Abstract
BACKGROUND:
Various techniques have been developed in the treatment of fractures. One of these techniques is the internal fixation, which has an important place in practice.
OBJECTIVE:
In this study, fractured tibia bone has been treated with implants as numerically to investigate the stress behavior and the effect of plate material, shape and dimensions under pressure load.
METHODS:
The outer part of the bone is chosen as orthotropic and the inner part is chosen as isotropic material. The plate has been modeled to take the form of the bone surface and the finite element method has been used for numerical analysis. The effect of stress on bones and implants has been examined for 1% healing by changing the plate length, plate width and plate material.
RESULTS:
It has been observed that the increase in plate length decreases cortical bone stress until a specific length. On the other hand, the increase in plate width has increased the stress on the bone.
CONCLUSIONS:
It is important to form the appropriate plate surface to the bone surface in terms of compliance with the bones.
Introduction
Various techniques have been developed in the treatment of fractures. One of these techniques is the internal fixation, which has an important place in practice. Internal fixation is usually performed by an open operation using plate, screws and wires. Many studies have been done on internal fixation technique and the contribution of various parameters to the treatment process has been examined.
Fouad [1] examined the effects of pressure and torsional load at different healing stages for the bone plate system. It was observed that the torsional load is very effective on the fracture fixation bone-plate system, and studies were carried out on the effect of using contacted and non-contact plate on stress. Fouad [2] formed 3D fractured bone and plate. Function-graded (FG), stainless steel (SS) and titanium (Ti) were used for the plate material. Stress behaviors were examined at different healing stages at the fracture site. The finite elements analysis was used to predict the healing of fractured bone for different type composite plates by Kim [3]. Having Young modulus, a composite bone plate that was used in the range of 30–70 GPa decreased the stress at fracture zone. In another study, Kim et al. [4] used the finite element analysis to investigate the use of composite bone plates on healing long-bone fractures. Mechanical properties of callus were taken depending on healing of fractured bone. Finite element analyses were made to predict the strain distribution at the fracture site of a tibia by Kim et al. [5]. A composite bone plate was used with simplified rectangular cross-section. Polymeric porous layers were modeled at the contact area. Additionally, Kim et al. [6] simulated the ossification process of fractured tibia bones by finite elements method. They used different types of composite plate to the fracture site. Three different initial loading conditions were investigated. The relationship between the initial loading condition and tissue differentiation was investigated. On the other hand, Kim et al. [7] investigated the healing efficiency of flexible composite bone plates on tibia by using finite element analysis. Mechanical properties of callus were taken depending on healing of fractured bone. Son et al. [8] investigated the bone healing process with the finite element analysis on fractured tibia. The analysis was done for the initial loading condition with oblique angles according to plate modulus. Loading is effective at fracture healing. While applying a load to the fracture site accelerates healing, reducing the load slows healing of the fracture [9]. Experimental and clinical studies have shown that extremity exercise and controlled loading have a stimulating effect on fracture healing [10–13].
In numerical studies carried out in the literature, it has been observed that the bone is in cylindrical form and the plate surface used for the treatment is flat or circular shaped [1–8]. In fact, the surface of the bone does not have an even shape. The flat plate cannot provide full contact with the variable actual bone surface and a gap appears between the bone and the plate. The presence of gap leads to a higher stress in the fracture site for all types of bone plates at all stages of healing [2]. Therefore, the performance of the fixation system that is applied mechanically reduces. To see the actual performance of the fixation system, the bone model should be as close to reality as possible. In this study, stress analysis of the fractured human tibia bone treated with the plate has been performed at pressure load. The plate geometry used is not flat and has been prepared in a form suitable for the surface of the real tibia model. This allows the plate to contact the tibia exactly. The plate material, length and width have been selected as the change parameters. Also, the stress distribution has been investigated in the fixation system under static and dynamic loading for 50% callus healing.
Materials and methods
Model
The tibia model with internal fixation has been prepared using the SolidWorks. Finite element solutions have been performed in the ANSYS Workbench [14]. The bone model has been taken from the relevant website [15] and cross-sectional measurements have been modeled according to measurements in the anterior and lateral views [16].
The dimensions of the three-dimensional and single-volume SolidWorks tibia bone model that are taken from [15] are remodeled according to an average human bone dimension, by multiplying by the scale factor in the same program. However, inside of this new model which is created is full. The full model is reduced by 1.37% to form spongious bone. From the full model, spongious bone was removed to obtain cortical bone with a thickness of 5 mm. At the last stage, the ideal tibia bone is modeled by adding spongious bone into the cortical bone.
