Development of a muscle force optimization algorithm to improve center of pressure during simulated walking

The Universal Musculoskeletal Simulator (UMS) was developed at the Cleveland Clinic to facilitate general purpose orthopaedic research that allows investigators to study the in vitro forces applied to bones, tendons and ligaments during simulated exercise of cadaver joint systems. In its original state, the UMS hardware consisted of a rotopod (a specialized hexapod robot), a single rotary tendon actuator and custom LabVIEW software for coordinated control and operation of the system. The focus of this work was to (1) enhance the UMS with a multi-tendon actuator system, (2) develop a muscle force optimization algorithm and evaluate it with a static model of the foot/ankle, (3) integrate the algorithm with the UMS software and evaluate it with cadaver specimens, and (4) utilize the enhanced UMS to investigate the individual muscle contributions to center of pressure using cadaver specimens.

Completion of the multi-tendon actuator system has enabled researchers to simulate exercise on cadaver joints by using up to five motorized actuators to simulate muscle forces that would occur during exercise while simultaneously contacting the joint with an external load generated by the rotopod. Although the multi-tendon actuator system was first conceived as a necessary enhancement to simulate the key extrinsic muscles of the ankle/foot, required to conduct simulated walking with cadaver feet, it was soon recognized that this system could be utilized to simulate muscles forces of other joints (i.e., shoulder, wrist, spine, etc.) and as such now provides a general purpose test bed for conducting orthopaedic research.

Initial cadaver studies of the foot/ankle using the UMS revealed that normal physiological center of pressure patterns were difficult to achieve during simulated walking. Therefore, the primary goal of this effort was to develop an algorithm that would optimize the muscle forces to better achieve the desired medial-lateral and anterior-posterior center of pressure profiles expected during physiologically accurate simulated walking. This algorithm was integrated with the existing arsenal of UMS optimization tools.

Optimization of muscle forces during simulated walking utilized the method of minimizing the cube of muscle stress and was solved through the use of sequential quadratic programming. Initially, for rapid debugging purposes, the muscle optimization technique was evaluated with a static model of the ankle/foot and then characterized using the UMS with cadaver feet. Simulated gait with three cadaver feet demonstrated that improvement to center of pressure (COP) is greatest in the mid stance portion of gate especially in the range of 41–50% stance (reduction in the mean error in the range of 83.0% to 93.4% for anterior COP and from 81.6% to 98.6% for medial COP after three iterations). Additionally, individual muscle contributions to the COP were investigated experimentally at estimated full-physiological levels. The significant finding of this test was that the triceps surae muscle groups acts as an everter (medial COP shift) at times before 65–70% stance and acts like an inverter (lateral shift in COP) at stance times above this range.