Intact knee model definition
A 3D nonlinear FE knee model of intact knee was developed from computed to mography (CT) of a 27-year-old healthy male subject. The medical records of the subject were reviewed, and no cases of musculoskeletal disorders or limb alignment problems were found; The CT image was performed with 0.1-mm slice thickness using a 320-channel CT scanner.
The medial images were processed and segmented using software (Mimics 21.0, Materialise, Leuven, Belgium) which was used to generate the 3D geometrical surfaces of the femur, tibia and fibula at full extension (Figure. 1a), The model was stored in standard triangle language(STL) format. The STL files exported to Geomagic (Geomagic wrap 2014, Geomagic, North Carolina United States) to form solid models for the femur, tibia, fibula, patella. and processed for denoising、smoothing、surfacing constructed. The model was stored in initial graphics exchange specification(IGES) format. The IGES files were imported into solidworks 2019 software and use this software to build Medial、lateral cartilage, Anterior cruciate ligament(ACL), Posterior cruciate ligament(PCL),than generate the intact knee model(Fig. 1b). The intact knee model files were imported into Hypermesh to generate the FE mesh (Fig. 1c), FE mesh were analyzed use ABAQUS2019.
Material properties
The material properties were assigned according to pertinent literature. The femur, tibia and the fibula were modeled as linear elastic isotropic material and isotropic material with Young's Modulus of 17000 Pa, Poisson’s ratio of 0.3[10].The Young's Modulus and Poisson’s ratio of cancellous bone were 350Pa and 0.25.The articular cartilage is considered as transversely isotropic and linearly elastic, homogeneous material with Young’s Modulus of 15 MPa, Poisson’s ratio of 0.46[11]. menisci were specified as transversely isotropic and linearly elastic, homogeneous material with Young’s Modulus of 27.5 MPa, Poisson’s ratio of 0.33[10, 12].
Bones were assumed to be rigid, because bone is much stiffer than the soft tissues. Ligament models were considered isotropic and hyperelastic materials, represented by an incompressible NeoHookean behavior with an energy density function of Ψ = C1× (I1 − 3), where C1 is the initial shear modulus and I1 the first modified invariant of the right CauchyGreen strain tensor [13][10] .C1 values were 6.06, 6.43, 5.83, and 6.06 MPa for the LCL,MCL,ACL and PCL.
The PE insert were modeled as elastoplastic the material properties with Young's Modulus of 685 MPa, Poisson’s Ratio of 0.4. The femoral and tibial components were modeled as linear elastic isotropic materials with Young's Modulus of 195000MPa, c of 0.3(Table 1).
Table 1
Young's Modulus and Young's Modulus
| Material | Young’s modulus(Mpa) | Poisson’s ratio |
| Cartilage | 15 | 0.46 |
| Meniscus | 27.5 | 0.33 |
| PE bearing | 685 | 0.4 |
| Cortical bone | 17000 | 0.3 |
| Cancellous bone | 350 | 0.25 |
| Femoral component | 195000 | 0.3 |
| Tibial tray | 195000 | 0.3 |
Finite element models with different positions of femoral and tibia component
Three dimension models of mobile-bearing UKA were scanned using a non-contact 3D laser scanner, Scanned point data were converted to 3D models, and scanning was repeated until the 3D model dimensions had geometrical errors < 100mm. The models were stored in standard tessellation language(STL) format STL files exported to Solidworks (Figure. 2a). Then extracted intact knee model exported to SolidWorks, follow Oxford's surgical technique, use Boolean Operations, according to the dimensions of the femur and tibia were chosen for the femoral and tibia component, PE thickness of 4mm was consider. The FE model of UKA is shown in Fig. 2b.
Five different FE models of distal femoral prosthesis intorsion and extorsion were adopted and investigated. Femoral prosthesis intorsion and extorsion at 0° set neutral position, other FEA models, femoral prosthesis intorsion 6°, intorsion 13°,extorsion 6°,extorsion 13°,respectively(Fig. 2c). Other settings were like Intact knee model.
Loads and boundary conditions
In intact knee model, the femoral and the tibial cartilage were fully bonded to the femur and tibia bone. The femoral was constrained only in flexionextension while the tibia and fibula were completely fixed at their distal ends [10, 14].
In UKA models, the femoral component and the tibial tray were fully bonded to the femur and tibia, respectively, simulating bone cement usage. The femoral component and tibia tray made contact with the PE insert. The coefficient of friction between PE and metal, was chosen as 0.04 [15]. The UKA FE model is shown in Fig. 2 (b). The distal end of the tibia was fixed in all degrees of freedom to prevent rigid body motions during the analysis. An axial force of 1000 N was applied to simulate the axial compressive load on the knee of an adult during single limb stance. The effect of axial load sharing between tibia and fibula was simulated by linking the two bones with virtual mechanical rigid links. The FE model was analyzed using ABAQUS software.