A modified Hill muscle model that predicts muscle power output and efficiency during sinusoidal length changes.

The power output of a muscle and its efficiency vary widely under different activation conditions. This is partially due to the complex interaction between the contractile component of a muscle and the serial elasticity. We investigated the relationship between power output and efficiency of muscle by developing a model to predict the power output and efficiency of muscles under varying activation conditions during cyclical length changes. A comparison to experimental data from two different muscle types suggests that the model can effectively predict the time course of force and mechanical energetic output of muscle for a wide range of contraction conditions, particularly during activation of the muscle. With fixed activation properties, discrepancies in the work output between the model and the experimental results were greatest at the faster and slower cycle frequencies than that for which the model was optimised. Further optimisation of the activation properties across each individual cycle frequency examined demonstrated that a change in the relationship between the concentration of the activator (Ca2+) and the activation level could account for these discrepancies. The variation in activation properties with speed provides evidence for the phenomenon of shortening deactivation, whereby at higher speeds of contraction the muscle deactivates at a faster rate. The results of this study demonstrate that predictions about the mechanics and energetics of muscle are possible when sufficient information is known about the specific muscle.