Predicting the energy cost of terrestrial locomotion: A test of the LiMb model in humans and quadrupeds

Washington University, 119 McMillan Hall, St Louis, MO 63130, USA.
Journal of Experimental Biology (Impact Factor: 2.9). 03/2007; 210(Pt 3):484-94. DOI: 10.1242/jeb.02662
Source: PubMed


The energy cost of terrestrial locomotion has been linked to the muscle forces generated to support body weight and swing the limbs. The LiMb model predicts these forces, and hence locomotor cost, as a function of limb length and basic kinematic variables. Here, I test this model in humans, goats and dogs in order to assess the performance of the LiMb model in predicting locomotor cost for bipeds and quadrupeds. Model predictions were compared to observed locomotor cost, measured via oxygen consumption, during treadmill trials performed over a range of speeds for both walking and running gaits. The LiMb model explained more of the variation in locomotor cost than other predictors, including contact time, Froude number and body mass. The LiMb model also accurately predicted the magnitude of vertical ground forces. Results suggest the LiMb model reliably links locomotor anatomy to force production and locomotor cost. Further, these data support the idea that limb length may underlie the scaling of locomotor cost for terrestrial animals.

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Available from: Herman Pontzer
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    • "However, a few comments are warranted. First, normalized measures of walking energy expenditure , such as the " cost of locomotion " (joules kg −1 sec −1 ) or the " cost of transport " (joules kg −1 m −1 ) [23], have been used to normalize the energy cost of treadmill walking referred to the experimentally preestablished walking speed. However, in the case of the 6 mWT, in spite of the encouragement of the patient provided by the assistant physiotherapist every minute throughout the test [19], walking speed is not experimentally preestablished but is in the control of the patient, thus introducing a further, unpredictable degree of freedom. "
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    ABSTRACT: Background: Although walking has been extensively investigated in its biomechanical and physiological aspects, little is known on whether lower limb length and body proportions affect the energy cost of overground walking in older persons. Methods: We enrolled 50 men and 12 women aged 65 years and over, mean 69.1 ± SD 5.4, who at the end of their cardiac rehabilitation program performed the six-minute walk test while wearing a portable device for direct calorimetry and who walked a distance comparable to that of nondisabled community-dwelling older persons. Results: In the multivariable regression model (F = 12.75, P < 0.001, adjusted R(2) = 0.278) the energy cost of overground walking, expressed as the net energy expenditure, in kg(-1) sec(-1), needed to provide own body mass with 1 joule kinetic energy, was inversely related to lower limb length and directly related to lower limb length to height ratio (β ± SE(β) = -3.72 × 10(-3) ± 0.74 × 10(-3), P < 0.001, and 6.61 × 10(-3) ± 2.14 × 10(-3), P = 0.003, resp.). Ancillary analyses also showed that, altogether, 1 cm increase in lower limb length reduced the energy cost of overground walking by 2.57% (95%CI 2.35-2.79). Conclusions: Lower limb length and body proportions actually affect the energy cost of overground walking in older persons.
    Full-text · Article · Jun 2014
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    • "Directly comparing the leg - swing cost estimated from running guinea fowl to running humans is of dubious value given the different design and mor - phology of the legs between these two species . Indeed , the LiMb model ( Pontzer 2007 ) predicts that the cost of swinging the legs can comprise be - tween 8% and 23% of the net cost of running in dogs , goats , and humans . One explanation for the dramatic difference between our estimate of leg swing cost and the LiMb model ' s estimate of leg swing cost is that the LiMb model uses stride - fre - quency to estimate the mass - specific rate of force production necessary to swing the leg . "
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    ABSTRACT: Compared with other species, humans can be very tractable and thus an ideal "model system" for investigating the metabolic cost of locomotion. Here, we review the biomechanical basis for the metabolic cost of running. Running has been historically modeled as a simple spring-mass system whereby the leg acts as a linear spring, storing, and returning elastic potential energy during stance. However, if running can be modeled as a simple spring-mass system with the underlying assumption of perfect elastic energy storage and return, why does running incur a metabolic cost at all? In 1980, Taylor et al. proposed the "cost of generating force" hypothesis, which was based on the idea that elastic structures allow the muscles to transform metabolic energy into force, and not necessarily mechanical work. In 1990, Kram and Taylor then provided a more explicit and quantitative explanation by demonstrating that the rate of metabolic energy consumption is proportional to body weight and inversely proportional to the time of foot-ground contact for a variety of animals ranging in size and running speed. With a focus on humans, Kram and his colleagues then adopted a task-by-task approach and initially found that the metabolic cost of running could be "individually" partitioned into body weight support (74%), propulsion (37%), and leg-swing (20%). Summing all these biomechanical tasks leads to a paradoxical overestimation of 131%. To further elucidate the possible interactions between these tasks, later studies quantified the reductions in metabolic cost in response to synergistic combinations of body weight support, aiding horizontal forces, and leg-swing-assist forces. This synergistic approach revealed that the interactive nature of body weight support and forward propulsion comprises ∼80% of the net metabolic cost of running. The task of leg-swing at most comprises ∼7% of the net metabolic cost of running and is independent of body weight support and forward propulsion. In our recent experiments, we have continued to refine this task-by-task approach, demonstrating that maintaining lateral balance comprises only 2% of the net metabolic cost of running. In contrast, arm-swing reduces the cost by ∼3%, indicating a net metabolic benefit. Thus, by considering the synergistic nature of body weight support and forward propulsion, as well as the tasks of leg-swing and lateral balance, we can account for 89% of the net metabolic cost of human running.
    Full-text · Article · May 2014 · Integrative and Comparative Biology
    • "We compared Fr (Eqn 1) and relative stride length (rSL; stride length divided by characteristic length, h) in a variety of species using two characteristic lengths (h): hip height (measured as the perpendicular distance from greater trochanter to the ground) and hindlimb COM position. Locomotor and morphological data included here are from previous studies of comparative biomechanics in the following taxa (Pontzer, 2007b; Raichlen, 2005a; Raichlen, 2005b; Raichlen, 2006; Shapiro and Raichlen, 2006; Shapiro and Raichlen, 2005; Sockol et al., 2007): infant Papio cynocephalus (baboons; n = 4), Pan troglodytes (chimpanzees; n = 5), Canis familiaris (dogs; n = 4), Capra hircus (goats; n = 4), and Homo sapiens (humans; n = 5). In a second experiment, we altered human hindlimb COM positions by strapping weights to their ankles (0.75 kg on each ankle). "
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    ABSTRACT: The Dynamic Similarity Hypothesis (DSH) suggests that when animals of different size walk at similar Froude numbers (equal ratios of inertial and gravitational forces) they will use similar size-corrected gaits. This application of similarity theory to animal biomechanics has contributed to fundamental insights in the mechanics and evolution of a diverse set of locomotor systems. However, despite its popularity, many mammals fail to walk with dynamically similar stride lengths, a key element of gait that determines spontaneous speed and energy costs. Here, we show that the applicability of the DSH is dependent on the inertial forces examined. In general, the inertial forces are thought to be the centripetal force of the inverted pendulum model of stance phase, determined by the length of the limb. If instead we model inertial forces as the centripetal force of the limb acting as a suspended pendulum during swing phase (determined by limb center of mass position), the DSH for stride length variation is fully supported. Thus, the DSH shows that inter-specific differences in spatial kinematics are tied to the evolution of limb mass distribution patterns. Selection may act on morphology to produce a given stride length, or alternatively, stride length may be a "spandrel" of selection acting on limb mass distribution.
    No preview · Article · Oct 2013 · Biology Open
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