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Biological findings show that the activity of the calf muscle group is controlled by the central nervous system during running. The central nervous system tries to retain the peak values of the ground reaction force at constant levels as well as to minimize the vibration amplitude of soft tissues of the lower leg. Furthermore, these objectives are functions of stiffness and damping (compliance properties) of the calf muscle-tendon unit, especially gastrocnemius-Achilles. In this article, a new model for the calf muscle-tendon unit activity is presented in which the coefficients of stiffness and damping are exponential functions of the force produced at the Achilles tendon in the duration of stance phase, that is, they are time variant instead of having constant values. Then, the central nervous system functionality to control the activity of the muscle-tendon unit is formulated through definition of an optimization problem. This problem is solved by additionally considering the hardness of sport shoes. The muscle activity is indeed controlled via optimally adjusting two tuning parameters of the muscle-tendon unit model in terms of the hardness of shoes. This idea is examined separately for two running speeds. The results show the following: (1) The hardness of shoes affects the muscle activity. We find safe areas of the hardness parameters to design sport shoes. (2) When hard shoes are worn, the running speed has negligible effects on the tuning parameters, while with soft shoes the tuning parameters significantly change the muscle activity and the ground reaction force depended on running speed. (3) The ability of muscle in changing its compliance properties (specified by bound limits over the muscle-tendon unit tuning parameters) has the most influence in the safe area. (4) Rising running speed leads to a decrease in the safe area of shoes' parameters.

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