Running, hopping and trotting: tuning step frequency to the resonant frequency of the bouncing system favors larger animals

A long-lasting challenge in comparative physiology is to understand why the efficiency of the mechanical work done to maintain locomotion increases with body mass. It has been suggested that this is due to a more elastic step in larger animals. Here, we show in running, hopping and trotting animals, and in human running during growth, that the resonant frequency of the bouncing system decreases with increasing body mass and is, surprisingly, independent of species or gait. Step frequency roughly equals the resonant frequency in trotting and running, whereas it is about half the resonant frequency in hopping. The energy loss by elastic hysteresis during loading and unloading the bouncing system from its equilibrium position decreases with increasing body mass. Similarity to a symmetrical bounce increases with increasing body mass and, for a given body mass, seems to be maximal in hopping, intermediate in trotting and minimal in running. We conclude that: (1) tuning step frequency to the resonant frequency of the bouncing system coincides with a lower hysteresis loss in larger, more-compliant animals; (2) the mechanism of gait per se affects similarity with a symmetrical bounce, independent of hysteresis; and (3) the greater efficiency in larger animals may be due, at least in part, to a lower hysteresis loss

Mechanical transients initiated by ramp stretch and release to P0 in frog muscle fibers

Single fibers from the tibialis muscle of Rana temporaria were subjected to ramp stretches during tetanic stimulation at a sarcomere length of ~2 \u3bcm. Immediately after the stretch, or after different time delays, the active fiber was released against a constant force equal to the isometric force (P0) exerted immediately before the stretch. Four phases were detected after release: 1) an elastic recoil of the fiber's undamped elements, 2) a transient rapid shortening, 3) a marked reduction in the velocity of shortening (often to 0), and 4) an apparently steady shortening (sometimes absent). Increasing the amplitude of the stretch from ~2 to 10% of the fiber rest length led to an increase in phase 2 shortening from ~5 to 10 nm per half-sarcomere. Phase 2 shortening increased further (up to 14 nm per half-sarcomere) if a time interval of 5-10 ms was left between the end of large ramp stretches and release to P0. After 50- to 100-ms time intervals, shortening occurred in two steps of ~5 nm per half-sarcomere each. These findings suggest that phase 2 is due to charging, during and after the stretch, of a damped element, which can then shorten against P0 in at least two steps of ~5 nm/half sarcomere each

The landing\u2013take-off asymmetry in human running

In the elastic-like bounce of the body at each running step the muscle\u2013tendon units are stretched after landing and recoil before take-off. For convenience, both the velocity of the centre of mass of the body at landing and take-off, and the characteristics of the muscle\u2013tendon units during stretching and recoil, are usually assumed to be the same. The deviation from this symmetrical model has been determined here by measuring the mechanical energy changes of the centre of mass of the body within the running step using a force platform. During the aerial phase the fall is greater than the lift, and also in the absence of an aerial phase the transduction between gravitational potential energy and kinetic energy is greater during the downward displacement than during the lift. The peak of kinetic energy in the sagittal plane is attained thanks to gravity just prior to when the body starts to decelerate downwards during the negative work phase. In contrast, a lower peak of kinetic energy is attained, during the positive work phase, due to the muscular push continuing to accelerate the body forwards after the end of the acceleration upwards. Up to a speed of 14 km h\u20131 the positive external work duration is greater than the negative external work duration, suggesting a contribution of muscle fibres to the length change of the muscle\u2013tendon units. Above this speed, the two durations (<0.1 s) are similar, suggesting that the length change is almost totally due to stretch\u2013recoil of the tendons with nearly isometrically contracting fibres