Bi-level inverse optimal control for preoperative prediction of postoperative squat kinematics after total knee replacement

Total knee replacement restores mobility in patients with advanced osteoarthritis, yet many individuals still experience limited ability to perform high-flexion tasks such as squatting. Current preoperative planning relies on static imaging and cannot predict how different implant alignment choices will affect postoperative dynamic function. This study developed a predictive simulation framework that uses bi-level inverse optimal control to link preoperative implant alignment directly to expected postoperative squat kinematics.

Subject-specific musculoskeletal models were constructed for six total knee replacement patients using experimental squat data. Bi-level inverse optimal control was applied to identify both individualised and group-level cost functions. The individualised setting provided subject-specific accuracy, while the group-level setting derived a single group-level cost function as an initial step toward preoperative use without requiring postoperative motion data.

The individualised setting reproduced experimental trajectories with low errors across all joints (mean apex difference 1.53°, root-mean-square error 5.15°, normalised root-mean-square error 11.15%, Pearson correlation 0.96). The group-level setting yielded higher but acceptable errors (mean apex difference 5.70°, root-mean-square error 6.75°, normalised root-mean-square error 17.53%, Pearson correlation 0.95) while preserving the general pattern and phasing of the motion. Squat depth emerged naturally from the optimisation rather than being prescribed.

This framework may provide a basis for future quantitative tools to evaluate how implant alignment choices influence postoperative squat performance, potentially improving functional outcomes in total knee replacement.

These results suggest that the proposed IOC framework can reproduce key features of post-TKR squat kinematics, but further out-of-sample validation is required before it can be used for preoperative prediction or translated into tools aimed at improving functional outcomes in total knee replacement.