Development of Methods for Analyzing Tibiofemoral Kinematics and Contact Kinematics using 3D Models

Background: Tibiofemoral kinematics describe the relative movement of the femur with respect to the tibia through flexion, which provides an objective assessment of joint function and can be used to determine whether an artificial knee restores natural movement following total knee arthroplasty (TKA). One way to measure tibiofemoral kinematics is by analyzing the anterior-posterior (AP) movement of the femoral condyles on the tibia. There are two common methods for identifying AP positions and hence condylar movements: 1) the flexion facet center (FFC), and 2) the lowest point (LP) methods. However, comparison of AP positions from the two methods in the native knee yielded contradictory findings. Three factors need to be considered before applying the FFC and LP methods. The first factor is the selected reference plane upon which the AP positions are measured. One useful plane is the plane perpendicular to the tibial mechanical axis, which allows the AP positions to be expressed in a direction consistent with the coordinate system of Grood and Suntay. However, to construct a reliable tibial mechanical axis and hence perpendicular plane, there is a need for a highly repeatable and reproducible method for identifying the distal point of the tibial mechanical axis (i.e. center of the talocrural joint). A second factor is the presence of cartilage on the 3D model of the femur, which may alter the shape of the femoral articular surface and hence positions of the FFCs and LPs. A third factor is the smoothness of the 3D model, which may also alter the shape of the femoral articular surface. Hence the objective of Chapter 1 was to determine the repeatability and reproducibility of a new method and two previously described methods for locating the center of the talocrural joint. After constructing the tibial mechanical axis using the most repeatable and reproducible method from Chapter 1, the objectives of Chapter 2 were to use the plane perpendicular to the tibial mechanical axis to determine how well the FFC and LP methods agree, and to determine whether the addition of articular cartilage and/or smoothing significantly affects the AP positions of the femoral condyles. Another subject of interest is tibiofemoral contact kinematics, which describe the movement of locations of contact by the femur on the tibia throughout flexion. Knowledge of the AP tibial contact locations in artificial knees is useful in assessing wear of tibial inserts and detecting posterior rim loading. However, existing methods for determining AP tibial contact locations based on analysis of images from single-plane fluoroscopy, such as the penetration method, are prone to error. Hence, the objectives of Chapter 3 were to create a new planar model that can determine AP tibial contact locations and determine whether errors of the planar model are lower than those of the penetration method. Methods: For Chapter 1, the medial-lateral (ML), AP, and proximal-distal (PD) coordinates of the center of the talocrural joint were determined in thirteen 3D bone models of the full tibia using the new method, termed the area centroid method, and the previously described diagonal intersection and biplanar methods. Intraobserver and interobserver intraclass correlation coefficients (ICCs) were computed to quantify the repeatability and reproducibility for each method. For Chapter 2, Magnetic Resonance (MR) images of the native knee were obtained from eleven subjects, who subsequently performed a deep knee bend under fluoroscopy. For each subject, four different MR models of the distal femur were created: femur bone, smoothed femur bone, femur bone with cartilage, and femur bone with smoothed cartilage. AP positions of the LPs and FFCs in each compartment were determined for each model type following 3D model-to-2D image registration. For Chapter 3, a slopes-of-sagittal profiles (SSP) model was created using mathematical functions to simulate articular surfaces of the tibial insert and femoral condyles. AP tibial contact locations were calculated using the model and the penetration method and simultaneously measured with a tibial force sensor in 10 cadaveric TKA knees for four flexion angles (0°, 30°, 60°, and 90°) in each compartment during passive motion. For each method, the overall bias, overall precision, and overall root mean square error (RMSE) were calculated from the differences between the computed AP tibial contact locations and the measured locations. Results: For Chapter 1, the area centroid method had excellent repeatability (ICC ≥ 0.97) and reproducibility (ICC ≥ 0.92). For the biplanar method, repeatability (ICC ≥ 0.86) was good and reproducibility (ICC ≥ 0.40) was fair. For the diagonal intersection method, repeatability (ICC ≥ 0.71) was moderate and reproducibility (ICC ≥ 0.46) was fair. For Chapter 2, the limits of agreement were ± 5.5 mm at 0° flexion, and bounded by ± 2.4 mm at 30°, 60°, and 90° flexion. The differences in AP positions between the four model types were minimal for both LPs and FFCs. For Chapter 3, the SSP model had an overall bias of 0.6 mm and precision of 2.8 mm which were significantly greater than the overall bias of -0.1 mm (p = 0.0369) and overall precision of 2.0 mm (p = 0.0021) of the penetration method. Conclusion: The area centroid method offered better repeatability and reproducibility than existing methods and is recommended when identifying the mechanical axis of the tibia. Meanwhile, the FFC and LP methods provided similar mean results during a deep knee bend at flexion angles of 30° and beyond but not at 0°. The lack of significant differences between model types in the AP positions of the femoral condyles indicate that addition of cartilage to 3D bone models is not required to accurately determine AP positions. Therefore, faster and less expensive imaging techniques such as CT can be used confidently to acquire the 3D bone models for the analysis of tibiofemoral kinematics. Finally, a planar model based on the analysis of single-plane radiographic images did not increase accuracy in AP tibial contact locations. Hence, the penetration method is preferred to determine AP tibial contact locations using single-plane radiography