scholarly journals Elastic energy savings and active energy cost in a simple model of running

2021 ◽  
Vol 17 (11) ◽  
pp. e1009608
Author(s):  
Ryan T. Schroeder ◽  
Arthur D. Kuo
Keyword(s):  
Elastic Energy ◽  
Energy Cost ◽  
Energy Savings ◽  
Mechanical Energy ◽  
Metabolic Cost ◽  
The Body ◽  
Metabolic Energy ◽  
Energetic Cost ◽  
Mass Model ◽  
Human Running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic “Spring-mass” computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.

scholarly journals Elastic energy savings and active energy cost in a simple model of running

2021 ◽  
Author(s):  
Ryan T. Schroeder ◽  
Arthur D. Kuo
Keyword(s):  
Elastic Energy ◽  
Energy Cost ◽  
Energy Savings ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
The Body ◽  
Metabolic Energy ◽  
Energetic Cost ◽  
Mass Model

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic Spring-mass computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. Conversely, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running. Here we add explicit actuation and dissipation to the Spring-mass model, resulting in substantial active (and thus costly) work for running on level ground and up or down slopes. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m/s) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.

scholarly journals Running backwards: soft landing–hard takeoff, a less efficient rebound

2010 ◽  
Vol 278 (1704) ◽  
pp. 339-346 ◽  
Author(s):  
G. A. Cavagna ◽  
M. A. Legramandi ◽  
A. La Torre
Keyword(s):  
Basic Property ◽  
Mechanical Energy ◽  
The Body ◽  
Metabolic Energy ◽  
Soft Landing ◽  
Average Force ◽  
Basic Force ◽  
Velocity Relation ◽  
Force Velocity ◽  
Human Running

Human running at low and intermediate speeds is characterized by a greater average force exerted after ‘landing’, when muscle–tendon units are stretched (‘hard landing’), and a lower average force exerted before ‘takeoff’, when muscle–tendon units shorten (‘soft takeoff’). This landing–takeoff asymmetry is consistent with the force–velocity relation of the ‘motor’ (i.e. with the basic property of muscle to resist stretching with a force greater than that developed during shortening), but it may also be due to the ‘machine’ (e.g. to the asymmetric lever system of the foot operating during stance). Hard landing and soft takeoff—never the reverse—were found in running, hopping and trotting animals using diverse lever systems, suggesting that the different machines evolved to comply with the basic force–velocity relation of the motor. Here we measure the mechanical energy of the centre of mass of the body in backward running, an exercise where the normal coupling between motor and machine is voluntarily disrupted, in order to see the relevance of the motor–machine interplay in human running. We find that the landing–takeoff asymmetry is reversed. The resulting ‘soft landing’ and ‘hard takeoff’ are associated with a reduced efficiency of positive work production. We conclude that the landing–takeoff asymmetry found in running, hopping and trotting is the expression of a convenient interplay between motor and machine. More metabolic energy must be spent in the opposite case when muscle is forced to work against its basic property (i.e. when it must exert a greater force during shortening and a lower force during stretching).

scholarly journals Latent power of basking sharks revealed by exceptional breaching events

2018 ◽  
Vol 14 (9) ◽  
pp. 20180537 ◽  
Author(s):  
Emmett M. Johnston ◽  
Lewis G. Halsey ◽  
Nicholas L. Payne ◽  
Alison A. Kock ◽  
Gil Iosilevskii ◽  
...  
Keyword(s):  
Energy Cost ◽  
Mechanical Energy ◽  
Metabolic Cost ◽  
White Shark ◽  
Energetic Cost ◽  
Data Logger ◽  
Filter Feeding ◽  
Video Footage ◽  
Great White Shark ◽  
Basking Shark

The fast swimming and associated breaching behaviour of endothermic mackerel sharks is well suited to the capture of agile prey. In contrast, the observed but rarely documented breaching capability of basking sharks is incongruous to their famously languid lifestyle as filter-feeding planktivores. Indeed, by analysing video footage and an animal-instrumented data logger, we found that basking sharks exhibit the same vertical velocity (approx. 5 m s −1 ) during breach events as the famously powerful predatory great white shark. We estimate that an 8-m, 2700-kg basking shark, recorded breaching at 5 m s −1 and accelerating at 0.4 m s −2 , expended mechanical energy at a rate of 5.5 W kg −1 ; a mass-specific energetic cost comparable to that of the great white shark. The energy cost of such a breach is equivalent to around 1/17th of the daily standard metabolic cost for a basking shark, while the ratio is about half this for a great white shark. While breaches by basking sharks must serve a different function to white shark breaches, their similar breaching speeds questions our perception of the physiology of large filter-feeding fish.

scholarly journals Does Elastic Energy Enhance Work and Efficiency in the Stretch-Shortening Cycle?

