Evaluation of In Situ and In Vitro Using 3D Finite Element Models Reconstructed from CT Scans with Validation Against Experiments of Proximal Femoral Fracture Load

Hip fracture is regarded as the most significant osteoporotic fracture in terms of health consequences, quality of life, and cost. Owing to the aging population, it has been estimated that the total number of hip fractures worldwide will increase from 1.3 million in 1990 to 2.6 million by the year 2025 and to 4.5 million by the year 2050 [1]. Approximately one-third of the population over the age of 65 suffer a fall each year, rising to over 50% by the age of 80 [1]. In the UK, 75,000 patients suffer hip fractures each year at an annual cost of approximately £2 billion [2]. The lifetime risk of sustaining a hip fracture in the United Kingdom from age 50 is around 11% for women and 3% for men [3]. Hip fractures have a devastating impact on patients including death, depression, disability, institutionalization, fear of falling, and social isolation [4,5]. Older patients presenting with hip fractures encompass some of the frailest and sickest patients, with complex medical difficulties and comorbidities, who have to surmount the additional physiological challenges posed by trauma and surgery [6]. Consequently, hip fractures related to morbidity and mortality remains high, with approximately 10% of patients dying within 1 month, 30% at 1 year and 80% at 8 years following hip fracture. Death tends to be associated with a patient’s comorbidities, rather than the hip fracture itself.


Introduction
Hip fracture is regarded as the most significant osteoporotic fracture in terms of health consequences, quality of life, and cost.
Owing to the aging population, it has been estimated that the total number of hip fractures worldwide will increase from 1.3 million in 1990 to 2.6 million by the year 2025 and to 4.5 million by the year 2050 [1]. Approximately one-third of the population over the age of 65 suffer a fall each year, rising to over 50% by the age of 80 [1]. In the UK, 75,000 patients suffer hip fractures each year at an annual cost of approximately £2 billion [2]. The lifetime risk of sustaining a hip fracture in the United Kingdom from age 50 is around 11% for women and 3% for men [3]. Hip fractures have a devastating impact on patients including death, depression, disability, institutionalization, fear of falling, and social isolation [4,5]. Older patients presenting with hip fractures encompass some of the frailest and sickest patients, with complex medical difficulties and comorbidities, who have to surmount the additional physiological challenges posed by trauma and surgery [6]. Consequently, hip fractures related to morbidity and mortality remains high, with approximately 10% of patients dying within 1 month, 30% at 1 year and 80% at 8 years following hip fracture.
Death tends to be associated with a patient's comorbidities, rather than the hip fracture itself.
In addition, nearly 40% of patients will not return to their preinjury residence [7]. For these reasons, research to help prevent hip fracture is essential. Finite element (FE) models are useful tools in helping to understand the underlying causes and mechanisms of hip fracture [4][5][6][7][8]. Recently, calculated tomographic (CT) scanbased FE models utilizing non-linear mechanical properties have been shown to predict proximal femoral fracture loads in vitro with a relatively high level of precision (r = 0.96 for measured vs. predicted fracture load) [9]. In the future, this modelling technique might be used in vivo for research or for clinical purposes. With this motivation, the present study scrutinizes whether FE models generated from CT scans of proximal femora in situ and in vitro in vitro produce comparable predictions of proximal femoral fracture load.

