Background:​ When calculated with single plane fluoroscopy in conjunction with 3D model to 2D image registration, tibiofemoral contact kinematics describe the anterior-posterior (A-P) movement of the tibial contact location in each of the medial and lateral compartments developed between the femoral component and tibial insert. Knowledge of A-P tibial contact locations provides an objective assessment of the relative motion of the tibia on the femur for total knee arthroplasty (TKA), which can be used to compare the performance of different components, surgical techniques, and alignment goals. Both the closest point method and the penetration method have been used to calculate A-P tibial contact locations in single plane fluoroscopy. In using either method, there are two sources of error. One source is the error in the relative 3D position and orientation of the components which is used as input data and the other source is the error inherent to the method per se. It is unknown how errors in the relative 3D position and orientation of the components propagate into errors in the calculation of the A-P tibial contact locations. The propagation of error is important to analyze because it places a lower bound on the error for each method. If the lower bound is excessive, then a method would be rendered unsuitable. The errors due to both sources in computing the A-P tibial contact locations also are unknown. Hence there were two objectives. One was to analyze the propagation of error in the A-P tibial contact locations due to the errors in the relative 3D position and orientation of the components to determine the lower bound on the error for each method. The other was to determine the errors contributed by both sources in calculating the A-P tibial contact locations with the two methods.

Methods:​ To determine the errors in the A-P tibial contact locations due to the errors in the relative 3D position and orientation of the components, 1000-iteration Monte Carlo simulations were performed for each of twelve different reference relative 3D positions and orientations of the femoral component. For each iteration, random errors were added to each of the six degrees of freedom of the reference relative 3D position and orientation of the femoral component. For each iteration, the A-P tibial contact location was computed using the closest point method and the penetration method. The errors in the A-P tibial contact location calculated with each method were quantified with a bias (mean), precision (standard deviation), and root mean squared error (RMSE).

To determine errors contributed by both sources, the A-P tibial contact locations were calculated with the closest point method and the penetration method and simultaneously measured in vitro in ten fresh frozen cadaveric knee specimens with a tibial contact force sensor which served as the gold standard. The A-P tibial contact locations were calculated from radiographs of the cadaveric knee specimens at 0°, 30°, 60°, and 90° of flexion in neutrally, internally, and externally rotated orientations. While the radiographs were exposed, reference AP tibial contact locations were simultaneously collected using the tibial force sensor. The RMSEs in the A-P tibial contact location calculated with the closest point method, the penetration method with penetration, and penetration method without penetration were computed.

Results:​ From the Monte Carlo simulations, the overall bias, precision, and RMSE for the A-P tibial contact location calculated with the closest point method and penetration method were 0.0 mm, 1.2 mm, and 1.2 mm, and -0.9 mm, 2.1 mm, and 2.4 mm, respectively. From the in vitro experiments, the RMSEs in the A-P tibial contact location calculated with the closest point method, the penetration method with penetration, and penetration method without penetration were 5.5 mm, 3.6 mm, and 8.9 mm, respectively.

Discussion:​ One key finding was that the lower bounds on the RMSEs of 1.2 mm and 2.4 mm for the closest point and penetration methods respectively were due primarily to random errors and are sufficiently small so that both methods have the potential to provide objective assessment of TKA performance. A second key finding was that even though the lower bound RMSE for the penetration method of 2.4 mm was twice that of the closest point method of 1.2 mm, the RMSE for the penetration method with penetration was smallest from the combined effects of both sources of error and is therefore the preferred method for calculating the A-P tibial contact locations using single plane fluoroscopy. Because the RMSE for the penetration method without penetration was over 5 mm greater than the RMSE for the penetration method with penetration and over 2 mm greater than the RMSE for the closest point method, if penetration does not occur, then the closest point method should be used.