A phenomenological muscle model to assess history dependent effects in human movement

Most musculoskeletal models used to analyze human movement utilize Hill-type muscle models that account for state dependent intrinsic muscle properties (e.g., force-length-velocity relationships), but rarely do these models include history dependent effects (e.g., force depression or enhancement). While the relationship between muscle shortening and force depression can be well characterized by muscle mechanical work, the relationship between muscle stretch and force enhancement is more complex. Further, it is not well known how these properties influence dynamic movements. Therefore, the goal of this study was to develop a modified Hill-type muscle model that incorporated stretch-induced force enhancement into a previously described model that included shortening-induced force depression. The modified muscle model was based on experimental data from isolated cat soleus muscles. Simulations of in situ muscle experiments were used to validate the model and simulations of a simple human movement task (counter-movement jumping) were used to examine the interactions of the history dependent effects. The phenomenological model of stretch-induced force enhancement was dependent on both the magnitude of stretch and relative length of the muscle fiber. Simulations of the in situ muscle experiments showed that the model could accurately reproduce force enhancement and force depression, as well as the complex additive relationship between these effects. Simulations of counter-movement jumping showed that a similar jump pattern could be achieved with and without history dependent effects and that a relatively minor change in muscle activation could mitigate the impact of these effects.