Part 1: Construction of 3D tibial models under different stem lengths of tibial plateau
Patients suffering from osteoarthritis with genu varum (excluding those with suspected infection before surgery, previous knee surgery, or RA) were included in the study from May 2018 to May 2019. Full-length radiographs were preoperatively taken for both lower extremities, and the angle of varus deformity and the medial proximal tibial angle (MPTA) of the knees were measured. Subsequently, a 0.6-mm thin-slice CT scan of both lower extremities was conducted and Mimics 14.0 (Materialise, Leuven, Belgium) was used to construct a 3D model. A coordinate system was set up, with the z-axis as the tibial alignment line (i.e., the line connecting the center of ankle mortise and the center of any axial plane below the proximal tibial articular surface and above the tibial tuberosity). The tibial length along the direction of the force line was measured on the 3D model of the tibia. The y-axis was defined as the anteroposterior (AP) axis, which was determined by an experienced orthopedist (connecting the medial 1/3rd of the tibial tuberosity and the midpoint of posterior cruciate ligament endpoint in a plane perpendicular to the z-axis). The x-axis was a straight line perpendicular to the y-axis and z-axis. This model was simplified by ignoring the measurements of the fibula. Tibial cutting planes with posterior slopes of 0° and 3° were made to be perpendicular to the tibial force alignment line and were placed 8 mm away from the lateral side tibial plateau to simulate tibial cut. If no defect was found in the medial tibia after simulated tibial cut, the patient was enrolled as a subject. If the medial tibia had a defect less than 4 mm away from the tibial cutting plane, the osteotomy volume of the tibia was increased until the defect in the medial tibia was eliminated. If defect in the medial tibia was further away than 4 mm, the case was excluded from this study. A total of 100 samples were obtained using the above method.
From these 100 samples, appropriate tibial models were chosen. The model profiles were acquired from the directly measured results by press-fit condylar (PFC) Sigma (Depuy Orthopaedics, Warsaw, IN, USA) and were assembled according to the manufacturer’s guidelines. The rotation of the tibial prothesis was consistent with the y-axis direction in the coordinate system (i.e., the AP axis of the tibia). The maximum length of the tibial prothesis stem that could be inserted and the distal end of the stem that impinged the tibial cortex when the tibial prosthesis was in the proper position were measured for the two groups undergoing tibial cut with different tibial posterior slopes (0° and 3°), as shown in Fig. 1.
Part 2: Establishment of finite element models to show the effect of different lengths of tibial plateau extension stems on the stress distribution of tibial prosthesis
Basic model
A 3D model with the tibial length equivalent to the median of the tibial length measured in Part 1 was chosen. Mimics software was used to establish models for the cortical and cancellous bones, and a coordinate system and alignment line were established, as described in Part 1. The models were simplified by ignoring the fibular measurements. Tibial cuts with tibial posterior slopes of 0° and 3° were simulated using the same tibial cut method, as described in Part 1. The basic models were obtained after checking their integrity following simulated tibial cut.
Tibial components
To determine the tibial components, an appropriate tibial plateau model was selected, and the model profile was obtained by direct measurement according to the PFC Sigma (DePuy Orthopaedics, Warsaw, IN, USA) and the model was assembled according to the manufacturer’s instructions. The rotation of tibial prothesis was consistent with the y-axis in the Part 1 method (i.e., the AP axis of the tibia). According to the confidence interval (CI) of the maximum stem length measured in Part 1, tibial plateau models with different stem lengths for prosthesis were set up. An 8-mm tibial spacer was selected. As knee motion was not considered during the modeling, the upper contour of the spacer was omitted and replaced by a plateau [15, 16]. Under the plateau, the thickness of bone cement was simulated as a 1-mm rigid body, which is in line with previous studies [17, 18, 19, 20].
Finite element models of tibia prostheses with different extension stem lengths
Two groups undergoing tibial cut with tibial posterior slopes of 0° and 3° were established as described in Part 1, with each group having five different extension stem lengths according to the CI of maximum range stem length measured in Part 1. They constituted a total of ten models with different extension stem lengths for tibial plateau prostheses and two posterior slopes. The models of tibial plateaus and spacers were installed, after which HyperMesh (Altair HyperWorks, Troy, MI, USA) was used for finite element meshing. The finite element models are shown in Fig. 2.
Material properties
Based on previous research data, the densities, Poisson’s ratios, and elastic moduli of the tibial cortical bone, cancellous bone, plateau, placers, sclerotic bone, and bone cement were defined, as shown in Table 1 [16, 17, 21, 22, 23]. The coefficients of friction were measured: between the tibia and bone cement = 1, between the bone cement and tibial plateau = 0.4, and between other contact surfaces = 0.4 [17, 18, 19, 20].
Load and boundary conditions
The inferior surface of the distal tibia was fixed in all directions. The maximum load and the medial and lateral distributions were similar to those described in previous studies. Static standing with exact mechanical alignment was simulated with 50% load on medial side and 50% on the lateral side of the spacer [24]. The force was set at three times the total body weight (e.g., total body weight 70 kg = 2100 N). The force-bearing site was the transverse diameter of the tibial prosthesis across the medial and lateral plateau center [15, 17, 21, 25]. The direction of the force was parallel to the tibial alignment (z-axis). The relative displacement of distal end of the prothesis and the stress distribution among the prosthesis and tibia were compared [16].
Statistical analysis
All data were expressed as mean ± standard deviation. Pearson’s correlation coefficient was provided to assess the extent of linear association in the 0° and 3° groups. Statistical significance was defined as p<0.1. Statistical analyses were performed using Statistical Package for the Social Sciences version 17.0 (SPSS, Chicago, IL, USA).