A model of scale effects in mammalian quadrupedal running

2002 ◽  
Vol 205 (7) ◽  
pp. 959-967 ◽  
Author(s):  
Hugh M. Herr ◽  
Gregory T. Huang ◽  
Thomas A. McMahon
Keyword(s):  
Time Course ◽  
Scale Effects ◽  
Metabolic Cost ◽  
Integrative Model ◽  
Stride Frequency ◽  
Published Data ◽  
Model Parameters ◽  
Cost Of Transport ◽  
Vertical Stiffness ◽  
Leg Stiffness

SUMMARYAlthough the effects of body size on mammalian locomotion are well documented, the underlying mechanisms are not fully understood. Here, we present a computational model of the mechanics, control and energetics that unifies some well-known scale effects in running quadrupeds. The model consists of dynamic, physics-based simulations of six running mammals ranging in size from a chipmunk to a horse (0.115-676 kg). The `virtual animals' are made up of rigid segments (head, trunk and four legs) linked by joints and are similar in morphology to particular species. In the model, each stance limb acts as a spring operating within a narrow range of stiffness, forward motion is powered and controlled by active hip and shoulder torques, and metabolic cost is predicted from the time course of supporting body weight. Model parameters that are important for stability (joint stiffnesses,limb-retraction times and target positions and velocities of the limbs) are selected such that (i) running kinematics (aerial height, forward speed and body pitch) is smooth and periodic and (ii) overall leg stiffness is in agreement with published data. Both trotting and galloping gaits are modeled,and comparisons across size are made at speeds that are physiologically similar among species. Model predictions are in agreement with data on vertical stiffness, limb angles, metabolic cost of transport, stride frequency, peak force and duty factor. This work supports the idea that a single, integrative model can predict important features of running across size by employing simple strategies to control overall leg stiffness. More broadly, the model provides a quantitative framework for testing hypotheses that relate limb control, stability and metabolic cost.

Reduced prosthetic stiffness lowers the metabolic cost of running for athletes with bilateral transtibial amputations

2017 ◽  
Vol 122 (4) ◽  
pp. 976-984 ◽  
Author(s):  
Owen N. Beck ◽  
Paolo Taboga ◽  
Alena M. Grabowski
Keyword(s):  
Lower Limb ◽  
Metabolic Cost ◽  
Ground Reaction Forces ◽  
Metabolic Rates ◽  
Distance Running ◽  
Cost Of Transport ◽  
Leg Stiffness ◽  
Metabolic Costs ◽  
In Series ◽  
Reaction Forces

Inspired by the springlike action of biological legs, running-specific prostheses are designed to enable athletes with lower-limb amputations to run. However, manufacturer’s recommendations for prosthetic stiffness and height may not optimize running performance. Therefore, we investigated the effects of using different prosthetic configurations on the metabolic cost and biomechanics of running. Five athletes with bilateral transtibial amputations each performed 15 trials on a force-measuring treadmill at 2.5 or 3.0 m/s. Athletes ran using each of 3 different prosthetic models (Freedom Innovations Catapult FX6, Össur Flex-Run, and Ottobock 1E90 Sprinter) with 5 combinations of stiffness categories (manufacturer’s recommended and ± 1) and heights (International Paralympic Committee’s maximum competition height and ± 2 cm) while we measured metabolic rates and ground reaction forces. Overall, prosthetic stiffness [fixed effect (β) = 0.036; P = 0.008] but not height ( P ≥ 0.089) affected the net metabolic cost of transport; less stiff prostheses reduced metabolic cost. While controlling for prosthetic stiffness (in kilonewtons per meter), using the Flex-Run (β = −0.139; P = 0.044) and 1E90 Sprinter prostheses (β = −0.176; P = 0.009) reduced net metabolic costs by 4.3–4.9% compared with using the Catapult prostheses. The metabolic cost of running improved when athletes used prosthetic configurations that decreased peak horizontal braking ground reaction forces (β = 2.786; P = 0.001), stride frequencies (β = 0.911; P < 0.001), and leg stiffness values (β = 0.053; P = 0.009). Remarkably, athletes did not maintain overall leg stiffness across prosthetic stiffness conditions. Rather, the in-series prosthetic stiffness governed overall leg stiffness. The metabolic cost of running in athletes with bilateral transtibial amputations is influenced by prosthetic model and stiffness but not height. NEW & NOTEWORTHY We measured the metabolic rates and biomechanics of five athletes with bilateral transtibial amputations while running with different prosthetic configurations. The metabolic cost of running for these athletes is minimized by using an optimal prosthetic model and reducing prosthetic stiffness. The metabolic cost of running was independent of prosthetic height, suggesting that longer legs are not advantageous for distance running. Moreover, the in-series prosthetic stiffness governs the leg stiffness of athletes with bilateral leg amputations.