Methods
For the current study, one human cadaver was selected from a 65-year-old male with the stature and weight of 180 cm and 84.5 kg respectively. This subject has the characteristic mass and stature close to the average adult male and cause of dearth was carcinoma of the heart. In the current study geometry of the left proximal femur complex has been scanned by CT scanner, with examination showing no signs of metastases or other abnormalities such as previous fractures present in the femur. Following initial examination, the left proximal femoral specimen was removed from the cadaver for in vitro CT scan. The in vivo and in vitro data was collected by the department of Radiology, Milad hospital, Tehran, Iran. From the CT scan, shown in Figure 1, cortical and cancellous bone can be distinguished, alongside soft tissue such as muscle. The CT scan also provided data in terms of bone density shown in Figure 2. The initial data was collected using the following parameters: Siemens, 110 kVp, 105 mAs, 5 mm thick slices at 2.5 mm interval, total of 255 slices, with an in-plane resolution of 0.7mmx0.7mm (pixel size). For in vitro CT scan of the of femur specimen the soft tissue was removed and immersed in water to maintain the properties of the femur as close to that of the femur in vivo, this will also reduce and cut down artefacts', see Figure 2. The in vitro CT scan in vitro used the same parameters as the in-situ scan, except that a pixel size of 0.75mm×0.75mm was used. This method has been used in previous studies, Keyak [10]. The different pixel sizes will not have influenced the study results because the image quality varies depending on the pixel spacing. The resolution is determined by the slice thickness and the finite elements, which are larger than the pixel size and therefore determined the overall model resolution.
The 235 slices of the CT scan data of each femur is collected in the DICOM format (Digital Imaging and Communications in Medicine), which is then uploaded to, SIMPLEWARE (version 3.1Simpleware, UK), to produce the solid model, see (Figures 3 & 4). The output of the Simple ware software was converted into the DXF format and transferred to the IGS format by using FEA software, in this case ANSYS. Then, the IGS data of each solid model, both in situ and in vitro, was translated to generate a 3D-FE model of the human pelvis-femur complex. The FE modelling was conducted using finite element software LS-DYNA. LS PREPOST 3.1 was used to analyze the results and also to create the models in the pre/postprocessor. The method of producing each of the FE models from CT scans, and mechanical testing procedures used in this study have been described in detail in a previous study, Razmkhah [11].     Therefore, in this study, the cancellous bone was treated as an anisotropic material, using the following equations:

Explicit Finite Element Analysis
Therefore, for cancellous bone, the Material model 54 of LS-DYNA was selected to model the damage of cancellous bone and The Chang-Chang failure criterion, which is a modification of the Hashin's failure criterion, was chosen for appraising the failure in each computer simulation (Table 1).

Mesh Sensitivity Analysis and Contact Constraint
The accuracy of the model as to the porosity and void inner parts is really important because this will determine the mechanical toughness of the femur and consequently, the future precision of the results obtained from impact simulations of different load cases. Figure 5 depicts the rendering of a translucent modelled femur obtained from ScanIP software with opacity of the external part at 0.2 and the cavity with no opacity to observe the structure. Figure   6 shows the distribution of mass density along the bone (a) and cross section of mass-density rendering (b) whilst Figure 7 shows the distribution of Young's modulus. Although each of these two images is represented in different orientation, it is well worth noting that the distribution of both parameters in the meshed elements of bone is the same. It is also remarkable, in Figure 6, there is less mass density in the head of the femur where the bone is trabecular, the porosity is higher and therefore the mass density of the tissue is lower. The head of femur, which part is almost a sphere, is di-

Finite Element Modelling (FEM)
The numerical example presented here follows closely include the transverse shear [16].

Force Application
The striker for each computer simulation was modelled as a rigid block, applying solid element and a node impacting surface with a friction coefficient of 0.35, which is measured experimentally to avoid lateral movements between the contact and rigid plate, and experiment in situ is less than 35% and in vitro is less than 28%. These results were also compared with the previous study by Razmkhah, 2014, which shows that, the difference in maximum force and energy absorption between the FEA model in situ is less than 22% and in vitro is less than 7.5%, shown in Figure 9.

Effect of Various Impact Velocities
After comparison of the previously validated models, the

Effect of Intertrochanteric Crack in Sideways Falls on Different Cortical Thicknesses and Impact Velocities
This study evaluated the ability of automatically generated, CT scan-based linear FE models of the proximal femur, to predict two aspects describing fracture location and fracture type. Fracture location was defined as the specific location of the fracture and was the more discriminating parameter. Fracture type was a categorical variable defined as either a cervical or a trochanteric fracture. Two loading circumstances were examined, single-limb stance and simulating an impact from a fall. These FE models have been validated previously for predicting proximal femoral fracture load [11]. Since fractures are unpleasant, debilitating events the mechanical performance of bone plays a crucial role in the quality of life that is experienced. Some kinds of fractures are quite clearly caused by the fact that bone is exposed to loads that surmount certain threshold levels (with regard to stress or damage); which can also be protracted (creep), or persistent (fatigue represent what may occur in reality, these types of fractures are the most common reported [20]. The crack dimensions used for these models have been previously defined by Koester [21].   The assumption of bonded contact between the two surfaces in order to achieve perfect Osseo integration is considered in FE models i.e. bony growth around the implant. In reality this may not affect results. This investigation focuses on the assessment of the mechanical behavior of the femur bone compared to the freshfrozen specimens experiment carried out by Keyak [21]  FEA on the other hand, has the ability to mimic loading conditions and extend data analysis far more than what is possible to perform in a laboratory setting. Two caveats must be kept in mind; firstly, experimental setups should be able to simulate real-world physiological conditions as much as possible even though their inevitable limitations are recognized. Secondly, accurate and proper verification, validation and sensitivity of the FEA analysis should be run to ensure that the models are working properly. The aim of this section will be to present practical tools for engineers and clinicians, who, using this information in combination with FEA studies to successfully carry out orthopedic biomechanics research to provide a more a detailed depiction of what is occurring during fracture.

