Background
Although proximal femoral fractures are common in the elderly, femoral shaft fractures are seen in all generations. Because of the difference of fracture type and bone quality, we may need individual consideration of proximal femoral fracture and femoral diaphyseal fracture.
Recently, computed tomography-based finite element analysis (CT-based FEA) has been widely used for mechanical analysis of the femur. Many reports have described fracture models of the femur following traffic accidents and simulations of stress distribution after joint replacement [
1‐
13]. When we consider a femoral diaphyseal fracture and the stress distribution for femoral diaphyseal after prosthesis replacement using FEA, the whole femoral shaft must be evaluated. However, there are no reports of FEA models of diaphyseal femoral fractures. Although experimental data can be used to validate CT-based FEA models, most of the fracture models in previous reports were of the proximal femur [
1‐
6]. The proximal of femur have abundant cancellous bone, while the femoral diaphysis mainly consists of cortical bone. The bone architecture of the proximal femur and the diaphysis are different, and thus, they should be examined separately.
The aim of this study is to validate the newly constructed CT-based FEA models of the femur by comparing with the data obtained from the actual mechanical fracture tests using the original fresh-frozen cadaveric femurs.
Discussion
The FEA was developed in 1970, and three-dimensional analysis using CT started around 1990 [
20]. In recent years, the FEA has been widely used in the field of orthopedic surgery. There are several validation studies reported, including those for the proximal femur, the vertebra, and the distal radius [
1‐
3,
5,
17,
21‐
23]. In validation studies of the proximal femur, Bessho et al. and Keyak reported a strong positive correlation between the FEA results and actual mechanical tests (
R2 = 0.96 and 0.94, respectively) [
2,
5]. For the vertebra and distal radius, Imai et al. and Matsuura et al. also reported positive correlations (
R2 = 0.96 and 0.97, respectively) [
17,
21]. However, to our knowledge, a validation study for the femoral diaphysis has not been reported. In the present study, the FEA showed significant correlations with the femoral shaft fracture load (
R2 = 0.76) and stiffness (
R2 = 0.54) calculated using the Keller-vertebra equation with a 0.4-mm shell thickness. The correlation coefficients in our study were not as high as those in the previous reports [
2,
5,
17,
21]. It may be due to the fact that those studies excluded an analysis of the stiffness. In the studies that investigated stiffness, the values were similar to the current study. Dall'Ara et al. [
6] showed strong similarity between the FEA and actual mechanical tests for fracture load (
R2 = 0.72) and stiffness (
R2 = 0.54) in a validation study of the proximal femur. In a vertebral study, Matsuura et al. also reported lower values for fracture load (
R2 = 0.48) and stiffness (
R2 = 0.79). We believe this is the first report on a successful validation of the FEA model of the femoral diaphysis.
Keyak’s equation has been widely used in the previous FEA reports [
2,
3,
5,
9‐
11,
21]. However, we could not find any correlation between the mechanical tests and values produced by the Keyak equation, nor by Carter’s or Keller’s equations, except for the Keller-vertebra equation. To explain this, we calculated stiffness and fracture load using two equations, Keyak’s equation and the Keller-vertebra equation. The ash density of cortical bone of the femoral diaphysis was substituted with 0.935 g/cm
3 by reference to Bousson’s report [
24]. As a result, stiffness showed about a fivefold difference between the Keyak and the Keller-vertebra equations (8911 and 1661 MPa, respectively). Moreover, the fracture load calculated using Keyak’s equation was less than half of that using Keller’s equation for the vertebra (101 and 243 MPa, respectively). Therefore, Keyak’s bone model seems too stiff to reproduce elasticity in bending. Using Keyak’s model, the fractures likely occur at an early stage due to the low yield stress. Although many studies have used Keyak’s equation, the present study suggests that it may provide an inaccurate estimate of the mechanical properties of the femoral diaphysis. We propose that the Keller-vertebra equation is a suitable material characteristic conversion equation for the FEA of the femoral diaphysis when an FEA of femoral diaphyseal fractures is applied to examine stress distribution.
The shell thickness has often been defined as 0.3–0.4 mm in previous validation studies [
5,
17,
23]. However, the optimum shell thickness is unknown. The current study showed that a shell thickness of 0.4 mm had the best correlation coefficient for the femoral diaphysis both for fracture load and stiffness. Further study is needed to determine the optimum shell thickness for other bone sites.
The present study has several limitations. First, only fractures from three-point bending tests were evaluated. Because of the limited number of cadavers, we could not perform other fracture tests. Clinically, there are various types of femoral diaphyseal fractures. Further study is necessary to validate our FEA for other types of fractures, such as spiral fractures or those from axial compression forces. Secondly, the steel bar model might not be made to exactly match the bar used for the mechanical test. But, in both cases, the load was applied to the center point of the femoral diaphyseal, and the behavior of the bone was similar, so we thought that the research had no influence. Third, all cadavers were from elderly individuals. It is possible that the fracture load or stiffness would be different in younger individuals. However, it is difficult to obtain femurs from young people. We studied matched pairs of right and left femurs in nearly equal numbers of men and women, and we observed high reproducibility without differences of laterality (data not shown). Thus, we think that the FEA of the femoral diaphysis is predictive of mechanical properties regardless of laterality or gender.