scholarly journals Quantifying Cause-Effect Relations Between Walking Speed, Propulsive Force, and Metabolic Cost

2021 ◽  
Author(s):  
Richard Pimentel ◽  
Jordan N Feldman ◽  
Michael D Lewek ◽  
Jason R Franz
Keyword(s):  
Young Adults ◽  
Health Status ◽  
Time Course ◽  
Walking Speed ◽  
Metabolic Cost ◽  
Propulsive Force ◽  
Metabolic Power ◽  
Cost Of Transport ◽  
Walking Speeds ◽  
Variance Explained

Walking speed is a useful surrogate for health status across the population. Walking speed appears to be governed in part by propulsive force (FP) generated during push-off and simultaneously optimized to minimize metabolic cost. However, no study to our knowledge has established empirical cause-effect relations between FP, walking speed, and metabolic cost, even in young adults. To overcome the potential linkage between these factors, we used a self-paced treadmill controller and real-time biofeedback to independently prescribe walking speed or FP across a range of condition intensities. Walking with larger and smaller FP led to instinctively faster and slower walking speeds, respectively, with about 80% of variance explained between those outcomes. We also found that comparable changes in either FP or walking speed elicited predictable and relatively uniform changes in metabolic cost, each explaining about ~53% of the variance in net metabolic power and ~15% of the variance in cost of transport, respectively. These findings build confidence that interventions designed to increase FP will translate to improved walking speed. Repeating this protocol in other populations may identify additional cause-effect relations that could inform the time course of gait decline due to age and disease.

scholarly journals Gait changes in a line of mice artificially selected for longer limbs

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e3008 ◽  
Author(s):  
Leah M. Sparrow ◽  
Emily Pellatt ◽  
Sabrina S. Yu ◽  
David A. Raichlen ◽  
Herman Pontzer ◽  
...  
Keyword(s):  
Stride Length ◽  
Stance Phase ◽  
Metabolic Cost ◽  
Limb Length ◽  
Stride Frequency ◽  
Practical Reasons ◽  
Cost Of Transport ◽  
Terrestrial Locomotion ◽  
Hind Limbs ◽  
Body Sizes

In legged terrestrial locomotion, the duration of stance phase, i.e., when limbs are in contact with the substrate, is positively correlated with limb length, and negatively correlated with the metabolic cost of transport. These relationships are well documented at the interspecific level, across a broad range of body sizes and travel speeds. However, such relationships are harder to evaluate within species (i.e., where natural selection operates), largely for practical reasons, including low population variance in limb length, and the presence of confounding factors such as body mass, or training. Here, we compared spatiotemporal kinematics of gait in Longshanks, a long-legged mouse line created through artificial selection, and in random-bred, mass-matched Control mice raised under identical conditions. We used a gait treadmill to test the hypothesis that Longshanks have longer stance phases and stride lengths, and decreased stride frequencies in both fore- and hind limbs, compared with Controls. Our results indicate that gait differs significantly between the two groups. Specifically, and as hypothesized, stance duration and stride length are 8–10% greater in Longshanks, while stride frequency is 8% lower than in Controls. However, there was no difference in the touch-down timing and sequence of the paws between the two lines. Taken together, these data suggest that, for a given speed, Longshanks mice take significantly fewer, longer steps to cover the same distance or running time compared to Controls, with important implications for other measures of variation among individuals in whole-organism performance, such as the metabolic cost of transport.

Hopping with degressive spring stiffness in a full-leg exoskeleton lowers metabolic cost compared with progressive spring stiffness and hopping without assistance

2019 ◽  
Vol 127 (2) ◽  
pp. 520-530
Author(s):  
Stephen P. Allen ◽  
Alena M. Grabowski
Keyword(s):  
Elastic Energy ◽  
Metabolic Cost ◽  
Spring Stiffness ◽  
Metabolic Power ◽  
Metabolic Demand ◽  
Nonlinear Spring ◽  
Vertical Stiffness ◽  
Leg Stiffness ◽  
Linear Spring ◽  
Stiffness Profile