1997 ◽  
Vol 13 (4) ◽  
pp. 389-415 ◽  
Author(s):  
Gerrit Jan van Ingen Schenau ◽  
Maarten F. Bobbert ◽  
Arnold de Haan
Keyword(s):  
Elastic Energy ◽  
Mechanical Energy ◽  
Mechanical Efficiency ◽  
The Body ◽  
Metabolic Energy ◽  
Whole Body ◽  
Levels Of Organization ◽  
Cyclic Movements ◽  
Stretch Shortening Cycle ◽  
Different Levels

This target article addresses the role of storage and reutilization of elastic energy in stretch-shortening cycles. It is argued that for discrete movements such as the vertical jump, elastic energy does not explain the work enhancement due to the prestretch. This enhancement seems to occur because the prestretch allows muscles to develop a high level of active state and force before starting to shorten. For cyclic movements in which stretch-shortening cycles occur repetitively, some authors have claimed that elastic energy enhances mechanical efficiency. In the current article it is demonstrated that this claim is often based on disputable concepts such as the efficiency of positive work or absolute work, and it is argued that elastic energy cannot affect mechanical efficiency simply because this energy is not related to the conversion of metabolic energy into mechanical energy. A comparison of work and efficiency measures obtained at different levels of organization reveals that there is in fact no decisive evidence to either support or reject the claim that the stretch-shortening cycle enhances muscle efficiency. These explorations lead to the conclusion that the body of knowledge about the mechanics and energetics of the stretch-shortening cycle is in fact quite lean. A major challenge is to bridge the gap between knowledge obtained at different levels of organization, with the ultimate purpose of understanding how the intrinsic properties of muscles manifest themselves underin-vivo-like conditions and how they are exploited in whole-body activities such as running. To achieve this purpose, a close cooperation is required between muscle physiologists and human movement scientists performing inverse and forward dynamic simulation studies of whole-body exercises.

Estimating instantaneous energetic cost during non-steady-state gait

2014 ◽  
Vol 117 (11) ◽  
pp. 1406-1415 ◽  
Author(s):  
Jessica C. Selinger ◽  
J. Maxwell Donelan
Keyword(s):  
Steady State ◽  
Energy Use ◽  
Mitochondrial Dynamics ◽  
Metabolic Cost ◽  
The Body ◽  
Metabolic Energy ◽  
Energetic Cost ◽  
Control Mechanisms ◽  
Input Output ◽  
Linear Differential

Respiratory measures of oxygen and carbon dioxide are routinely used to estimate the body's steady-state metabolic energy use. However, slow mitochondrial dynamics, long transit times, complex respiratory control mechanisms, and high breath-by-breath variability obscure the relationship between the body's instantaneous energy demands (instantaneous energetic cost) and that measured from respiratory gases (measured energetic cost). The purpose of this study was to expand on traditional methods of assessing metabolic cost by estimating instantaneous energetic cost during non-steady-state conditions. To accomplish this goal, we first imposed known changes in energy use (input), while measuring the breath-by-breath response (output). We used these input/output relationships to model the body as a dynamic system that maps instantaneous to measured energetic cost. We found that a first-order linear differential equation well approximates transient energetic cost responses during gait. Across all subjects, model fits were parameterized by an average time constant (τ) of 42 ± 12 s with an average R2 of 0.94 ± 0.05 (mean ± SD). Armed with this input/output model, we next tested whether we could use it to reliably estimate instantaneous energetic cost from breath-by-breath measures under conditions that simulated dynamically changing gait. A comparison of the imposed energetic cost profiles and our estimated instantaneous cost demonstrated a close correspondence, supporting the use of our methodology to study the role of energetics during locomotor adaptation and learning.

