## Abstract

Fractures of the mandibular angle have been well-described and, in most societies, their incidence is decreasing. In this study we analysed the stabilisation of fractures using a single plate (standard or optimised model). The finite element model was developed based on a mandibular computed tomographic scan, together with a miniplate from DePuy Synthes and an optimised plate. Using the finite element model we looked in turn at the four screws for fixation of the standard plate, and the six screws for the optimised plate, in a complete and an incomplete favourable fracture of the mandibular angle, using two screw diameters, 1.5 and 2 mm.

The results indicated that a complete fracture is critical, with 10% more strain at the bone holes. The maximum microstrain was found for the 1.5mm diameter, in screws number 2 and 4, with 7270με and 6872με in the complete fractures, respectively. There were similar microstrains in screws number 1 and 2 of the optimised plate with six screws showing similar strains. Micromovements in the fracture line achieved 60με. The position of the screws influences the microstrains along the fracture line, suggesting that the surgeon places the screws along that line at a distance of 2.5 times the diameter of the screw. The optimised geometry with more screws does not prevent screws from loosening.

## Introduction

Fractures of the mandibular angle can have several causes, violence and traffic accidents being the most common (45% of cases). Such fractures are difficult to treat because of the complex geometry of the mandible, and complications after surgical treatment develop in 20%- 26% of patients. The most common surgical technique for repair consists in fixing a small bendable plate over the fracture with monocortical screws. It was developed by Michelet et al who used different systems to stabilise the fracture, stability being the most important criterion.

Some studies have suggested using not only one plate, but two, to stabilise the fracture.

Finite element models have been used to analyse several factors: the position of the plate, different shapes and combinations of plates, and the use of 3-dimensional plates (they concluded that the linear plates gave similar stability). Other studies have analysed different sites of fracture, or used plates of different thickness. Some experimental studies have been done to verify the influence of screws, of the geometry of the plates (and suggested new shapes), or of the use of custom-made CAD/CAM plates to improve the gaps between plate and bone. The most commonly-used material for plates is metal (titanium alloy) but some studies have described resorbable plates and screws to avoid a second operation. This technique should present the same resistance and stability, and is therefore more suitable for children. Other studies with new plate designs present custom-made solutions, with some improvements in stability, and increasing the number of screws.

The hypothesis of the present study was that there was no difference between using a standard plate with four screws or a new optimised design with screws of different diameters when stabilising fractures of the mandibular angle.

## Material and methods

The finite element method was used to test and predict the behaviour of mandibular fractures to predict bony stresses and strains. The geometry of the mandible was first constructed from the computed tomographic scan of a 45-year-old patient to create a geometric model in the ScanIP software (Simpleware). Next, the model was imported into Msc Marc software to develop a finite element model. Two complementary types of geometry were considered, the cortical and the cancellous bone tissues, with the teeth considered as cortical bone. Two supplementary CAD models were developed, one with a complete fracture, and the other with a partial fracture of the mandible in the left side ( Fig. 1 ). The geometry of the fracture was designed according to that most often found for favourable fractures of the mandibular angle (where the fracture angle is lower than 45º and compresses the fracture line), and has a full fracture line while the other presents an intact inferior region ( Fig. 1 ).

A miniplate (DePuy Synthes) was designed to stabilise the angle fracture. The titanium alloy plate was 29 mm long and 1.25 mm thick and was inserted using four unicortical screws – 2.0 and 1.5 mm in diameter successively and 6 mm long – the plate position was perpendicular to the fracture line according to Champy’s method. The mandibular external surface was smooth to improve contact with the plate and simulate a surgical procedure; the plate was bent to adapt the mandibular geometry ( Fig. 1 ). In addition, we analysed an optimised plate system described by Suer et al which had been proved in experimental tests to have good stability. This system used two more screws, was the same thickness, and 32.8 mm long.

Two types of fractures, two sizes of screws, and two plates generated eight different finite element models ( Table 1 ), which were developed with tetrahedral quadratic elements and a mesh convergence test. Convergence was achieved with 446 000 elements, but the finite element models had a mean of 800 000 elements, justified by the complex geometry of the screws and bone around fracture line.

Model | Type of fracture | Plate | Diameter of screw (mm) |
---|---|---|---|

Fc – D 1.5 | Complete | Standard | 1.5 |

Fc – D 2.0 | Complete | Standard | 2.0 |

Fc -O- D 1.5 | Complete | Optimised | 1.5 |

Fc -O- D 2.0 | Complete | Optimised | 2.0 |

Fp – D 1.5 | Partial | Standard | 1.5 |

Fp – D 2.0 | Partial | Standard | 2.0 |

Fp -O- D 1.5 | Partial | Optimised | 1.5 |

Fp -O- D 2.0 | Partial | Optimised | 2.0 |

The boundary conditions considered the degrees of mastication and biting that may occur during bony healing, the loading corresponding to incisors biting at a force load of 200N. According to previous studies the boundary condition in the condyle allows movement. The position of the screws is defined in Fig. 1 , starting with screw number 1 nearest the condyle and screw number 4 nearer the frontal regions; the reference numbers for the optimised plate were similar.

The mechanical characteristics of the materials assumed were 14.7GPa for cortical bone, 0.4GPA for cancellous bone, and 114GPa for the titanium screws and plate, considering the materials as isotropic and assuming linear elastic behaviour in the load conditions. The material interactions that we considered were that cancellous and cortical bones bonded together, and that there was contact between metal components and bony tissue. A friction factor (0.3) was taken into account between the plate or the screws and the mandible. The fracture line was considered in contact with no penetration between two parts, and without friction, which is the most realistic picture.

## Statistical analysis

The data were analysed by Student’s *t* test and one-way ANOVA using the IBM SPSS Statistics for Windows software package (version 22, IBM Corp, Armonk), and probabilities of <0.05 were accepted as significant.

## Results

The results of the finite element models present a high level of principal strains in the bone holes of screws in both conditions (complete and partial fracture), suggesting that bone has cracked around the screws or that they may have loosened. The mean maximum strain distributions in the bone holes for the behaviour of both fractures are similar, and the maximum principal strain is more critical in the complete fracture, with a 10% difference (maximum difference 564με in screw number 3). Critical maximum principal strain values are reached around screws number 2 and 4 for the complete fracture when using 1.5mm diameter screws.

The diameter of the screw is important for distribution near the holes (p=0.0007) in both types of fracture: the 2.0mm diameter screw presents less strain around the bone with a reduction of 40%: the biggest reduction was 3085 με in screw number 4. For fixation with 2mm screws, the critical position changed to screws number 2 and 3 nearer the fracture. The optimised concept showed no significant improvement (p=0.065) compared with the standard plate, with greater strain equivalent in holes number 1 and 2 than in the standard solution for the same diameter of screw in both types of fracture.

The minimum principal strains around the holes shows similar behaviour to the maximum principal strains, but with less intensity ( Fig. 2 ). In the optimised plate the two additional screws, numbers 5 and 6, showed less intensity and the other four gave values similar to those of the standard plate in positions 1 and 2.