Thomas J. Roberts

SUMMARY The function of many muscles during natural movements is to accelerate a mass. We used a simple model containing the essential elements of this functional system to investigate which musculoskeletal features are important for increasing the mechanical work done in a muscle-powered acceleration. The muscle model consisted of a muscle-like actuator with frog hindlimb muscle properties, operating across a lever to accelerate a load. We tested this model in configurations with and without a series elastic element and with and without a variable mechanical advantage. When total muscle shortening was held constant at 30%, the model produced the most work when the muscle operated with a series elastic element and an effective mechanical advantage that increased throughout the contraction (31 J kg^-1 muscle vs 26.6 J kg^-1 muscle for the non-compliant, constant mechanical advantage configuration). We also compared the model output with the dynamics of jumping bullfrogs, measured by high-speed video analysis, and the length changes of the plantaris muscle, measured by sonomicrometry. This comparison revealed that the length, force and power trajectory of the body of jumping frogs could be accurately replicated by a model of a fully active muscle operating against an inertial load, but only if the model muscle included a series elastic element. Sonomicrometer measurements of the plantaris muscle revealed an unusual, biphasic pattern of shortening, with high muscle velocities early and late in the contraction, separated by a period of slow contraction. The model muscle produced this pattern of shortening only when an elastic element was included. These results demonstrate that an elastic element can increase the work output in a muscle-powered acceleration. Elastic elements uncouple muscle fiber shortening velocity from body movement to allow the muscle fibers to operate at slower shortening velocities and higher force outputs. A variable muscle mechanical advantage improves the effectiveness of elastic energy storage and recovery by providing an inertial catch mechanism. These results can explain the high power outputs observed in jumping frogs. More generally, our model suggests how the function of non-muscular elements of the musculoskeletal system enhances performance in muscle-powered accelerations.

We tested the hypothesis that the hindlimb muscles of wild turkeys(Meleagris gallopavo) can produce maximal power during running accelerations. The mechanical power developed during single running steps was calculated from force-plate and high-speed video measurements as turkeys accelerated over a trackway. Steady-speed running steps and accelerations were compared to determine how turkeys alter their running mechanics from a low-power to a high-power gait. During maximal accelerations, turkeys eliminated two features of running mechanics that are characteristic of steady-speed running: (i) they produced purely propulsive horizontal ground reaction forces, with no braking forces, and (ii) they produced purely positive work during stance, with no decrease in the mechanical energy of the body during the step. The braking and propulsive forces ordinarily developed during steady-speed running are important for balance because they align the ground reaction force vector with the center of mass. Increases in acceleration in turkeys correlated with decreases in the angle of limb protraction at toe-down and increases in the angle of limb retraction at toe-off. These kinematic changes allow turkeys to maintain the alignment of the center of mass and ground reaction force vector during accelerations when large propulsive forces result in a forward-directed ground reaction force. During the highest accelerations, turkeys produced exclusively positive mechanical power. The measured power output during acceleration divided by the total hindlimb muscle mass yielded estimates of peak instantaneous power output in excess of 400 W kg^-1 hindlimb muscle mass. This value exceeds estimates of peak instantaneous power output of turkey muscle fibers. The mean power developed during the entire stance phase increased from approximately zero during steady-speed runs to more than 150 W kg^-1muscle during the highest accelerations. The high power outputs observed during accelerations suggest that elastic energy storage and recovery may redistribute muscle power during acceleration. Elastic mechanisms may expand the functional range of muscle contractile elements in running animals by allowing muscles to vary their mechanical function from force-producing struts during steady-speed running to power-producing motors during acceleration.

Similarly sized bipeds and quadrupeds use nearly the same amount of metabolic energy to run, despite dramatic differences in morphology and running mechanics. It has been shown that the rate of metabolic energy use in quadrupedal runners and bipedal hoppers can be predicted from just body weight and the time available to generate force as indicated by the duration of foot–ground contact. We tested whether this link between running mechanics and energetics also applies to running bipeds. We measured rates of energy consumption and times of foot contact for humans (mean body mass 78.88 kg) and five species of birds (mean body mass range 0.13–40.1 kg). We find that most (70–90 %) of the increase in metabolic rate with speed in running bipeds can be explained by changes in the time available to generate force. The rate of force generation also explains differences in metabolic rate over the size range of birds measured. However, for a given rate of force generation, birds use on average 1.7 times more metabolic energy than quadrupeds. The rate of energy consumption for a given rate of force generation for humans is intermediate between that of birds and quadrupeds. These results support the idea that the cost of muscular force production determines the energy cost of running and suggest that bipedal runners use more energy for a given rate of force production because they require a greater volume of muscle to support their body weight.

This paper integrates the results of a series of studies on the supply of O₂ and substrates for oxidative muscle metabolism and draws conclusions on the role of structural design in partitioning and limiting substrate supply. The studies compared dogs and goats exercising at different intensities and combined physiological, biochemical and morphometric investigations. In both species, the rate of fatty acid oxidation reached an upper limit at low exercise intensities, and only glucose consumption was increased at higher exercise intensities. The supply of both glucose and fatty acids from the capillaries reached maximal rates at low exercise intensities; this limitation is related to the design of the sarcolemma as calculations suggest that the endothelium introduces only a small resistance to substrate flux. From these findings, it appears that the capillaries are designed to satisfy O₂ supply up to maximal O₂ demand. The increase in substrate supply to the mitochondria at higher exercise intensities is achieved by drawing on intracellular stores of glycogen and lipids. The size of these stores is larger in dogs than in goats, providing the athletic species with twice the fuel reserves. These findings are interpreted on the basis of a network model with fluxes partitioned between direct and indirect pathways and with some structures shared by more than one function. Whereas O₂ is supplied through a direct pathway, the supply of both substrates is split temporally to allow, during exercise, immediate fuel supply to the mitochondria from intracellular stores; these are replaced from the vasculature, during periods of rest, to a size commensurate with high rates of combustion. Considering this complexity, we conclude that the results are compatible with the principle of symmorphosis applied to a network structure and that the adjustment of design to functional demand involves different structures for O₂ and for substrates.