A point-mass model of gibbon locomotion

1999 ◽  
Vol 202 (19) ◽  
pp. 2609-2617 ◽  
Author(s):  
J.E. Bertram ◽  
A. Ruina ◽  
C.E. Cannon ◽  
Y.H. Chang ◽  
M.J. Coleman
Keyword(s):  
Energy Exchange ◽  
Forest Canopy ◽  
Mechanical Energy ◽  
Single Point ◽  
Metabolic Cost ◽  
Point Mass ◽  
Mass Model ◽  
Natural Behavior ◽  
Continuous Contact ◽  
Mechanical Factors

In brachiation, an animal uses alternating bimanual support to move beneath an overhead support. Past brachiation models have been based on the oscillations of a simple pendulum over half of a full cycle of oscillation. These models have been unsatisfying because the natural behavior of gibbons and siamangs appears to be far less restricted than so predicted. Cursorial mammals use an inverted pendulum-like energy exchange in walking, but switch to a spring-based energy exchange in running as velocity increases. Brachiating apes do not possess the anatomical springs characteristic of the limbs of terrestrial runners and do not appear to be using a spring-based gait. How do these animals move so easily within the branches of the forest canopy? Are there fundamental mechanical factors responsible for the transition from a continuous-contact gait where at least one hand is on a hand hold at a time, to a ricochetal gait where the animal vaults between hand holds? We present a simple model of ricochetal locomotion based on a combination of parabolic free flight and simple circular pendulum motion of a single point mass on a massless arm. In this simple brachiation model, energy losses due to inelastic collisions of the animal with the support are avoided, either because the collisions occur at zero velocity (continuous-contact brachiation) or by a smooth matching of the circular and parabolic trajectories at the point of contact (ricochetal brachiation). This model predicts that brachiation is possible over a large range of speeds, handhold spacings and gait frequencies with (theoretically) no mechanical energy cost. We then add the further assumption that a brachiator minimizes either its total energy or, equivalently, its peak arm tension, or a peak tension-related measure of muscle contraction metabolic cost. However, near the optimum the model is still rather unrestrictive. We present some comparisons with gibbon brachiation showing that the simple dynamic model presented has predictive value. However, natural gibbon motion is even smoother than the smoothest motions predicted by this primitive model.

scholarly journals Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

1999 ◽  
Vol 86 (1) ◽  
pp. 383-390 ◽  
Author(s):  
Timothy M. Griffin ◽  
Neil A. Tolani ◽  
Rodger Kram
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Gravitational Potential Energy ◽  
Reduced Gravity

Walking humans conserve mechanical and, presumably, metabolic energy with an inverted pendulum-like exchange of gravitational potential energy and horizontal kinetic energy. Walking in simulated reduced gravity involves a relatively high metabolic cost, suggesting that the inverted-pendulum mechanism is disrupted because of a mismatch of potential and kinetic energy. We tested this hypothesis by measuring the fluctuations and exchange of mechanical energy of the center of mass at different combinations of velocity and simulated reduced gravity. Subjects walked with smaller fluctuations in horizontal velocity in lower gravity, such that the ratio of horizontal kinetic to gravitational potential energy fluctuations remained constant over a fourfold change in gravity. The amount of exchange, or percent recovery, at 1.00 m/s was not significantly different at 1.00, 0.75, and 0.50 G (average 64.4%), although it decreased to 48% at 0.25 G. As a result, the amount of work performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

THE ENERGETIC COSTS OF CALLING IN THE BUSHCRICKET REQUENA VERTICALIS (ORTHOPTERA: TETTIGONIIDAE: LISTROSCELIDINAE)

1993 ◽  
Vol 178 (1) ◽  
pp. 21-37 ◽  
Author(s):  
W. J. Bailey ◽  
P. C. Withers ◽  
M. Endersby ◽  
K. Gaull
Keyword(s):  
Body Mass ◽  
Sound Pressure ◽  
Metabolic Cost ◽  
Acoustic Power ◽  
Metabolic Energy ◽  
Energetic Cost ◽  
Metabolic Efficiency ◽  
Metabolic Costs ◽  
Sound Pressure Levels ◽  
The Relationship

