EFFECT OF THE SCREW TORQUE LEVEL ON THE INTERFRAGMENTARY STRAIN AND THE INTERFRAGMENTARY MODULUS

The screw torque is applied at the screw head to fi x the plate and the bone. It generates the compress ive force between the plate and the bone to stabilize t hem. The interfragmentary strain is the main factor for healing the bone fractured. The screw torque level aff cts the interfragmentary strain and the stabili ty of the fixation between the plates an the bone. The interf ragmentary modulus is the new factor of the plate f ixation stability and it is affected by the torque level. T his research is proposed to study the effect of the scr w torque level on the interfragmentary strain and the int rfragmentary modulus. The interfragmentary str ain and the interfragmentary modulus decrease by increa sing the screw torque level.


INTRODUCTION
Internal fixation is the main method to cure the human bone fracture (Wahnert et al., 2012). The plate fixation is the main choice of the internal fixation. The Dynamic Compression Plate (DCP) and the Limited Contact Dynamics Compression Plate (LC-DCP) are generally used to fix the broken bone. For the DCP, only the conventional screws are used. The conventional screws fix the plate and the bone by the compressive force that is generated by the applied torque at the screw head (Kanchanomai et al., 2008;Field et al., 2004;Kabak et al., 2004;Gao et al., 2011;Kumar et al., 2013). For the LC-DCP, the locking screws are used to make the distance between plate and bone. The conventional screw can be used in the LC-DCP as the DCP.
The contact between the plate and the femur affects the periosteal blood supply to the femur (Haasnoot et al., 1995;Ahmad et al., 2007). The LC-DCP is developed to solve this problem by using the locking screws (Borgeaud et al., 2000;Field et al., 2004;Kabak et al., 2004;Miller and Goswami, 2007).
However, the stability of the plate and the bone must be conscious. The plate fixation with the conventional screws has more stable than the locking screws because the locking screw cannot generates the compressive force (Haasnoot et al., 1995;Ahmad et al., 2007;Kumar et al., 2013).
In the human bone fracture, the screw tensile force (internal force) ranges from 2000 N to 3000 N (Kim et al., 2010). Ahmad et al. (2007) applied the screw torque of 4 N⋅m in their research.
The interfragmentary strain (ε IF ) is a main factor of femur fractured healing. It has the best ranges from 2-10% (Perren, 1979;Kim et al., 2010). It is defined as the ratio of the fracture gap displacement after the body load applied and the original fracture gap as shown in Fig. 1.
The Equation (1) of ε IF is: (1) ∆L = The fracture gab displacement after the body load (W) applied L = The original fracture gap length (L = 10 mm for this study) The physician will cut the fracture and form a gap of 1-10 mm when the fracture occurs at the middle part of the femur. In this present work, a gap of 10 mm was applied.

AJAS
The normal stress in the plate at the fracture gab is the combine stress from the normal stress and the bending stress (Fouad, 2011). For the normal stress, the equation of the normal stress can be written as Equation (2): Where: σ IF = Normal stress or interfragmentary stress W = Body load A = Plate cross section area The equation of the bending stress is Equation (3) In the present work, the interfragmentary strain and the interfragmentary modulus is the goal to study at various bone screw torques level.

MATERIALS AND METHODS
The 3406 large left fourth generation femur of Pacific Research Lab is used in the present work. The Pacific research laboratories bone are usually used in biomechanics research (Greer and Wang, 1999;Stoffel et al., 2003;Ahmad et al., 2007). The 12-holes LC-DCP from synthes Inc. with the ten conventional screws are attached on the femur.
The 10 mm gap is generated at the middle point of the femur. The Kyowa DTC-A-5 clip-type displacement transducer with specification listed in Table 1 is used to measure ∆L.
The lowest of the femur is fixed with epoxy resin while the femur head is fixed by one bolt as shown in Fig.  2. The jig at the femur head can be rotated about this bolt and touched the femur head for transferring the compressive force from the compressive testing machine.
The compressive force from the compression testing machine and displacement signals are converted to digital signals by the Kyowa PCD-300A. The PCD-300A software is used for data recording.  Figure 3 shows the torque applyed on the screw head. The level of the screw torque is varies from 1 to 5 N.m. The compressive force F on the femoral head is varies from 0 to 300N.

RESULTS
The graphs of ε IF versus the compressive force for all cases of the screw torque level are shown in Fig. 4.
By using the Equation (2) and (4), the graphs of σ IF versus ε IF for all cases of the screw torque level are shown in Fig. 5.
The relations between ε IF and F are generated by using the linear regression in Equation (5): The results of a and b with R 2 are in Table 2. By using Equation (4), IM and k are calculated and shown in Table 3.

DISCUSSION
From Fig. 4, it has been found that the slopes of the graph decreased by increasing the screw torque level. In other words; for the same compressive force applied at the femoral head, the interfragmentary strain decreased when the screw torque level is increased.
From the data in Table 2, It has been seen that the relation between ε IF and F is the linear function with high R 2 because the plate, the femur and the screws are linear materials. In the present work, the applied force at the femur head is not exceeding the elastic limit of all parts.

AJAS
The graphs of the ε IF and F must be stayed in the elastic zone of material (linear zone). Table 3 shows that the relations between σ IF and ε IF are linear with high R 2 . The slope (IM) of the graphs in Fig. 5 decreased when the screw touque level is increased. Because the meaning of IM is the spring stiffness and the stabilliy of the bone-plate fixation. Thus, the stabilliy of the bone-plate fixation decresed when the screw touque level is increased.

CONCLUSION
• The interfragmentary strain decreased by increasing the screw torque level • The interfragmentary modulus decreased by increasing the screw torque level

ACKNOWLEDGEMENT
The researcher is grateful to Kasetsart University, Si Racha Campus and the Center for Advanced Studies in Industrial Technology for the research grants.