarding the screws, although the exact shape and thread design were not considered, an external diameter of 2 mm was used. This corresponds to the diameter of a 2-mm real screw including the threads. The bone structure was differentiated between cortical and trabecular, in which the cortical structure has an average thickness of 2 mm. No pre-tension was applied.
Types of osteosynthesis tested
Type 1 comprised two straight non-locking four-hole plates, one positioned along the posterior mandibular border and the other bellow the sigmoid notch in an oblique fashion, at the anterior border of the condylar process, with two screws on each side of the fracture ( Fig. 1 A ).
Type 2 comprised one seven-hole lambda plate, which is a locking plate, positioned along the posterior border of the mandible with the oblique extension under the sigmoid notch and two screws in the condylar fragment and the remaining five distributed along the ramus ( Fig. 1 B).
Type 3 comprised one four-hole trapezoidal plate, also a locking plate, positioned with the wider base centred in the distal fragment and the narrow end in the proximal condylar fragment. Two screws were placed on each side of the fracture ( Fig. 1 C).
Properties of materials
For the FEM analysis, the models were considered homogeneous, isotropic, and linear elastic: homogeneous due to the same mechanical properties in all their points; isotropic, because in all points the mechanical properties do not change with direction; and linear elastic because they return to the original shape when tensions are removed. The necessary mechanical properties required for this analysis are Young’s module ( E ) and the Poisson coefficient ( ν ), which, according to previous studies, are 13,700 MPa and 0.3 for cortical bone, 7930 MPa and 0.3 for medullary bone, and 115,000 MPa and 0.34 for plates and screws.
Loads and constraints
A simplified 250 N static force was applied perpendicularly to the occlusal plane of the mandibular first molar; this has been termed ‘bite forces’ by Wagner et al. and corresponds to the reaction forces of the muscles of mastication. Mandibular movements were restricted at the condyles in all directions, and the fracture interface (proximal and distal segments) was in contact but free to displace or separate. The interfaces between screws and plate were determined to be in perfect contact and firmly fixed with the cortical and trabecular bone (no slip and no clearance), simulating the locking plating system (lambda and trapezoidal); as for the straight plate, the screw–plate and plate–bone interfaces were considered free for displacement. Furthermore, the plates were assumed not to receive or transmit any force directly from the bone segments, rather, the chain of force transfer was defined as progressing from bone to screw, from screw to plate, and finally returning via the screws back to the bone. The mandible was previously submitted to testing by applying the force on both ipsilateral and contralateral sides, aiming to reduce the amount of analysis to be done by taking into consideration only the most critical situation. In order to do that, a fractured mandible without the condylar fragment was used. The right condyle and the left fractured area had their movements restricted so the displacement would not be possible. The tests showed that for the studied conditions force applied to the contralateral side of the fracture was more critical than that applied to the ipsilateral side.
Analysis of results
The models were evaluated according to the main tension using a ratio in MPa (N/mm 2 ). The tension fields over bone and osteosynthesis material were evaluated using von Mises analysis (average stress level) for the plates and screws and maximum tension for bone. A colour scale with tension values varying in MPa was used and each colour map presented a specific scale according to the result under study. After quantitative and qualitative analysis of the results, the tested models were compared verifying the tendencies of behaviour of the different fixation methods, considering the distribution of tensions and displacement (measured in millimetres).
Results
Analysis of displacement
The fixation methods studied behaved qualitatively in a very similar fashion. There was only a very small difference in displacement values. Since the mandible model was geometrically identical in all tests, this suggests that the two straight plates provided a somewhat more rigid construct, followed by the lambda and trapezoidal plates ( Table 1 ).
| Osteosynthesis type | Displacement (mm) |
|---|---|
| Two straight plates | 0–0.42 |
| Lambda plate | 0–0.44 |
| Trapezoidal plate | 0–0.45 |
Analysis of tension distribution
The von Mises analysis showed that when two miniplates were used for fracture fixation there was a concentration of tensions on the anterior plate, with high values particularly between the two central holes close to the fracture line ( Fig. 2 ). For the posterior border plate, the behaviour was neutral, indicating low tensions developing over the plate. The lambda plate displayed a better distribution of tensions throughout the whole surface of the plate with much lower values ( Fig. 2 ). For the trapezoidal plate, an intermediate situation occurred regarding tension values, with a distribution that resembled that of straight plates, concentrating tension on the side of the plate close to the sigmoid notch ( Fig. 2 ). Similar observations could be described for the screws. The greater tension concentration occurred upon the screws closer to the sigmoid notch when the straight or trapezoidal plates were used, with much higher values for the trapezoidal configuration. Greater tension close to the screw head was observed in all situations, especially regarding the screws fixed to the proximal segment ( Fig. 3 ). Data are provided in Table 2 .
| Osteosynthesis type | von Mises (MPa) | Maximum tension (MPa) |
|---|---|---|
| Two straight plates | 1694 | 234 |
| Lambda plate | 957 | 150 |
| Trapezoidal plate | 988 | 508 |
| Screws – straight plates | 789 | – |
| Screws – lambda plate | 514 | – |
| Screws – trapezoidal plate | 1053 | – |
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