1. The metabolic costs of calling for male Requena verticalis Walker (Tettigoniidae: Listroscelidinae) were measured by direct recordings of oxygen consumption. The acoustic power output was measured by sound pressure levels around the calling bushcricket. 2. The average metabolic cost of calling was 0.143 ml g-1 h-1 but depended on calling rate. The net metabolic cost of calling per unit call, the syllable, was calculated to be 4.34×10-6+/−8.3×10-7 ml O2 syllable-1 g-1 body mass (s.e.) from the slope of the relationship between total V(dot)O2 and rate of syllable production. The resting V(dot)O2, calculated as the intercept of the relationship, was 0.248 ml O2 g-1 body mass h-1. 3. The energetic cost of calling for R. verticalis (average mass 0.37 g) was estimated at 31.85×10-6 J syllable-1. 4. Sound pressure levels were measured around calling insects. The surface area of a sphere of uniform sound pressure level [83 dB SPL root mean square (RMS) acoustic power] obtained by these measurements was used to calculate acoustic power. This was 0.20 mW. 5. The metabolic efficiency of calling, based on total metabolic energy utilisation, was 6.4 %. However, we propose that the mechanical efficiency for acoustic transmission is closer to 57 %, since only about 10 % of muscle metabolic energy is apparently available for sound production. 6. R. verticalis emits chirps formed of several syllables within which are discrete sound pulses. Wing stroke rates, when the insect is calling at its maximal rate, were approximately 583 min-1. This is slow compared to the rates observed in conehead tettigoniids, the only other group of bushcrickets where metabolic costs have been measured. The thoracic temperatures of males that had been calling for 5 min were not significantly different from those of non-calling males. 7. For R. verticalis, calling with relatively slow syllable rates may reduce the total cost of calling, and this may be a compensatory mechanism for their other high energetic cost of mating (a large spermatophylax).

scholarly journals Multi-objective control in human walking: insight gained through simultaneous degradation of energetic and motor regulation systems

2019 ◽  
Vol 16 (158) ◽  
pp. 20190227
Author(s):  
Kirsty A. McDonald ◽  
Joseph P. Cusumano ◽  
Peter Peeling ◽  
Jonas Rubenson
Keyword(s):  
Energy Minimization ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Energetic Cost ◽  
Leg Length ◽  
Multi Objective ◽  
Speed Regulation ◽  
Speed Error ◽  
Objective Control ◽  
Error Regulation

Minimization of metabolic energy is considered a fundamental principle of human locomotion, as demonstrated by an alignment between the preferred walking speed (PWS) and the speed incurring the lowest metabolic cost of transport. We aimed to (i) simultaneously disrupt metabolic cost and an alternate acute task requirement, namely speed error regulation, and (ii) assess whether the PWS could be explained on the basis of either optimality criterion in this new performance and energetic landscape. Healthy adults ( N = 21) walked on an instrumented treadmill under normal conditions and, while negotiating a continuous gait perturbation, imposed leg-length asymmetry. Oxygen consumption, motion capture data and ground reaction forces were continuously recorded for each condition at speeds ranging from 0.6 to 1.8 m s −1 , including the PWS. Both metabolic and speed regulation measures were disrupted by the perturbation ( p < 0.05). Perturbed PWS selection did not exhibit energetic prioritization (although we find some indication of energy minimization after motor adaptation). Similarly, PWS selection did not support prioritization of speed error regulation, which was found to be independent of speed in both conditions. It appears that, during acute exposure to a mechanical gait perturbation of imposed leg-length asymmetry, humans minimize neither energetic cost nor speed regulation errors. Despite the abundance of evidence pointing to energy minimization during normal, steady-state gait, this may not extend acutely to perturbed gait. Understanding how the nervous system acutely controls gait perturbations requires further research that embraces multi-objective control paradigms.

scholarly journals The rising cost of warming waters: effects of temperature on the cost of swimming in fishes

2011 ◽  
Vol 8 (2) ◽  
pp. 266-269 ◽  
Author(s):  
Andrew M. Hein ◽  
Katrina J. Keirsted
Keyword(s):  
Water Temperature ◽  
Fish Species ◽  
Global Climate ◽  
Swimming Performance ◽  
Metabolic Cost ◽  
Quantitative Model ◽  
The Body ◽  
Energetic Cost ◽  
Cost Of Transport ◽  
The Cost

Understanding the effects of water temperature on the swimming performance of fishes is central in understanding how fish species will respond to global climate change. Metabolic cost of transport (COT)—a measure of the energy required to swim a given distance—is a key performance parameter linked to many aspects of fish life history. We develop a quantitative model to predict the effect of water temperature on COT. The model facilitates comparisons among species that differ in body size by incorporating the body mass-dependence of COT. Data from 22 fish species support the temperature and mass dependencies of COT predicted by our model, and demonstrate that modest differences in water temperature can result in substantial differences in the energetic cost of swimming.

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