When humans hop with a passive-elastic exoskeleton with springs in parallel with both legs, net metabolic power (Pmet) decreases compared with normal hopping (NH). Furthermore, humans retain near-constant total vertical stiffness ( ktot) when hopping with such an exoskeleton. To determine how spring stiffness profile affects Pmet and biomechanics, 10 subjects hopped on both legs normally and with three full-leg exoskeletons that each used a different spring stiffness profile at 2.4, 2.6, 2.8, and 3.0 Hz. Each subject hopped with an exoskeleton that had a degressive spring stiffness (DGexo), where stiffness, the slope of force vs. displacement, is initially high but decreases with greater displacement, linear spring stiffness (LNexo), where stiffness is constant, or progressive spring stiffness (PGexo), where stiffness is initially low but increases with greater displacement. Compared with NH, use of the DGexo, LNexo, and PGexo numerically resulted in 13–24% lower, 4–12% lower, and 0–8% higher Pmet, respectively, at 2.4–3.0 Hz. Hopping with the DGexo reduced Pmet compared with NH at 2.4–2.6 Hz ( P ≤ 0.0457) and reduced Pmet compared with the PGexo at 2.4–2.8 Hz ( P < 0.001). ktot while hopping with each exoskeleton was not different compared with NH, suggesting that humans adjust leg stiffness to maintain overall stiffness regardless of the spring stiffness profile in an exoskeleton. Furthermore, the DGexo provided the greatest elastic energy return, followed by LNexo and PGexo ( P ≤ 0.001). Future full-leg, passive-elastic exoskeleton designs for hopping, and presumably running, should use a DGexo rather than an LNexo or a PGexo to minimize metabolic demand. NEW & NOTEWORTHY When humans hop at 2.4–3.0 Hz normally and with an exoskeleton with different spring stiffness profiles in parallel to the legs, net metabolic power is lowest when hopping with an exoskeleton with degressive spring stiffness. Total vertical stiffness is constant when using an exoskeleton with linear or nonlinear spring stiffness compared with normal hopping. In-parallel spring stiffness influences net metabolic power and biomechanics and should be considered when designing passive-elastic exoskeletons for hopping and running.

scholarly journals A Critical Characteristic in the Transverse Galloping Pattern

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaohui Wei ◽  
Yongjun Long ◽  
Chunlei Wang ◽  
Shigang Wang
Keyword(s):  
Metabolic Cost ◽  
Underlying Mechanism ◽  
Critical Value ◽  
The Body ◽  
Cost Of Transport ◽  
Leg Stiffness ◽  
Angular Velocities ◽  
The Cost ◽  
Optimal Stiffness ◽  
Transverse Galloping

Transverse gallop is a common gait used by a large number of quadrupeds. This paper employs the simplified dimensionless quadrupedal model to discuss the underlying mechanism of the transverse galloping pattern. The model is studied at different running speeds and different values of leg stiffness, respectively. If the horizontal running speed reaches up to a critical value at a fixed leg stiffness, or if the leg stiffness reaches up to a critical value at a fixed horizontal speed, a key property would emerge which greatly reduces the overall mechanical forces of the dynamic system in a proper range of initial pitch angular velocities. Besides, for each horizontal speed, there is an optimal stiffness of legs that can reduce both the mechanical loads and the metabolic cost of transport. Furthermore, different body proportions and landing distance lags of a pair of legs are studied in the transverse gallop. We find that quadrupeds with longer length of legs compared with the length of the body are more suitable to employ the transverse galloping pattern, and the landing distance lag of a pair of legs could reduce the cost of transport and the locomotion frequency.

Joint-Space Dynamic Model of Metabolic Cost With Subject-Specific Energetic Parameters

2014 ◽  
Author(s):  
Dustyn Roberts ◽  
Howard Hillstrom ◽  
Joo H. Kim
Keyword(s):  
Dynamic Model ◽  
Metabolic Cost ◽  
Joint Space ◽  
Human Motion ◽  
Metabolic Energy ◽  
Model Parameters ◽  
Cost Of Transport ◽  
Walking Speeds ◽  
The Cost ◽  
Metabolic Energy Expenditure

Metabolic energy expenditure (MEE) is commonly used to characterize human motion. In this study, a general joint-space dynamic model of MEE is developed by integrating the principles of thermodynamics and multibody system dynamics in a joint-space model that enables the evaluation of MEE without the limitations inherent in experimental measurements or muscle-space models. Muscle-space energetic components are mapped to the joint space, in which the MEE model is formulated. A constrained optimization algorithm is used to estimate the model parameters from experimental walking data. The joint-space parameters estimated directly from active subjects provide reliable estimates of the trend of the cost of transport at different walking speeds. The quantities predicted by this model, such as cost of transport, can be used as strong complements to experimental methods to increase the reliability of results and yield unique insights for various applications.

scholarly journals The converse effects of speed and gravity on the energetics of walking and running

2017 ◽  
Author(s):  
S.J. Hasaneini ◽  
R.T. Schroeder ◽  
J.E.A. Bertram ◽  
A. Ruina
Keyword(s):  
Optimization Model ◽  
Human Subjects ◽  
Metabolic Cost ◽  
Energetic Cost ◽  
Model Parameters ◽  
Gravity Level ◽  
Reduced Gravity ◽  
Cost Of Transport ◽  
Highly Sensitive ◽  
Length Changes