Specimen Preparation
Three medium-size fourth generation composite bones (model number: 3403) from Sawbones (Pacific Research Laboratories, Inc., Vashon Island, WA, USA) were examined in this study.
Each composite femur was fixed by a clamp then the femur was subsequently sectioned at two-thirds of its length below the femoral head, and at 250 mm distal to the lesser trochanter and then cut. The composite femur bone was inserted into a jig to a depth of 100mm and secured inside the jig with 8 bolts to provide a mechanical restraint, and the jig was secured onto the baseplate of the test machine, this method has been used previously by Kayak (2001) and more recently by Razmkhah [10][11].

Anatomy and the Loading Conditions of the Force on Hip
This section describes the methodology used for both the experimental and computational studies. The two forces acting on the bone are Fpelvis and Ftibia: Fpelvis is acting on the femoral head, thereby the mechanical axis; Ftibia is acting on the tibia, in the upwards direction in the femoral axis which can see in Figure   15. The mechanical axis is defined as the line between the two forces acting on the femur in its anatomical position. The femoral axis is the line that is parallel to the shaft of the femur. The angle between the femoral axis and the transverse plane is θ. In this study, the angle between the mechanical and the femoral axis is α, which was set at 11°, and the composite femur bone was aligned at 20° adduction as shown in Figure 16. The vertical and horizontal edges of this jig fixture base also served as a coordinate system that was fixed in relation to the femur to facilitate accurate vectorial derivation and modeling of the applied load. The positioning of the femur bone at the given angle of θ = 20° was necessary so as to try and replicate the way a natural femoral head is distally referenced in the two-legged stance of a human being [25,26]. In this regard, values close to those acquired from the simulations of tensile stress loadings experienced on the natural femoral head could be obtained. The composite model was then loaded on to an axial load testing machine between a platen and a jig secured to a datum as shown in Figure 17.

Results of Validation
Experimental data pertaining to the mechanical behavior of the femur was conducted to validate the numerical methods, which are

Discussion
The research has demonstrated that the FFE results obtained from CT data gathered from the in-situ femur, in comparison to the CT data gathered from the femur in vitro showed a 7.3% difference in the fracture loads experienced by the femur following FEA simulation, Figure 19.  properties and the theory of distortion-energy failure affected results generated from the FE model. Also, loading situations were made less complex in that the force was applied in the coronal plane, and excluded muscle forces, that would normally be acting upon the femur in situ. In contrast, distinctions between the FE models constructed from in situ and in vitro CT data could be affected by interactions of density and mechanical properties of the femur. However, fracture loads and applied forces may need to be determined for additional loading circumstances and forces attributable to muscular action may also be required and considered. This study has shown that FE models constructed from in situ CT data can provide accurate information to construct an FE model that will be able to predict fracture loads that are likely to occur in a femur fracture. The quality of the CT data will ensure that mechanical properties of bone are closer to what may actually occur during an incidence of fracture.

Conclusion
The present study examined whether FE models produced from Cyclic loading of the femoral pairs might similarly be more physiologically relevant. Nevertheless, quasi-static axial loading of the fe-murs using the described testing configuration provided a comparative means to quantify strength reductions in femurs containing high-risk lesions of the proximal femur, and believe the findings are translatable to the real-world situation. The selection of a loading rate of 2 mm/s is likely to be more in line with those undergone by the hip during the activities of daily life, contrasted with those experienced during a fall, which have been approximated to be roughly 100 mm/s. Unlike fractures of normal, healthy bone, pathologic fractures are known to occur during regular activities or following minor trauma as a result of enervating of the bone by metastatic disease, adding justification to our use of this loading rate.