A biomechanical test is a good evaluation method that describes the structural, functional, and pathological differences in the bones, such as osteoporosis and fracture. The tensile test, compression test, and bending test are generally performed to evaluate the elastic modulus of the bone using mice. In particular, the femoral head compression test is mainly used for verifying the osteoporosis change of the femoral neck. This study conducted bone mineral density analysis using in vivo microcomputed tomography (microCT) to observe changes in osteoporosis over time. It proposed a method of identifying the elastic modulus of the femur in the normal group (CON group) and the osteoporotic group (OVX group) through finite element analysis based on the femoral head compression test and also conducted a comparative analysis of the results. Through the femoral head compression test, it was verified that the CON group’s ultimate and yield loads were significantly higher than those of the OVX group. It was considered that this result was caused by the fact that the bone mineral density change by osteoporosis occurred in the proximal end more often than in the femur diaphysis. However, the elastic modulus derived from the finite element analysis showed no significant difference between the two groups.
As the aging of the population has increased due to the development of medical technology, the frequency of fracture patients is gradually increasing [
The treatment of most femur fracture patients requires surgery with internal fracture fixation using intramedullary nails and bone plates. Therefore, understanding the biomechanical characteristics, such as load distribution, micromovement, and bone strength change affecting the fixation force of the implants used for the internal fixation, in particular, including the elastic modulus of the bone, provides important information regarding recovery and rehabilitation [
A threepoint bending test and fourpoint bending test are mainly used as evaluation methods for the elastic modulus of the bone in mice [
This study restructured the shape of the femur and analyzed changes in bone mineral density (BMD) by time based on the microCT images of the femur after breeding 12weekold mice for 20 weeks in the OVX group and CON group. In addition, the femoral head compression test was carried out by extracting the femur, and the elastic modulus of the femur was identified through femoral head compression finite element analysis. Then, the comparison and analysis of the femur elastic modulus between the OVX group and the CON group were carried out.
The experimental animals used in this study were 20 healthy female C57BL/6 mice at the age of 12 weeks (Samtako, Republic of Korea) (21.5 ± 1.3 g). They were divided into two groups of 10 each: the osteoporotic group (OVX group) in which osteoporosis was caused through ovariectomy and 10 in the normal group (CON group). They were bred for 20 weeks. The animal breeding room maintained a constant temperature (23
The right femurs were extracted for the femoral head compression test.
In the microCT scan, the voxel size was set in 18
With 10 femurs of the OVX group and 10 femurs of the CON group extracted from the 32weekold mice after breeding for 20 weeks, a femoral head compression test was conducted, using an Instron E3000 (Norwood, MA, USA). Femur specimens were kept in a freezer at −20°C for 2 weeks after harvesting and stored in a saline solution before the test. Referring to the literature for the anatomical axis of the femur [
Setup of the femoral head compression test. (a) The femur was potted in a cylindrical lower jig at a 9° angle. (b) The gage length is the distance from the center point of the femoral head to the medial surface of the diaphysis.
Femoral head compression test jig. (a) Upper jig. (b) Lower jig.
A compression load was applied at a rate of 10 mm/min. The compression test was performed until the femur specimens fractured or the load generated decreased by more than 20% from the ultimate load (Figure
Loaddisplacement curve for the femoral head compression test of the CON group. Two characteristic curve regions are marked for loaddisplacement curve: (I) increasing contact region of the upper jig with the femoral head and (II) nearly linear region.
The explanation regarding the loaddisplacement curve obtained through Figure
For the finite element analysis, a 3D finite element model was constructed based on the 2D microCT crosssectional images of the OVX group and CON group on week 0 and week 20 from the beginning of the test (age of 12 weeks) using 3D modeling software Mimics 18.0 (Materialise, Leuven, Belgium) (Figure
The schematic illustrations of the rearrangement of a femur for finite element analysis. (a) The local
3D femur models, constructed for head compression analysis of the femur in the same condition as that of the femoral head compression test, were relocated based on the same coordinate system (Figure
Load and boundary conditions for finite element analysis.
For elastic modulus identification through a finite element analysis, the elastic region up to the yield load of the compression test was applied. The region (B–F) connecting point B and point F was set to the elastic region and defined as stiffness
The elastic modulus of the femur applied to the finite element analysis was defined as nonlinear interaction equation (
A finite element analysis was conducted in a contact nonlinear analysis condition, and the friction coefficient between the upper jig model and the femur model was assumed to be 0.3, and Poisson’s ratio of 0.3 [
A statistical analysis (
The bone mineral density measurement through the microCT scan of the OVX group and CON group during the 20week breeding period of the 12weekold mice revealed that the mean bone mineral density was similar between both groups between week 0 and week 4. There was no significant difference between the two groups. However, from week 8, the difference in the mean bone mineral density between the CON group and the OVX group rapidly increased. On week 8, there was a significant difference of 5.6%; week 12, 4.8%; week 16, 5.5%; and week 20, 3.2% (Figure
Bone mineral density by period from week 0 to week 20.
Comparisons of femur mean bone densities in animal model.
BMD  CON group (mean)  OVX group (mean) 


