Short Communication Power Output from Skeletal Muscle During Linear and Sinusoidal Shortening

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Abstract
Several recent accounts have estimated the maximum sustainable mechanical power available from a skeletal muscle based on measured or assumed force–velocity characteristics of the muscle and the assumption that the muscle, when active, shortens constantly at the velocity that is optimal for power output. Curtin and Woledge (1988) used this approach in estimating how much mechanical power is available from the myotomal muscles of a dogfish to power swimming. The muscles of a fish operate cyclically, shortening and doing work for half a cycle and being lengthened, possibly absorbing work, for the other half-cycle. Curtin and Woledge allowed for the periodic nature of power output by assuming that only half the muscles were active at any time, which is equivalent to assuming that the sustainable power is half the peak power. During swimming, the shape of the trunk of a fish changes sinusoidally with time (Hess and Videler, 1984), and the shortening velocity of a trunk muscle fiber must also vary approximately sinusoidally. Thus shortening velocity cannot be at the optimum velocity for power output through the entire shortening half-cycle: the assumption of shortening at a constant, optimum velocity must overestimate the power output. Weis-Fogh and Alexander (1977) and Pennycuick and Rezende (1984) have also estimated the maximum sustainable power output of muscle based on the assumption of shortening at constant velocity. The principal muscles considered in the latter two studies were flight muscles. For flight muscles, as for swimming muscles, a sinusoidal length trajectory and a sinusoidally varying shortening velocity are more realistic assumptions than a linear length change and a constant velocity of shortening. The following analysis was begun to determine the magnitude of the error that is likely to enter into estimates of power output from the assumption that muscle shortening during normal locomotion is at constant velocity rather than at a velocity which varies sinusoidally with time. It is shown that the assumption of shortening at constant velocity overestimates maximum power output by 20 % or less.