An analytical examination of muscle force estimations using optimization techniques.

Muscle forces are often estimated during human movement using optimization procedures. The optimization procedures involve the minimization of an objective function relating to the muscle forces. In this study 15 different objective functions were evaluated by examining the analytical solutions to the objective functions and by comparing their force predictions with the forces estimated using a validated muscle model. The muscle forces estimated by the objective functions were shown to give poor correspondence with the muscle model predicted muscle forces. The objective function estimates were criticized for not taking sufficient account of the physiological properties of the muscles. As a consequence of the analysis of the objective functions an alternative, simpler function was presented with which to estimate muscle forces in vivo. This function required that to satisfy a given joint moment, the force exerted by each of the muscles divided by the maximum force possible by the muscle was constant for all muscles. For this function the maximum muscle force was determined using a muscle model assuming maximal activation.