The Effect of Contact Model on Stress Distribution on Internal Fixation of Fibula Fracture

The fibula is a bone with a small cross-sectional area that is located in the calf parallel to the tibia bone and includes part of the lower leg. Technically, this bone only receives a load of approximately 15% of the total load received by the lower leg. However, under certain conditions, the fibula can be broken and require medical attention to repair it. The most common medical solution to improve this condition is to install an internal fixation. The main function of internal fixation is to keep fractured bones stabilized and in alignment. When the internal fixation is in place, the internal fixation will receive tension, at least by the patient’s body weight while supporting the legs. The magnitude of the received stress value will certainly influence the strength of the material from the internal fixation. Experimental studies are very difficult to carry out. Therefore, in this study a numerical analysis of the stress distribution on the internal fixation of the fibula bone was carried out, using the finite element method. The influence of the contact model between the bones used, namely friction and bonding, on the results of the finite element analysis was studied before further research could be carried out. The load given is considered equivalent to the average body weight of the Indonesian population, which is around 63 kg. The material employed is AISI 316. Parameters for friction and bonded models used refer to previous researchers. The results of the analysis show significant differences in the distribution and magnitude of stress on the fixation plate due to the use of different contact models.


Introduction
The fibula is one of the bones that supports the skeletal structure in the lower leg.Geometrically, the fibular bone is a long and thin bone, which lies parallel to the tibia bone in the calf.It is covered by a layer of muscle and fat; the presence of fibula bone sometimes is not recognized because of its small size.The fibula does not experience much weight, only about 15% [1] of the load received by the lower leg, but it plays a very important role in stabilizing the ankle and supporting the muscles of the lower leg.Despite receiving a small load, under certain conditions the risk of fracture of the fibula is still possible [2].Fracture is a condition where damage makes the bone lose its continuity.Although rare, fractures that occur in the fibula usually occur due to vehicle accidents, certain types of work that are at risk for fractures, sports injuries, and other causes of fractures.The medical solution offered to overcome the problem of fractures in the fibula is by placing a fixation device through a series of surgical activities.
There are two types of fixation equipment for fractures, namely external and internal fixation.In external fixation, a plate, and the other mechanics are placed outside the skin on the bone fracture area.While internal fixation is a surgical procedure by placing temporary or permanent implants in the form of plates and screws on the inside of the skin at the fracture area with the aim of maintaining and stabilizing the fractured bone.The healing process is expected to be more complete if the fractured bone is stable and in alignment.
Technically, when fixation performs its function, it will experience stress due to the working load, at least the load due to body weight when supporting conditions when standing, walking or other activities that require lower leg support.Experimental studies to measure the stress that occurs, especially in internal fixation for cases of fibular fractures, are very difficult to carry out.This is due to the relatively small size of the fibula bone, as well as its hidden location behind the tibia bone in the calf muscle.Numerical studies using the finite element method are an alternative that can be employed to study the magnitude and distribution of stresses that occur in the internal fixation plate.Before further research can be carried out, it is necessary to study several factors that might influence the results of the numerical analysis, among these factors is the model contact between two fractured bones.Previous researchers [3], have studied the stress distribution on internal fixation for loading conditions that represent the standing position.Human activities, including patients who have been installed with internal fixation, not only standing but also doing other activities such as walking.Therefore, the objective of this study is to study the effect of the previously developed contact model on the stress distribution on the internal fixation plate for conditions representing the walking position.

Geometry and Material
The stress distribution on the internal fixation plate was obtained from the finite element analysis using ANSYS Release 19.2 software.The fibular model and geometry used in this study were taken from the literature [4], shown in figure 1(a).The shape and geometry of other components such as plates and screws were also adopted from other previous researchers [5], as shown in figure 1(b) and 1(c).Stainless steel material of type AISI 316 was chosen as the plate and screw material, with the mechanical properties shown in tabel 1 [6].AISI 316 stainless steel is the most widely used material because it is IOP Publishing doi:10.1088/1742-6596/2739/1/0120463 more economical in terms of cost, has high biocompatibility, and also has corrosion resistance to the physiological salt content in the human body [7].The mechanical properties of bone used in finite element analysis were adopted from previous researchers [8].

Meshing and Boundary Condition
In this study, the mesh used was a tetrahedron mesh.This type of mesh is more suitable for models with complex geometries following the results of previous studies [9].The analysis was carried out using a fine mesh size, for bone as well as plates and screws, as shown in figure 2. The boundary conditions used in the analysis were as close as possible to the actual conditions as shown in figure 3. The force components in the x, y, and z directions for conditions representing the walking state were adopted from the literature [10].

Figure 2. Finite element mesh
The contact between the bone and plate and screw was modelled with a friction model with a coefficient of friction parameter of 0.2 [11].For the contact between two broken bones, two types of contact were tested, namely bonded and friction.The effect of the two contact models used on the stress distribution on the plate surface will be studied and discussed in the results and discussion section.

Results and Discussion
The results of the analysis of the effect of the two contact models used on the stress distribution on the internal fixation plate can be seen in figure 4(a) and figure 4(b), while figure 4(c) shows the magnitude of the stress value in the running condition for 1.4 seconds.From figure 4, it can be seen that for the bonded contact model, the stress distribution on the plate looks more even than the friction contact model.The same phenomenon is also seen in the distribution of stress that occurs in bone.The magnitude of the stress that occurs is also seen to be higher in the bonded contact model than in the friction contact model.When compared to the real physical condition, the bonded contact model may be more suitable for the analysis of where the bones have started to fuse.While the friction contact model describes the condition of the bones not yet fused.Overall, the average difference in the magnitude of the stress that occurs is 29%.This shows that the choice of contact model will affect the distribution and magnitude of the stress on the analysis results.

Conclusion
From the results of this study, it can be concluded that two models of contact between broken bones in the case of internal fixation analysis of fibula fractures, namely the bonded contact model and the friction contact model, show different stress distribution patterns and stress magnitudes.The use of the appropriate contact model must be adapted to the conditions to be analyzed.

Figure 4 .
Figure 4. Von Misses stress distribution on the bone, plate and screw, (a) bonded contact model, (b) friction contact model, (c) comparison of the magnitude of von Mises stress

Table 1 .
Mechanical properties of stainless steel 316