Sandercock, Thomas G. and C. J. Heckman. Force from cat soleus muscle during imposed locomotor-like movements: experimental data versus Hill-type model predictions. J. Neurophysiol. 77: 1538–1552, 1997. Muscle is usually studied under nonphysiological conditions, such as tetanic stimulation or isovelocity movements, conditions selected to isolate specific properties or mechanisms in muscle. The purpose of this study was to measure the function of cat soleus muscle during physiological conditions, specifically a simulation of a single speed of slow walking, to determine whether the resulting force could be accurately represented by a Hill-type model. Because Hill-type models do not include history-dependent muscle properties or interactions among properties, the magnitudes of errors in predicted forces were expected to reveal whether these phenomena play important roles in the physiological conditions of this locomotor pattern. The natural locomotor length pattern during slow walking, and the action potential train for a low-threshold motor unit during slow walking, were obtained from the literature. The whole soleus muscle was synchronously stimulated with the locomotor pulse train while a muscle puller imposed the locomotor movement. The experimental results were similar to force measured via buckle transducer in freely walking animals. A Hill-type model was used to simulate the locomotor force. In a separate set of experiments, the parameters needed for a Hill-type model (force-velocity, length-tension, and stiffness of the series elastic element) were measured from the same muscle. Activation was determined by inverse computation of an isometric contraction with the use of the same locomotor stimulus pattern. During the stimulus train, the Hill-type model fit the locomotor data fairly well, with errors <10% of maximal tetanic tension. A substantial error occurred during the relaxation phase. The model overestimated force by ∼30% of maximal tetanic tension. A nonlinear series elastic element had little influence on the force predicted by a Hill model, yet dramatically altered the predicted muscle fiber lengths. Further experiments and modeling were performed to determine the source of errors in the Hill-type model. Isovelocity ramps were constructed to pass through a selected point in the locomotor movement with the same velocity and muscle length. The muscle was stimulated with the same locomotor pulse train. The largest errors again occurred during the relaxation phase following completion of the stimulus. Stretch during stimulation caused the Hill model to underestimate the relaxation force. Shortening movements during stimulation caused the Hill model to overestimate the relaxation force. These errors may be attributed to the effects of movement on crossbridge persistence, and/or the changing affinity of troponin for calcium between bound and unbound crossbridges, neither of which is well represented in a Hill model. Other sources of error are discussed. The model presented represents the limit of accuracy of a basic Hill-type model applied to cat soleus. The model had every advantage: the parameters were measured from the same muscle for which the locomotion was simulated and errors that could arise in the estimation of activation dynamics were avoided by inverse calculation. The accuracy might be improved by compensating for the apparent effects of velocity and length on activation. Further studies are required to determine to what degree these conclusions can be generalized to other movements and muscles.
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