Since the bone consists of two layers, the outer cortical bone (hard layer) and the inner spongious bone (soft layer), the tibia bone model was prepared in two layers (Fig. 1). The bone was fractured from mid-point and 1 mm thick callus was formed. The upper and lower parts of the tibia were trimmed to make the applied force to model at maximum level (Fig. 1). In the model, the cortical bone thickness of the tibia bone was set to be 5 mm throughout the bone. The size of the tibia was determined to be 365 mm according to the dimensions of the anterior and lateral views [16]. There are various types of bone fractures [17]. In the study, the fracture from the midpoint was chosen. The callus was modeled by cutting from the midpoint of the tibia at a distance of 0.5 mm to both sides, perpendicular to the bone axis. Thus, in the middle of the tibia, a callus geometry with a thickness of 1 mm, which takes the cross-sectional form of the bone, was formed [2]. In addition, screw-like cavities were formed in the bone for the placement of the screws used in the bone fracture (Fig. 1). Since the outer surface of the tibia did not have a geometric shape, the plane plates were limited in their contact with the tibia. For this reason, in the study, the bone form was considered and the portion of the plate that came into contact with the bone surface was modeled in the same form as the bone. Thus, full contact was established between the plate and the tibia so that no gaps occurred (Fig. 2). Gaps in the form of screws were formed in the plate so that the screw was allowed to move within the plate. Therefore, it was ensured that the screw and the plate were in full contact. The plate thickness was taken as e = 3.8 mm [1–8]. The plate length was chosen as d = 70, 103 and 120 mm. The plate width was determined as c = 10, 12 and 15 mm. There were four screws that provided coupling between the plate and bone. The length of the used screws was 32 mm. The measurements are given in Table 1 (for geometry see Fig. 3) [18].
Material
The cortical bone, which is the outer part of the tibia, is orthotropic and the spongious bone, which is the inner part of bone, and callus are isotropic. The mechanical properties of the materials used in the tibia model are presented in Table 2 [1–5,19]. Three different types of isotropic materials, which are Stainless Steel, Titanium and Cobalt-Chromium, are used for the plate materials. The screw material is Titanium. After the fracture in the bone, callus formation starts in the fracture area with healing. The quality of callus tissue is affected by the type of treatment applied. In the presence of motion in the fracture line, the formation of callus is accelerated [20]. In the study, the situation was evaluated shortly after the treatment of the broken tibia bone. Therefore, the elasticity modulus of the callus at the fracture site under static loading is chosen for a 1% healing. Since the healing phase is new, the patient has not yet started to walk. The patient can walk when the callus heals up to 50%. In this case, where dynamic loading is modeled, the mechanical properties of callus are chosen for a 50% healing.
Boundary conditions
Since the cortical bone is chosen as orthotropic, the tibia model has been positioned by considering the mechanical properties of bone. Because the elasticity modulus of the cortical bone is high in the axial direction, the bone has been placed along this axis and loaded [3]. The finite element model and boundary conditions are given in Fig. 4. The model consists of cortical bone, spongious bone, callus, plate, and screw. Tetrahedron SOLID 187 element type is used to divide these parts models into finite elements. The contact features have been taken bonded between cortical bone, spongious bone and callus but the coefficient of friction has been taken as 0.4 between plate-screw, plate- cortical bone, plate-callus, screw- cortical bone and screw- spongious bone [4]. Under static loading in the study, the mechanical properties of callus are selected for a 1% healing. In this case, the patient only stands up and carries the body weight. In this condition, considering the body weight, the force is applied as 800 N, since the patient can stand but is not able to walk [2].
Results and discussion
A study in the literature has been resolved to control the solution technique [2] (Fig. 5). The bone is modeled as in full contact with the plate and with a gap of 0.5 mm. The coefficient of friction between all contact parts is 0.9. The plate materials are Stainless Steel (SS) and Titanium (Ti). Maximum von Mises stresses are found in callus for a pressure load of 2.5 MPa [2]. In Fig. 6, the results obtained are demonstrated in a graphic. The maximum von Mises stress of the callus according to different healing rates are in accordance with the literature.
