Estimation of muscle forces during motion involves solving an indeterminate problem (more unknown muscle forces than joint moment constraints), frequently via optimization methods. When the dynamics of muscle activation and contraction are modeled for consistency with muscle physiology, the resulting optimization problem is dynamic and challenging to solve. This study sought to identify a robust and computationally efficient formulation for solving these dynamic optimization problems using direct collocation optimal control methods. Four problem formulations were investigated for walking based on both a two and three dimensional model. Formulations differed in the use of either an explicit or implicit representation of contraction dynamics with either muscle length or tendon force as a state variable. The implicit representations introduced additional controls defined as the time derivatives of the states, allowing the nonlinear equations describing contraction dynamics to be imposed as algebraic path constraints, simplifying their evaluation. Problem formulation affected computational speed and robustness to the initial guess. The formulation that used explicit contraction dynamics with muscle length as a state failed to converge in most cases. In contrast, the two formulations that used implicit contraction dynamics converged to an optimal solution in all cases for all initial guesses, with tendon force as a state generally being the fastest. Future work should focus on comparing the present approach to other approaches for computing muscle forces. The present approach lacks some of the major limitations of established methods such as static optimization and computed muscle control while remaining computationally efficient.Electronic Supplementary MaterialThe online version of this article (doi:10.1007/s10439-016-1591-9 contains supplementary material, which is available to authorized users.

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Background: The influence of aging on reactive control of balance during walking has been mainly investigated in the sagittal plane, whereas balance control in response to frontal plane perturbations is largely unexplored in the elderly. This is remarkable, given that walking mainly requires active control in the frontal plane. An extensive gait perturbation protocol was used to test whether reactive control of walking balance changes with aging and whether these changes are more pronounced in the frontal than in the sagittal plane. Research question: We hypothesize that alterations in reactive muscle activity cause an age-related shift from lateral ankle to stepping strategy in response to perturbations in the frontal and sagittal plane, and that the alterations in the frontal plane will be larger than the alterations in the sagittal plane. Method: A treadmill-based perturbation protocol imposed frontal and sagittal plane perturbations of different magnitudes during different phases of the gait cycle. Motion capture and electromyography measured the response to the different perturbations in a group of eighteen young and ten older adults. Results: Only for a small subset of the perturbations, reactive muscle activity and kinematic strategies differed between young and older subjects. When perturbation magnitude increased, the older adults relied more on a stepping strategy for inward directed frontal plane perturbations and for sagittal plane perturbation just before heelstrike. Tibialis anterior activity increased less in the older compared to the young subjects. Using simulations, we related tibialis anterior activity to backward and outward movement of the center of pressure in the stance foot and confirmed its contribution to the ankle strategy. We concluded that deficient tibialis anterior activity predisposes elderly to use stepping rather than lateral ankle strategies to control balance. Significance: Rehabilitation targets for fall prevention in elderly need to also focus on ankle muscle reactivity.