Linear and nonlinear analyses of femoral fractures: Computational/experimental study
Introduction
Characterization of the fracture behavior of human proximal femur under various loading orientations requires accurate and reliable stress analysis. It has been shown that the quantitative computed tomography (QCT)-based finite element (FE) method can provide reliable stress analysis results through creation of very accurate 3D solid models of femur and assignment of the bone mineral density (BMD)-based mechanical properties (Keyak et al., 1998, Keyak, 2001, Keyak et al., 2001, Keyak and Falkinstein, 2003, Keyak et al., 2011, Cody et al., 1999, Bessho et al., 2007, Bessho et al., 2009, Yosibash et al., 2007, Schileo et al., 2008, Schileo et al., 2014, Trabelsi et al., 2009, Trabelsi et al., 2011, Dragomir-Daescu et al., 2011, Dragomir-Daescu et al., 2014, Koivumäki et al., 2012, Dall'Ara et al., 2013, Nishiyama et al., 2013, Mirzaei et al., 2012, Mirzaei et al., 2014, Mirzaei et al., 2015). Nevertheless, the nonlinear analysis of the related FE models is rather difficult, computationally expensive, and time consuming. Fortunately, it has been shown that comparable results can be obtained through the linear-elastic analysis of these models using the maximum principal strain (Nishiyama et al., 2013, Schileo et al., 2014) and strain energy-based measures (Mirzaei et al., 2012, Mirzaei et al., 2014, Mirzaei et al., 2015). The effectiveness of strain energy in characterization of hip fractures has also been reported by Kheirollahi and Luo (2015). They proposed a hip fracture risk index which can predict the fracture risk level and the potential fracture location, during the single-leg stance and the sideways fall. However, the linear methods can only be used to predict the overall fracture strength and the potential locations for damage, and the comprehensive simulations of crack growth require more sophisticated nonlinear schemes.
There have been several attempts on nonlinear FE modelling of femoral fractures by using different techniques (Gasser and Holzapfel, 2007, Hambli et al., 2012, Hambli, 2013, Ali et al., 2014). However, the focus of the current study is on the cohesive finite element method (CFEM) because of its versatility and robustness in both crack initiation and growth simulations. A basic feature of the cohesive zone model (CZM) is the implementation of traction-separation relationship that can handle the nonlinear fracture process. These specifications, along with numerous successful application of this method to different materials (reviewed by Park and Paulino (2011)), have motivated the researchers to apply the method to bone fracture analysis. However, most of these studies have used experimental fracture specimens and were aimed at evaluation of the fracture resistance of the bone tissues (Yang et al., 2006a, Yang et al., 2006b, Tomar, 2009, Pereira et al., 2012, Dourado et al., 2013, Hamed and Jasiuk, 2013).
The only attempt on the usage of CFEM for fracture simulation of a whole bone segment was reported by Ural and Mischinski, 2013, Ural et al., 2013. They succeeded to simulate bone fracture at micro- and macroscale. However, their model represented the distal section of a human radius bone. Hence, it should be emphasized that the implementation of the CZM within the QCT voxel-based FE for the fracture analysis of proximal femur has not been reported in the literature. In view of the above arguments, the specific objectives of this research can be summarized as follows:
- (1)
Determination of the fracture strengths and damage initiation patterns of the proximal femur by using a strain energy density-based risk factor and a new linear FE scheme.
- (2)
Computational simulation of the crack initiation and growth for two specific types of subtrochanteric fractures by using the CZM and a nonlinear FE scheme.
Section snippets
Sample preparation
A group of 15 fresh-frozen human femora were used in this study (see Table 1). The group included 8 specimens from previous studies (Mirzaei et al., 2014), plus 7 new specimens. The initial treatment of the specimens included standard excision, freezing, and bagging procedure by the Iranian Tissue Bank (ITB). The death causes announced by ITB were the three categories of coronary failure, cerebral death, and fatal trauma.
QCT scanning
The specimens were placed inside a Plexiglas container filled with water,
Fracture strength and stiffness results
Fig. 5 shows the linear correlation between the experimental and predicted failure loads obtained for 15 specimens. It is clear that the predictions of the fracture loads correlate very well with the experimental results. It should also be noted that this correlation has been obtained for a variety of specimens (with different specifications) subjected to various loading orientations.
Fig. 6 shows typical variations of the failure strength and stiffness with the loading orientation which were
Analysis of linear-FE load and fracture pattern predictions
The correlation presented in Fig. 5 shows that the predictions of the failure loads were in very good agreement with the experimental results (R2 = 0.89, slope = 0.99, P < 0.01). The fact that the slope of the correlation is very close to 1, is an indication of the robustness of the proposed method.
An interesting application for the validated FE models is the parametric studies like those depicted in Fig. 6. Such studies can be used for identification of the loading orientations under which the
Conclusions
In this study we created and analyzed a variety of subcapital, transcervical, basicervical, intertrochanteric, and subtrochanteric fractures by testing and modeling different femoral specimens. In practice, these fractures can be the result of accidents or extreme loading conditions that may occur in sport activities. Although the overall fracture behaviour of healthy femurs can generally be specified by the loading direction and boundary conditions, the densitometric heterogeneity and
Acknowledgments
The authors wish to thank Mr. Alireza Bokaei for his valuable assistance in several aspects of the experimentations. The help of Akbar Alinia, Firuz Kargar, and Hushang Firuzi in the sample preparation and mechanical testing is highly appreciated. Special thanks also go to Mehdi Fathi and Dr. Divmand for helping us with imaging procedures. This research was funded and supported by Tarbiat Modares University and the INSF (Iran National Science Foundation).
Funding
This work was funded by Tarbiat Modares University and INSF (Iran National Science Foundation).
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
Not required.
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