Viscous elements have little impact on measured passive length–tension properties of human gastrocnemius muscle–tendon units in vivo

Abstract

Several studies have measured the elastic properties of a single human muscle–tendon unit in vivo. However the viscoelastic behavior of single human muscles has not been characterized. In this study, we adapted QLV theory to model the viscoelastic behavior of human gastrocnemius muscle–tendon units in vivo. We also determined the influence of viscoelasticity on passive length–tension properties of human gastrocnemius muscle–tendon units. Eight subjects participated in the experiment, which consisted of two parts. First, the stress relaxation response of human gastrocnemius muscle–tendon units was determined at a range of knee and ankle angles. Subsequently, passive ankle torque and ankle angle were collected during cyclic dorsiflexion and plantarflexion at a range of knee angles. Viscous parameters were determined by fitting the stress relaxation experiment data with a two-term exponential function, and elastic parameters were estimated by fitting the QLV model and viscous parameters to the cyclic experiment data. The model fitted the experimental data well at slow speeds (RMSE: 1.7±0.5 N) and at fast speeds (RMSE: 1.9±0.2 N). Muscle–tendon units demonstrated a large amount of stress relaxation. Nonetheless, viscoelastic passive length–tension curves estimated with the QLV model were similar to elastic passive length–tension curves obtained using a model that ignored viscosity. There was little difference in the elastic passive length–tension curves at different loading rates. We conclude that (a) the QLV model can be used to quantify viscoelastic behaviors of relaxed human gastrocnemius muscle–tendon units in vivo, and (b) over the range of velocities we examined, the velocity of loading has little effect on the passive length–tension properties of human gastrocnemius muscle–tendon units.