Analysis and Implications of Compliance on Joint Biomechanics Measurements in Superposition Testing

To quantify the contributions of specific ligaments to overall joint movement, the principle of superposition has been used for nearly 30 years. This principle relies on using a robotic test system to move a biological joint to the same position before and after transecting a specific ligament. The resulting difference in joint forces is assumed to be the transected ligament's tension. However, the robotic test system's ability to accurately return the joint to the commanded pose is dependent on the compliance of the system's various components, which is often neglected. Accordingly, there were three objectives in this paper: (1) Explain the influence of system compliance on positioning error in superposition testing with a mathematical model, (2) Quantify the compliance of components within the robotic test system, and (3) Provide a framework to evaluate uncertainty in published superposition based in situ force measurements and demonstrate their implications on published anterior cruciate ligament (ACL) forces. A system stiffness model (SSM) was derived to explain that compliance of test system components will cause the superposition method to underestimate ligament tension and stiffness. Based on typical test system component and joint stiffness ranges measured in this study, it was determined that with decreasing robot and/or bone stiffness, or increasing joint stiffness values, ligament load error could increase to values greater than 50%. Results indicate that experimentalists should (1) maximize test system component stiffness relative to joint stiffness and/or (2) compensate for compliance induced deflection of the test system components.