## 4 Discussion
In particular, the L/M translation, typically the least accurate component in SbMBT, obtained an over 65% improvement in precision (averageprecision values: from 3.6 mm to 1.1 mm during isolated flexion, from 3.2 mm to 0.6 mm during lunge, and from 2.9 mm to 1.0 mm during sit-to-stand; Tables 1-3. This improvement might be attributed to the step-two analysis, where the two-level optimization effectively separates the guidance of the joint model on the out-of-plane translation (z-axis) of the tibia. The other 11-DOFs were thereafter fine-tuned given the model-determined tibial z-axis translation to maximize the image registration criteria. This compromise strategy between the kinematic model and the image matching was shown to not notably influence the accuracies in individual bone 6-DOFs (Figure 6) but slightly adjusted the relative poses of the two bones to increase the precision in determining the three translation components (Tables 1-3). In the present study, the contribution of the personalized kinematic model to the accuracy of tibofemoral rotations was relatively minor (Tables 1-3). The reasons may be twofold. First, the SbMBT-determined Flex/Ext and I/E rotation during the three activities were sufficiently representative of standard reference kinematics, as revealed in agreement analysis where the R\({}^{2}\) values were above 0.98. The capability of the model is not adequate to further diminish the errors in these two components owing to the model imperfections and uncertainties in the model parameters. Second, our MbMBT strategy was not intended to strictly guide the joint rotations by the kinematic model, as the most suitable model parameters for a particular motion task were unknown. In other words, discrepant tibofemoral rotation patterns are sure to result in different behaviors in ligament elongation [43; 44] and articular contacts [45] and should have different settings for the model parameters. Therefore, such subject-specific and motion-related model parameters were represented by polynomial equations determined using tibofemoral kinematics after the completion of step-two analysis. The role of the kinematic model in the determination of joint rotations was to provide physical constraints to the bone pose during image registration, which enabled eliminating largely deviated joint angles and improving the angle smoothness throughout the motion task. The effectiveness of the model could be observed in the Add/Abd component (Tables 1-3), in which the R\({}^{2}\) values were slightly increased with the MbMBT approach. The precision values were also statistically improved in the two weight-bearing tasks (Tables 2 and 3). The model inaccuracy is believed to have an impact on the performance of the MbMBT. In the current study, subject-specific ligament insertion points were not available, as MR images were absent. Instead, bone templates embedding known ligament endpoints were deformed to predict the subject's ligament insertion sites. However, the subjects enrolled in the present study were young Chinese people, but the reference ligament endpoint coordinates were not obtained from similar groups [35]. Potential morphological differences may be present in the bones and soft tissues among different ethnic groups and ages. Some studies have shown morphological differences in the knee [46] and ankle [47] joints between Caucasian and Chinese populations. A validation study is also required to assess the endpoint prediction accuracy and its influences on the performance of the MbMBT in the determination of tibofemoral kinematics.