Data collection
A healthy male volunteer (32 years of age, 70 kg, 171 cm) and a healthy female volunteer (27 years of age, 51 kg, 162 cm) were included in our study. The following gait kinematic data of the two volunteers during the current experiment and the follow-up period were obtained.
Imaging data:
Candidates who had abnormalities in pelvic posture and hip morphology in pelvic X-ray and CT imaging were excluded. The region from 1 cm above the highest point of the iliac crest to 3 cm below the trochanter was scanned using X-ray. The pelvis and the femur were examined by CT (0.5 mm slice thickness, 5 mm wavelength interval, and image resolution of 1024×1024). CT images were saved as DICOM format and exported for 3D rigid-body modeling.
Gait kinematic data:
Hip position data of standing posture and gait data of volunteers during walking were collected using the optical 3D gait analysis system (BTS Bioenginering, Italy). During the experiment, the two participants received adaptive training to walk continuously and freely prior to the tests. Then, they underwent 3 rounds of 5-m walk tests to ensure that both feet stepped into the force platform during at least one complete gait cycle in the one-way walking path. Infrared reflective markers were attached to the trunk, arms and legs and gait trajectories were formally collected and saved as the C3D file format for subsequent procedures.
Subject-specific musculoskeletal dynamics simulation
The dynamic hip motion of musculoskeletal model was simulated in the AnyBody modeling system (AnyBody Technology Company, Denmark). Custom musculoskeletal dynamics and inverse dynamics were analyzed using a modified fullbody model. As the function and application of AnyBody were reported elsewhere[20], this article focused on the custom simulation process.
Model customization:
To preliminarily adjust scaling, the body fat was measured using the built-in formulas in the AnyBody modeling system (volunteers’ BMI: 23.94/ 19.4). To achieve a more accurate self-customization, DICOM data extracted from CT images were used for 3D reconstruction of the ilium and femur using Mimics software (version 16.0, Mateialise, Belgium) (Figure 1). After reconstruction, 3D model files were imported into AnyBody for morphological scaling torealize the subject-specific registration ofthepelvis and thigh segment of general musculoskeletal model in AnyBodybased on spatial coordinates of the characteristic points of the iliofemoral modelsby point-to-point scaling codes. Moreover, the scaling was adjusted to match the starting and ending points of the muscles and ligaments surrounding the hip joint so that the anatomical features of human hip movements could be simulated more accurately.
Gait customization:
C3D files containing volunteers’ gait data were imported to AnyBody, and the locations of virtual markers alongside their 3D coordinates were adjusted to create the fully-matched models in accordance with the locations of markers attached to the trunk, arms and legs of volunteers. The simulated models were optimized using the built-in kinematic-parameter optimization algorithm in AnyBody which called kinematics optimization, and simultaneously the movement angles of the hip, knee, and ankle joints and the excursion of markers were calculated. The dynamic hip motion containing 8 phases in a gait cycle was simulated using the each one of optimized multibody model (Fig.2).
Inverse dynamic analysis
Data obtained through kinematics optimization above were re-extracted for inverse dynamics analysis. Muscle recruitment was solved by formulating a third-order polynomial optimization problem.After the musculoskeletal models completed corresponding walking gait during inverse dynamics loading, the data of muscle forces and joint reaction forces of the legs were obtained(Fig.3). Data of the muscle strength and the kinematics of the hip during a complete gait cycle were extracted for verification.
FEA for the contact stress distribution in the left hemipelvis FE models
Geometric definition:
While subject-specific geometric cartilage model is crucial for biomechanical analysis. Bone morphology has been reported to play an important role to predict cartilage stress[21], it has also been shown that the optimal alignment of the joint was not sensitive to the choosing of cartilage thickness distribution. Therefore, we performed an 3D dilation on the surface of the femoral head and lunate surface of acetabular fossa to reconstruct a constant thickness (1.8 mm) cartilage layers of the femur and acetabulum[21].
Material properties and boundary conditions:
As illustrated elsewhere[22], the cartilage of a normal hip joint was modeled using homogeneous, isotropic and linear elastic materials, while the cortical bone and trabecular of the ilium and femur were modeled using homogeneous isotropic materials (Table 1).
According to the method described elsewhere[23], data of the 8 phases during a single gait cycle of the left foot were introduced to analyze the contact stress of the hip joint during walking using the FEA. In the FE model, rigid transformation parameters of the hip during a gait cycle were adjusted using the kinematic data from the musculoskeletal simulation analysis, and realized by rotating coordinates of all unit nodes of the femur part. Assuming that the original coordinate of the femoral node was P(𝑥0,𝑦0,𝑧0), the angles of hip rotation along the three axes of x, y, and z were𝜃𝑥, 𝜃𝑦, and 𝜃𝑧, and then the three rotation matrices were:
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)
Based on a standard boundary condition described by Phillips et al.[24], data constraints were applied to the top of the ilium and pubic areas when all 6 degrees of freedom were constrained to 0. The rotation center of the femoral head obtained by a least-squares spherical fitting was selected as the reference node, and the nodes on the femoral head surface were constrained by the reference node using a kinematic coupling. The resultant force was applied at the reference point, and the direction of the resultant force at each gait phase were consistent with the reaction force (including the corresponding muscle forces[20]of the hip joint derived from inverse dynamics analysis). The interaction between the femoral head and the acetabulum was simulated by face to face contact in ABAQUS, and the contact was assumed to be frictionless as it was used elsewhere[25].
The mesh sensitivity was performed on a cartilage component rather than the skeletal for contact stress analysis,since we mainly focus on the contact stress of the hip joint, and a finer mesh was used. Three different mesh sizes were tested on the cartilage models, and the suitability was assessed based on the results of the contact stress analysis (the mesh selection criteria was defined as the changes in contact pressure and area with the difference between the meshes within 1%).
Table 1
Properties of materials, the number of elements and elastic modulus in FE models
Components
|
Element type
|
Number of elements
|
Elastic modulus (MPa)
|
Poisson’s ratio
|
Cortical bone (femur + ilium)
|
C3D10
|
Model 1: 22827
Model 2: 19881
|
15100
|
0.3
|
Trabecular bone
(femur + ilium)
|
C3D10
|
Model 1: 45642
Model 2: 41043
|
445
|
0.22
|
Cartilage (femoral head)
|
C3D10M
|
Model 1: 56783
Model 2: 51480
|
15
|
0.45
|
Cartilage
(acetabulum)
|
C3D10M
|
Model 1: 60100
Model 2: 56104
|
15
|
0.45
|