The effect of plate length
The length of the plates used in fracture combination varies based on the shape of fracture. For this purpose, first of all, the effects of plate length change on stresses are investigated. In static analysis, the healing in callus is chosen as 1%. The variable according to Fig. 7 is only the plate length. Analyses are performed for plate length d = 70, 105, 120 mm. The stresses that occur in the screw with increasing size of the plate show different results (Fig. 8). The greatest stresses are obtained at the plate and the smallest stress occurs in the callus. The effect of the change of the plate length on the callus is minimal compared to the cortical bone, plate and screw. The greatest difference in stress caused by the change of the plate length is formed on 4th screw (Fig. 8a). Screw 4 is the closest screw to the surface where the load is applied. As the plate length increases, the free plate length on the right side of the Screw 4 increases. Due to the stress, the 4th screw is the screw that is most affected by the plate length. As the plate length increases, the free plate length on the left side of the Screw 1 increases. However, the change in the plate length due to the bending of the callus does not affect the stress in the Screw 1 as much as it does the Screw 4. After d = ∼107 mm, the stresses remain stable in these two screws. The similar situation is valid for cortical bone. The greatest stress change according to Fig. 8(b) occurs in the cortical bone. The occurred stress on the plate material is in the safe limit. The stress is reduced significantly on cortical bone and reduced partially on the plate with the increase of plate length. Therefore, the increase of the length of the plate brings about a favorable mechanical effect for both the bone and the plate. In addition, the stress on the cortical bone remains constant after ∼107 mm and the stresses on the screws are close to each other with the increase of plate length. Therefore, increasing the length of the plate must be within the specific limits. Because after a specific plate length the stresses on the system remain constant. Also, the body needs large cuts in order to place the long plate to the body in practice. Table 3 shows von Mises stress distribution on callus, tibia and plate. It seems that the stress is maximum in the lower region on callus. The stress has spread around all the screw (number 1–4) holes and the maximum values occurred on the 2nd and 3th screws. In the same way on the plate, the maximum stresses have formed around the holes of the 2nd and 3th screws. The stress concentration in the cortical bone is due to the screw holes which cause notch in the bone. Since the bone section is not symmetrical, the force of the applied pressure creates a bending moment. The bending moment forces to break the two parts of the bone from the weak callus region. Thus, the stress in the 2nd and 3th screw holes closest to the callus is maximum. The increase in plate length has not significantly changed the maximum stress distribution on the plate (Table 3).
Effect of plate width
The stress effect on the model forming components of the plate width are investigated for c = 5, 6 and 7.5 mm (Fig. 9). The analysis is made using a Stainless Steel plate and a Titanium screw for 1% healing. As the plate width increases, the maximum von Mises stress on screws increases. The stress values and changes on screws 1, 3 and 4 are similar. However, the stress value of the 2nd screw is 30% more than the other 3 screws. The cross-section of the left part of the bone becomes smaller as it approaches to the fixed support. For this reason, the stress value is greater in the screw 2 near callus due to the effect of the bending. The increase of plate width causes the decrease of plate stress a lot. This situation is seen in Table 4 more clearly. With increased plate width, a reduction in maximum stresses, especially in the screw holes in the interior, has been achieved. The decrease of plate stress has increased the stress on the cortical bone. An increase in stress on the bone of the cortical bone is an undesirable condition for the patient. Due to the use of Stainless Steel as a plate material, the strength of the plate is very high. The stresses occurring on the plate are well below this strength value. Thus, increasing the plate width to reduce the stress in the plate is not very important and it is harmful to the bone. The callus has not been affected by the plate width. If a flat plate is used instead of a plate in the form of a bone surface, the stresses are observed to increase (Fig. 2). To examine this situation, the solutions for the flat panel model are repeated and the obtained results are compared with the model used in this study. For the solutions, the bonded boundary condition is used for the entire surfaces and the stresses are found to be larger for the flat plate (Table 5).