0 week  0.192  0.191  0.86 
4 weeks  0.193  0.190  0.74 
8 weeks  0.200  0.189  0.01 
12 weeks  0.199  0.191  0.01 
16 weeks  0.196  0.188  0.001 
20 weeks  0.192  0.187  0.05 
Unit: g/cm^{3}.
The femoral neck showed damage from both the CON group and the OVX group (Figure
Example of femur neck fracture. (a) MicroCT image. (b) 3D reconstruction image for femoral head.
Results of mechanical bone properties. (a) Ultimate load, (b) experimental stiffness, (c) yield load, and (d) yield displacement for CON and OVX groups.
The mean stiffness
For the yield load (Figure
In the finite element analysis based on the femoral head compression test (Figure
Comparison of Young’s modulus in the CON group and OVX group.
Mean density (kg/m^{3})  Mean 
Mean 
Mean Young’s modulus (MPa)  

CON group  192  0.042  2.00  1600 
OVX group  187  0.047  2.00  1683 
The mean values of constants
Regarding the results of the calculation of the elastic modulus, when substituting the mean bone mineral density of the CON group (192 kg/m^{3}) and OVX group (187 kg/m^{3}) in the proposed equation (
Comparison of Young’s modulus.
Mean Young’s modulus (MPa)  Calculated Young’s modulus (MPa)  Error rate  

CON group  1600  1539  3.8% 
OVX group  1683  1633  3.0% 
This study divided C57BL/6 mice into the OVX group and CON group and proposed an elastic modulus identification of the femur through microCT, a mechanical strength test, and finite element analysis. This study conducted a femoral head compression test in order to investigate the property change according to the bone mineral density difference. Through a finite element analysis, this study found no significant changes in the elastic modulus consistent with osteoporosis. In addition, this study proposed a bone mineral densityelastic modulus equation of the mouse femur and showed an error of less than 3.8% from the elastic modulus, calculated by applying the mean bone mineral density and elastic modulus identified through tests and finite element analysis.
According to Turner and Burr [
This study performed a head compression test of the right femur extracted from 32weekold mice and found significant differences in the ultimate load and yield load between the OVX group and the CON group. It was considered that this was the impact of changes in bone mineral density consistent with osteoporosis as Ekeland et al. [
This study performed a finite element analysis based on test results to identify an elastic modulus. However, in order to analyze the behavior of fracture injuries, it is necessary to include the plastic area as well as the elastic region. It is also necessary to conduct an analysis considering the anisotropic and inhomogeneous characteristics of the bone. In addition, for inhomogeneous bone mineral density, it is desirable to apply a different value to each region. However, this study conducted an analysis, applying the mean value of the entire femur for the bone mineral density of the finite element model to calculate an equation of the single bone mineral density. In the future, for a more accurate bone strength analysis, it will be necessary to conduct an analysis applying a different bone mineral density by region.
In previous studies of mice, mechanical strength tests were conducted in order to analyze the growth of mice or osteoporosis change over time. However, a bending test and torsion test calculated an elastic modulus in the cortical bone and used this to predict fractures and observed changes in osteoporosis. Thus, in bone material property evaluation for the prediction of fractures and observation of changes in osteoporosis, the type of load, distribution of bone mineral density, and load of the bone, physiologically and functionally applied, should be considered.
This study identified a more accurate elastic modulus of the CON group and OVX group of C57BL/6 female mice through a finite element analysis based on a femoral head compression test. It is considered that, in the future, through the method proposed in this study, it will be possible to investigate the changes in the elastic modulus according to changes in bone mineral density of the cancellous bone by period and predict fracture risks of both normal and osteoporosis bones of the femoral neck utilizing the derived findings.
Bone mineral density
Control group
Ovariectomy group
Microcomputed tomography
Elastic modulus or Young’s modulus
Finite element
Hounsfield unit
Experimental stiffness
Calculated stiffness
Bone mineral density
Mean bone mineral density
Calculated elastic modulus of the control group
Calculated elastic modulus of the osteoporotic group.
The authors declare that they have no conflicts of interest.
The authors gratefully acknowledge Mr. Taemin BYUN for his sincere help on computational simulations and data analysis. This study was supported by grants from Korea Institute of Industrial Technology and by the National Research Council of Science and Technology (NST) grant by the Korean Government (MSIP) (no. CAP1509KIMS).