Hill muscle model errors during movement are greatest within the physiologically relevant range of motor unit firing rates

This study evaluated the accuracy of Hill-type muscle models during movement. Hill-type models are ubiquitous in biomechanical simulations. They are attractive because of their computational simplicity and close relation to commonly measured experimental variables, but there have been surprisingly few experimental validations of these models during functionally relevant conditions. Our hypothesis was that model errors during movement are largest at the low motor unit firing rates most relevant to normal movement conditions. This hypothesis was evaluated in the cat soleus muscle activated either by electrical stimulation at physiological rates or via the crossed-extension reflex (CXR) thereby obtaining normal patterns of motor unit recruitment and rate modulation. These activation paradigms were applied during continuous movements approximately matched to locomotor length changes. The resulting muscle force was modeled using a common Hill model incorporating independent activation, tetanic length-tension and tetanic force-velocity properties. Errors for this model were greatest for stimulation rates between approximately 10-20Hz. Errors were especially large for muscles activated via the CXR, where most motor units appear to fire within this range. For large muscle excursions, such as those seen during normal locomotion, the errors for naturally activated muscle typically exceeded 50%, supporting our hypothesis and indicating that the Hill model is not appropriate for these conditions. Subsequent analysis suggested that model errors were due to the common Hill model's inability to account for the coupling between muscle activation and force-velocity properties that is most prevalent at the low motor unit firing rates relevant to normal activation.