Effect of plate material
In the study, Stainless Steel (SS), Titanium (Ti) and Cobalt--Chrome (Co--Cr) are used as the plate material to observe the effect of the plate material. The analysis is done statically using Titanium material for screws for 1% healing. The mechanical properties of the materials are given in Table 2. With the change of the plate material, the greatest stresses occur in the plate and the screw, but the stresses formed are smaller than the critical strength value for the plate and screw (Fig. 10). The use of different materials on the plate have not caused large stress differences in screws, bone, and plate. The greatest stress in the cortical bone occurs when Titanium plate material is used. Since large stress is not required in the cortical bone, the use of Titanium as plate material is mechanically unfavorable. However, the lowest stresses on all the screws and plates are obtained for Titanium plate material. The Table 6 shows the stress distributions for bone, plate and callus for different plate materials. When Steel is used as the plate material the maximum stress distribution occur in the internal screw holes, this is partially offset when Titanium is used. Likewise, the use of plate material Titanium reduces the stress on screws to a certain extent compared to Steel use (Table 7). The young modulus of Co--Cr material is close to steel. However, the young modulus of titanium is about half the steel. In Table 6 the screw materials are titanium. When using steel plate with high young modulus depending on the screw material, the stresses on the plate are obtained high. In Table 7, the plates used are different materials, Titanium. When the SS plate with the young module, which is higher than the titanium screw material, is used, the stresses in the screw obtains higher at this time. Therefore, the use of a plate with a higher Young modulus compared to the screw material increases stresses on both the plate and the screw. However, cortical bone stress reduces. Because the SS plate material withstand the applied load.
Effect of dynamic loading
Controlled micro movement or controlled rhythmic movement affects fracture healing positively [10,20]. For this reason, a force that varies with time has been applied during walking to the bone. Since walking cannot be possible when bones are broken, dynamic loading has been applied for cases where 50% of the healing is complete. During walking, the effect of the change of force on the tibia for one second has been investigated (Fig. 11) [22]. The analysis is done statically and dynamically using stainless Steel plate and Titanium screw. Static and dynamic load have applied for models with the same material properties and dimensions given the cross-sectional view in Fig. 7 and the results are given in Fig. 12. In the case of dynamic loading, behaviors similar to static loading have been achieved. The maximum von Mises stress for both loading cases has been found on the 2nd screw. Stress differentials reach the highest level among the screws when applied load to tibia/body weight ratio is maximum in 0.15 and 0.5 seconds. The stress values on the other screw outside the second screw are close to each other. As shown in Fig. 9, the reason why the stress of the second screw is larger than the other screws, is because this screw is closer to the callus and it is applied to a smaller tibia section. Since the dynamic load reaches maximum at 0.15 and 0.5 seconds, the stress differences between the 2nd screw and the other screws have reached maximum at these seconds. The maximum stresses that occur in the plate have occurred at the same time as the bolts. At other times, the maximum stress values for all parts are similar to static stresses. The stress that occurs in the plate during walking in one-second has not approached the strength value of the used Stainless Steel material (380–450 MPa). In the dynamic loading on the cortical bone, according to static loading there is more stress at ∼0.15 to ∼0.7 seconds time interval but the bone can resist the stress that occurs because of 50% healing completed. Since the tibia bone has a compressive strength of ∼200 MPa [23], it can be seen that the stresses are safe. The callus stresses are small compared to the plate and cortical bone.
Conclusions
In this study, the applied static and dynamic loads, which were calculated by three-dimensional finite element method, caused stress in the fractured bone, plate and screws. The results obtained can be summarized as follows;
The stress that occurs on the plate and cortical bone decreases with the increasing plate length. The reduction of stresses on the plate is mechanically insignificant so the unnecessary lengths in the choice of plate length should not be used because long plate use will lead to greater surgical treatment. Stress has decreased with increasing plate width. The decrease of plate stress increases the stress in cortical bone. The cortical bone stress is not desired to increase. Since a specific width must be maintained for body adaptation and the stresses in the plate are safe for the material there is no need to increase the plate thickness too much. The use of different plate materials has not significantly affected stresses. The greatest stress occurred in the cortical bone when Titanium was used. Since stress is not required in cortical bone, the use of Titanium as plate material mechanically makes this material disadvantageous. However, the use of Titanium is important because of the compatibility with the tissue and the lack of too many differences on stress. Increasing the width and length of the plate or the use of different plate materials has not caused a significant change in callus and screws. However, the inside of the callus, which is close to the screws, has been subjected to greater stresses depending on bending. During dynamic loading, the stress obtained for the prepared Steel plate model is lower than the compression strength of Steel plate. For this reason, plate width and length are suitable for the model. In dynamic loads, when the load is at its maximum, the stresses on the plate reach the maximum level and the stress differentials with the bones grow. However, when the load is not at maximum, the stresses are close to static stresses or lower than them. It seems appropriate to increase the plate size within specific limits. It is also important to form the appropriate plate surface to the bone surface in terms of compliance with the bones. However, in order to use the ideal plate size in practice, it is necessary to take into account the patient’s bone measurements.
Footnotes
Conflict of interest
None to report.