Forces of individual cat ankle extensor muscles during locomotion predicted using static optimization

In order to test the principles of the control of synergistie muscles that were proposed in the literature, forces of cat soleus (SO), gastrocnemius (GA), and plantaris (PL) measured during locomotion were compared with the corresponding forces predicted using different optimization criteria. Forces of cat SO, GA, and PL, and the corresponding cat kinematics were recorded simultaneously using E-shaped force transducers and high-speed video, respectively. Measurements were obtained from three cats walking and trotting on a treadmill at five nominal speeds ranging from 0.4 to 1.8 ms−1. Muscle forces were predicted using static optimization and a musculoskeletal model of the cat hindlimb consisting of three segments (foot, shank, and thigh) and three muscles (SO, GA, and PL). Six optimization criteria which had been proposed in the literature were tested. Linear criteria based on the principles of minimum muscle force and stress predicted forces during the stance phase with an average normalized error of 59–322%. Three other criteria—minimization of the sum of the relative muscle forces squared, minimization of the sum of the muscle stresses cubed, and minimization of the upper bound for all of the muscle stresses—showed a better performance: (i) the average error was 43–119% and (ii) the correlation coefficient calculated between the predicted and actual forces exceeded 0.9 for all three muscles. A criterion that was based on the principle of minimum fatigue and accounted for the percentage of slow-twitch fibers in the muscles, had the lowest average error (26–52%). The high correlation (0.97–0.99) between the measured forces and forces predicted by using the minimum fatigue criterion suggested that force sharing among SO, GA, and PL during cat locomotion may be the same for a given set of joint moments and muscle moment arms. It was concluded that static optimization with the appropriate criterion can predict muscle forces adequately for specific movement conditions.