A Validated Forward Solution Dynamics Mathematical Model of the Knee Joint: Can It Be an Effective Alternative for Implant Evaluation?

Mathematical modeling is among the most common computational tools for assessing total knee arthroplasty (TKA) mechanics of different implant designs and surgical alignments. The main objective of this study is to describe and validate a forward solution mathematical of the knee joint to investigate the effects of TKA design and surgical conditions on TKA outcomes.

A 12-degree of freedom mathematical model of the human knee was developed. This model includes the whole lower extremity of the human body and comprises major muscles and ligaments at the knee joint. The muscle forces are computed using a proportional–integral–derivative controller, and the joint forces are calculated using a contact detection algorithm. The model was validated using telemetric implants and fluoroscopy, and the sensitivity analyses were performed to determine how sensitive the model is to both implant design, which was analyzed by varying medial conformity of the polyethylene, and surgical alignment, which was analyzed by varying the posterior tibial tilt.

The model predicted the tibiofemoral joint forces with an average accuracy of 0.14× body weight (BW), 0.13× BW, and 0.17× BW root-mean-square errors for lateral, medial, and total tibiofemoral contact forces. With fluoroscopy, the kinematics were validated with an average accuracy of 0.44 mm, 0.62 mm, and 0.77 root-mean-square errors for lateral anteroposterior position, medial anteroposterior position, and axial rotation, respectively. Increasing medial conformity resulted in reducing the paradoxical anterior sliding midflexion. Furthermore, increasing posterior tibial slopes shifted the femoral contact point more posterior on the bearing and reduced the tension in the posterior cruciate ligament.

A forward solution dynamics model of the knee joint was developed and validated using telemetry devices and fluoroscopy data. The results of this study suggest that a validated mathematical model can be used to predict the effects of component design and surgical conditions on TKA outcomes.