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Using Subject-Specific Models to find Differences in Underlying optimization Criteria of Sprinting with and without Prostheses

A comprehensive knowledge of the underlying criteria of sprint motions, both of non-amputee and below-knee amputee athletes, is helpful for design improvement of prosthetic devices or towards a fair judgment of (dis-)advantage due to the running-specific prosthesis. For the study of sprint motions with and without running-specific prostheses, we created rigid multi-body system models of three non-amputee and one unilateral transtibial amputee athlete. We restricted the motions to the sagittal plane, ending up with 16 degrees of freedom (DOFs). The internal rotational DOFs are controlled by joint torque actuators. As the prosthetic device has to be passive, the joint torque actuator is replaced by a linear spring-damper system in the prosthetic ankle joint. The aim of our study is to identify the optimal weight factors which combine five elementary optimization criteria in such a way that the resulting synthesized motions comes as close as possible to recorded reference motions. To this aim, we formulated an inverse optimal control problem (IOCP) as a bi-level problem: In the outer loop, the weight factors are adapted such that the comparison of the reference motion and the solutions of the optimal control problem (OCP) which computes sprint motions in the inner loop match each other as close as possible. In contrast to previous studies, we investigated more athletes, added subject-specific joint torque limits based on Muscle Torque Generators and left the average velocities of the running motions free. For all four athletes, we identified a set of optimal weights that generates sprint motions which closely match the recorded reference motion. Significant differences in the identified weights between amputee and non-amputee sprinting have been found. Especially angular momentum control plays a decisive role in unilateral transtibial amputee sprinting.