Patient Information
The female patient was admitted to the hospital on 14 May 2019 because of hip pain on the left side, and x-ray revealed femoral fracture. She was 71 years old, 165 cm tall and weighed 58 kg. The patient was notified and consented to contribute her medical records and images for the research. The study was approved by the ethical committee of the hospital.
Model Reconstruction and Mesh Creation
Computed Tomography (CT) of the right hip was acquired using CT (Siemens, Munich, Germany) at 2 mm slice interval. The CT data in DICOM format was imported into the software Mimics (Materialise, Leuven, Belgium) for processing, in which the femoral bone were segmented based on their grayscale at a threshold from 226 to 3017. Geomagic Studio (Geomagic, 3D Systems, Rock Hill, USA) was used to generate surfaces and reconstructed the three-dimensional geometry of the femur. The Hypermesh (Altair, Troy, USA) was used to tetrahedral meshing and developed the femur into a composited model containing cortical layer and trabecular core by organizing the elements. The size of the mesh was 2 mm.
Five intertrochanteric fracture models (T1, T2, T3, T4, and T5) at different lateral femoral wall thickness were created on the reconstructed femur of the patient based on the classification of 31A1.3 fractures. Specifications of the five models are listed in Table 1. The procedure to create the fracture line was as followed: Firstly, the first osteotomy line was created by linking the apex of the greater trochanter and the base of the lesser trochanter on the frontal plane, which corresponded to the first fracture model (T1) with a measured lateral femoral wall thickness of 27.6 mm. Secondly, the second osteotomy line was created by rotating the first osteotomy line around the base of the lesser trochanter at 5 anticlockwise on the frontal plane for the second fracture model (T2). Lastly, the other osteotomy lines and fracture models (T3, T4, and T5) were constructed by repeating the second step and rotated the line every 5 intervals. The five intertrochanteric fracture models are shown in Figure 2.
Table 1. The lateral femoral wall thickness and osteotomy line angle of the five fracture models.
Fracture Model
|
Lateral Femoral Wall Thickness (mm)
|
Osteotomy Line Angle ()
|
T1
|
27.6
|
60
|
T2
|
25.4
|
55
|
T3
|
23.4
|
50
|
T4
|
21.4
|
45
|
T5
|
19.3
|
40
|
Regarding the implant, the three-dimensional geometry of PFNA (Dabo Medical Devices Co., Ltd.Xiamen, China) was built in SolidWorks (Solidworks Inc., Dassault Systèmes, Vélizy-Villacoublay, France). The PFNA implant consisted of a nail, a spiral blade, and a locking screw. The length of the PFNA nail was 200 mm with a neck stem angle of 130°. The proximal and distal diameters of the nail were 16 mm and 10 mm, respectively. The length of the spiral blade was 107 mm with a diameter of 10 mm. The PNFA implant model was assembled with the intertrochanteric fracture models according to the PNFA surgical guidelines. In brief, the Tip Apex Distance (TAD) on both the anteroposterior and lateral views, shall be not more than 27mm [7].
Material Properties
The material properties are listed in Table 2. The Elastic modulus of the cancellous bone and cortical bone were assigned based on the constitutive equation between apparent density and elastic modulus. Material failure simulation was enabled for the bone and implant. Elastoplastic material properties were assigned including the yielding stress, failure strain, and the strain rate effects (Cowper-Symonds model) [8]. Material fracture or failure could be resembled by the propagation of element deletion in the FE simulation.
Table 2. Material properties of the trabecular, cortical bone, and PFNA implant used in the FE model.
Parameters
|
Trabecular bone
|
Cortical Bone
|
Titanium alloy (PFNA)
|
Apparent density (g/cm3)
|
0.589
|
1.525
|
4.43 [9]
|
Elastic modulus (GPa)
|
0.496
|
8.318
|
110 [10]
|
Poisson’s ratio
|
0.30
|
0.30
|
0.31 [11]
|
Tangent modulus (MPa)
|
49.6
|
831.8
|
1,592 [11]
|
Yield stress (MPa)
|
17.45 [12]
|
109 [12]
|
250
|
Hardening parameter
|
0.10 [8]
|
0.10 [8]
|
0.12 [13]
|
Failure strain(%)
|
0.7 [12]
|
0.9 [14]
|
0.2 [15]
|
Cowper-Symonds model parameter
|
C: 2.5
P: 7.0 [8]
|
C: 2.5
P: 7.0 [8]
|
C: 80000
P: 1.1 [16]
|
Boundary and Loading Conditions
We simulated a critical loading case resembling the suggested high loading condition during walking [17]. The femoral head was loaded 2,100 N at 10° lateral to the inferior axis on the frontal plane and 9° posterior to the inferior axis on the sagittal plane [17], as demonstrated in Figure 3. The distal section of the femur was fully fixed throughout the simulation.
The coefficients of friction between the implant interfaces, between the fractured bone fragments, and between the implant and the bone were 0.23 [18], 0.46 [18], and 0.3 [19] respectively.
Model Output and Data Analysis
FE analysis was conducted using LS-DYNA software (LSTC, Livermore, CA, USA). The von Mises stress and displacement of the bone and PFNA, as well as the breakage condition of the implant among the 5 intertrochanteric fracture models with different lateral femoral wall thickness were extracted and analyzed.