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Determination of Feasible Muscle Forces in Human Walking Using Static Optimization and Hill's Muscle Dynamics Constraints

Static optimization is a widely used technique for solving the redundant problem of muscle‐force determination for given inverse dynamics. There are different cost functions, such as minimal metabolic energy, minimal forces, minimal fatigue, which lead to different results. One problem in this setting is that the resulting time histories of the ensuing equilibrium forces may not be feasible with respect to the muscle dynamics, i.e., the resulting force gradients at the muscle cannot be reproduced by the dynamics of the corresponding muscle. In this paper, a combined method is presented which takes into account the limitations induced by the muscle dynamics by applying static optimization techniques at each time step and prescribing minimal and maximal constraints for the forces by extrapolating the force values from previous steps using feasible muscle activation values. Thus, both the advantages of fast static optimization and the guarantee of feasible time histories of the muscle forces can be achieved. Moreover, joint forces turn out to be 20–40% higher in swing phase than those predicted with classical static optimization. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)