An active model for gastrocnemius muscle activity to predict the impact force during running

Several mass-spring-damper (MSD) models have been developed to study biodynamical characteristics of the body during running, especially the ground reaction force. The MSD models are mainly categorized into passive and active models. Plenty of the passive models have been proposed in which compliant properties of the elements modeling the soft tissues of the leg musculoskeletal system remain invariable regardless of the ground viscoelastic conditions, the type of the footwear, etc. Additionally, the passive models do not take the muscle activity into account. This paper aims at presenting a new active biomechanical model for the musculoskeletal system of the human leg to predict the impact force during running, especially, with various speeds. This idea is established on the LNZN model with replacing the passive package of lower soft-tissue in an active Kelvin-Voigt type model of the gastrocnemius muscle. In fact, the stiffness of the spring and the damping coefficient of the viscose dashpot are both exponential functions of the Achilles tendon force. This model is examined for two types of hard and soft shoes. Tuning parameters included in the gastrocnemius muscle model are determined using the least square error (LSE) method so that the difference of predicted ground reaction forces between the LNZN model and the new active model is minimized. Finally, in order to develop the model for a continuous range of running speeds, an artificial neural network (ANN) is designed to estimate the muscle's tuning parameters according to a desired speed. The results, obtained by numerical simulations, show a good agreement with the data reported in literature.