Sensitivity of muscle force estimates to variations in muscle-tendon properties.

The aim of this study was to determine the sensitivity of muscle force estimates to changes in some of the parameters which are commonly used to describe models of muscle-tendon actuation. The sensitivity analysis was performed on three parameters: optimal muscle-fiber length, muscle physiological cross-sectional area (PCSA), and tendon rest length. The muscles selected for the analysis were posterior gluteus medius/minimus, vasti, soleus, and sartorius. Each parameter was perturbed from its nominal value, and an optimization problem was solved to determine the relative influence of each parameter on the calculated values of muscle force. Muscle forces were calculated for a simulated cycle of normal walking. Parameter sensitivity was quantified using two new metrics: an integrated sensitivity ratio, which quantified the effect of changing a single parameter for any muscle on the time history of force developed by that muscle; and a summed cross-sensitivity ratio, which quantified the effect of changing one parameter for any muscle on the time histories of forces developed by all of the other muscles. The results showed that muscle force estimates for walking are most sensitive to changes in tendon rest length and least sensitive to changes in muscle PCSA. For soleus, for example, the integrated sensitivity ratios for tendon rest length were an order of magnitude greater than those for muscle-fiber length and PCSA. For vasti, the integrated sensitivity ratios for tendon rest length were twice as large as those for muscle-fiber length and nearly an order of magnitude greater than those for PCSA. Overall, changes in the tendon rest lengths of vasti and soleus and changes in the fiber length of vasti were most critical to model estimates of muscle force. Our results emphasize the importance of obtaining accurate estimates of tendon rest length and muscle-fiber length, particularly for those actuators that function as prime movers during locomotion (gluteus maximus, gluteus medius/minimus, vasti, soleus, and gastrocnemius).