A healthy female (48 years old, 165 cm height, 65 kg weight) with no history of knee degeneration or trauma as confirmed by X-ray and magnetic resonance imaging (MRI) was recruited in the study. Following a signed informed consent for imaging, 256-slice spiral CT (Philips, Brilliance iCT) was performed for full length CT scan of the left lower limb, ranging from hip- to ankle joint. The scanning layer thickness was 1 mm; A 3.0 T magnetic resonance scanner (Combined image UI770) was used to perform sagittal MR scan at the left knee joint with a thickness of 1 mm.

Mimics 20.0 (Materialise Ltd., Leuven, Belgium) was used to extract 3D models of bone, cartilage, meniscus, anterior and posterior cruciate ligaments, medial and lateral collateral ligaments from CT and MR images. Rapidform 2006 reverse engineering software (INUS Technology, Inc., Seoul, South Korea) was used to materialize the 3D model of each structure. Abaqus 6.14–2 finite element analysis software (Dassault Systemes SimuliaCoip., Providence, RI, USA) was imported for assembly and registration, and the 3D solid model of healthy knee joint was developed.

3D point cloud data of femoral prosthesis (S), tibial prosthesis (A) and polyethylene insert were obtained using 3D scanner (ARTEC, EVA), and the Rapidform software was used for reverse 3D reconstruction to obtain the geometric model of the prosthesis. On the basis of the above established healthy knee joint, according to the Oxford III generation UKA standard surgical technique, a 7 mm thickness osteotomy was performed with Boolean operation with the 0° inclination in the coronal plane and the 7° posterior inclination in the sagittal plane. On the basis of this model, the tibial prosthesis was rotated to establish 3°, 5°, 9° and 11° posterior inclination models (Fig. 1).

The finite element model of 7°posterior inclination of tibial component and the other different posterior inclinations (3°, 5°, 9° and 11°) of tibial component

All models were divided by ten-node modified tetrahedral elements. There were 153,727 units of healthy knee joint model. A total of five MB UKA finite element models with different posterior inclinations of tibial prosthesis were established, and each model had about 300,000 units. Cartilage and meniscus were defined as isotropic linear elastic materials [14]. The ligament was defined as an incompressible transversely isotropic hyperelastic material [14], and the Neo Hookean constitutive model was applied. Its constitutive equation is:

$$\Psi = C_ \times (I_ - 3)$$

where C1 is the initial shear modulus and I1 is the first modified invariant of Cauchy Green strain tensor. C1 values used for the anterior and posterior cruciate ligaments, the medial and lateral collateral ligaments were 6.06, 6.43, 5.83 and 6.06 MPa, respectively. The material parameters of other structures are shown in Table 1.

Healthy knee joint finite element model using frictionless and limited slip surface-to-surface contact relations of the six (contact on location for: room between the medial and lateral cartilage of the femur and tibia, the femoral cartilage and meniscus between surface under the surface, tibial cartilage and meniscus) was made and the calculation made based on penalty function algorithm. MB UKA model had five contacts to set; the medial compartment surface contact which was using a frictionless contact, and the lateral compartment which was using coulomb friction contact, with a friction coefficient of 0.04.

Model verification under axial load: The degree of freedom in flexion and extension direction of femur was fixed, whereas the degree of freedom in other directions of femur was not fixed. While the lower surface of tibia and fibula remained completely fixed, the cartilage and bone as well as ligament and bone were connected in a binding form, and the front and back corners of the meniscus were bound to the tibial plateau. The reference point of femur was defined at the midpoint of the medial chamber and medial epicondyles of femur. An axial load was applied to this reference point (the direction of the load was down the mechanical axis, and the load size was 1000N), and the load distribution of the medial and lateral compartment was calculated and verified by comparison with the literature results [15].

Tibialis anterior drawer under the force model validation: Tibial reference point was defined at the center of the ankle, tibia and fibula coupling constraint main limit degree of freedom completely fixed in the direction of flexion and extension, femoral and tibial reference points put on forward force (the size of the force of 134 N), and the displacement of the tibia compared with literature results [16].

Static standing load model: Model verification was done under constrained coaxial load. A load of 325 N was applied along the mechanical axis of the tibia at the reference point of the femur, with a buckling angle of 0°. The load ratio of the medial and lateral compartment was then calculated.

Model under gait cycle load: The femur reference point was coupled with the proximal femur, and the model verification done under constrained coaxial load. A force load along the mechanical axis of the tibia and a sagittal angle (flexion and extension) were applied at the femur reference point. The force load and flexion angle were provided by the joint forces and range of motion of the subjects at different points in the gait cycle [17] (Fig. 2). The knee joint force and the angle of flexion and extension at the first peak of ground reaction force and the second peak of ground reaction force in the gait cycle were selected as the loading boundary conditions to calculate the load distribution of the medial and lateral compartments of the knee joint, and the maximum contact pressure between the polyethylene insert and the tibial cartilage of the lateral compartment.

Knee flexion angle and joint force during the stance phase of the gait cycle