The scaling or ontogeny of human gait kinetics and walk-run transition: The implications of work vs. peak power minimization

Abstract

A simple model is developed to find vertical force profiles and stance durations that minimize either limb mechanical work or peak power demands during bipedal locomotion. The model predicts that work minimization is achieved with a symmetrical vertical force profile, consistent with previous models and observations of adult humans, and data for 487 participants (predominantly 11–18 years old) required to walk at a range of speeds at a Science Fair. Work minimization also predicts the discrete walk-run transition, familiar for adult humans. In contrast, modeled peak limb mechanical power demands are minimized with an early skew in vertical ground reaction force that increases with speed, and stance durations that decrease steadily with speed across the work minimizing walk-run transition speed. The peak power minimization model therefore predicts a continuous walk-run gait transition that is quantitatively consistent with measurements of younger children (1.1–4.7 years) required to locomote at a range of speeds but free to select their own gaits.

Why are the fastest runners of intermediate size? Contrasting scaling of mechanical demands and muscle supply of work and power

“…Here, we approach the question by addressing the scaling implications of demand-specifically, of mechanical work each stride and of mechanical power during stance-and supply of muscle work, muscle power and physiological supply for muscle activation. We follow recent work accounting for scaling phenomena [9] ranging from posture [10] to the kinetics of young children [11] to the flapping and bounding flight of birds [12] by assuming that muscle is limited in its capacity to supply work and power.…”

Limb work and joint work minimization reveal an energetic benefit to the elbows-back, knees-forward limb design in parasagittal quadrupeds

“…These are widely observed in bipeds, including young children, human sprinters and birds. Potential explanations for this range from energetic (children: [ 21 ]; birds: [ 22 ]) to stability [ 23 ] to anatomical (sprinters: [ 24 ]; birds: [ 17 , 25 – 27 ]). Whatever account for early skew is favoured for bipeds, late skew—a common feature of quadruped forelimb vertical force profiles ( figure 2 )—is not consistent with any of the accounts for skew in bipeds.…”

Simple models highlight differences in the walking biomechanics of young children and adults

“…propulsive forces) is a skill learned much later in childhood, which requires tuning and control to achieve balance and elicit the desired motion in the forward direction (Brenière and Bril, 1998; Bril et al, 2015). Several studies have also highlighted differences between the typical ground reaction profiles generated by young children and adults (Dewolf et al, 2020; Takegami, et al, 1992), and have used simple models to suggest mechanical work minimization may not be the optimal strategy for young children (Usherwood et al, 2018b). This raises the question as to how the walking pattern of young children should be modeled, recognizing that that their walking mechanics may not simply be scaled down versions of adults.…”

“…Dynamic similarity means that multiplying all linear dimensions, time intervals, and forces by constant factors would result in identical walking patterns. Deviations from dynamic similarity are observed in young children (Kramer and Sarton-Miller, 2008; Usherwood et al, 2018b), and the Froude number makes no allowance for differences in shape. Differences in shape, or anthropomorphic proportions, may be an important consideration when making metabolic comparisons within a species, or in animals relatively close in size (Kramer and Sylvester, 2013).…”