AbstractThe energetic cost of transport for walking is highly sensitive to speed but relatively insensitive to changes in gravity level. Conversely, the cost of transport for running is highly sensitive to gravity level but not much to speed. Gait optimization with a minimally constrained bipedal model predicts a similar differential energetic response for walking and running even though the same model parameters and cost function are used for both gaits. This challenges previous assertions that the converse energetic responses are due to fundamentally different energy saving mechanisms in each gait. Our results suggest that energetics of both gaits are highly influenced by dissipative losses occurring as leg forces abruptly alter the center of mass path. The observed difference in energetic consequence of the performance condition in each gait is due to the effect the movement strategy of each gait has on the dissipative loss. The optimization model predictions are tested directly by measuring metabolic cost of human subjects walking and running at different speeds in normal and reduced gravity using a novel reduced gravity simulation apparatus. The optimization model also predicts other, sometimes subtle, aspects of gait such as step length changes. This is also directly tested in order to assess the fidelity of the model’s more nuanced predictions.

scholarly journals Mechanics, energetics and implementation of grounded running technique: a narrative review

2020 ◽  
Vol 6 (1) ◽  
pp. e000963
Author(s):  
Sheeba Davis ◽  
Aaron Fox ◽  
Jason Bonacci ◽  
Fiddy Davis
Keyword(s):  
Postural Stability ◽  
Injury Risk ◽  
Metabolic Cost ◽  
Duty Factor ◽  
Vertical Oscillation ◽  
Leg Stiffness ◽  
Speed Range ◽  
Impact Attenuation ◽  
Acute Increase ◽  
Recreational Runners

Grounded running predominantly differs from traditional aerial running by having alternating single and double stance with no flight phase. Approximately, 16% of runners in an open marathon and 33% of recreational runners in a 5 km running event adopted a grounded running technique. Grounded running typically occurs at a speed range of 2–3 m·s−1, is characterised by a larger duty factor, reduced vertical leg stiffness, lower vertical oscillation of the centre of mass (COM) and greater impact attenuation than aerial running. Grounded running typically induces an acute increase in metabolic cost, likely due to the larger duty factor. The increased duty factor may translate to a more stable locomotion. The reduced vertical oscillation of COM, attenuated impact shock, and potential for improved postural stability may make grounded running a preferred form of physical exercise in people new to running or with low loading capacities (eg, novice overweight/obese, elderly runners, rehabilitating athletes). Grounded running as a less impactful, but metabolically more challenging form, could benefit these runners to optimise their cardio-metabolic health, while at the same time minimise running-related injury risk. This review discusses the mechanical demands and energetics of grounded running along with recommendations and suggestions to implement this technique in practice.

Use of ionic currents to identify and estimate parameters in models of channel blockade

1990 ◽  
Vol 259 (2) ◽  
pp. H626-H634
Author(s):  
C. F. Starmer ◽  
V. V. Nesterenko ◽  
F. R. Gilliam ◽  
A. O. Grant
Keyword(s):  
Time Course ◽  
Experimental Studies ◽  
Ionic Currents ◽  
Blocking Agent ◽  
Model Parameters ◽  
Protein Conformations ◽  
Channel Blockade ◽  
Channel Blocking ◽  
Individual Contributions ◽  
Modulated Receptor

Models of ion channel blockade are frequently validated with observations of ionic currents resulting from electrical or chemical stimulation. Model parameters for some models (modulated receptor hypothesis) cannot be uniquely determined from ionic currents. The time course of ionic currents reflects the activation (fraction of available channels that conduct in the presence of excitation) and availability of channels (the ability of the protein to make a transition to a conducting conformation and where this conformation is not complexed with a drug). In the presence of a channel blocking agent, the voltage dependence of availability appears modified and has been interpreted as evidence that drug-complexed channels exhibit modified transition rates between channel protein conformations. Because blockade and availability both modify ionic currents, their individual contributions to macroscopic conductance cannot be resolved from ionic currents except when constant affinity binding to a bindable site is assumed. Experimental studies of nimodipine block of calcium channels and lidocaine block of sodium channels illustrate these concepts.

scholarly journals New Mathematical Modeling Approach for Predicting Microbial Inactivation by High Hydrostatic Pressure

2007 ◽  
Vol 73 (8) ◽  
pp. 2468-2478 ◽  
Author(s):  
Bernadette Klotz ◽  
D. Leo Pyle ◽  
Bernard M. Mackey
Keyword(s):  
Microbial Inactivation ◽  
Inactivation Kinetics ◽  
Published Data ◽  
Model Parameters ◽  
Order Kinetic ◽  
Square Root ◽  
Additional Time ◽  
Decimal Reduction Time ◽  
First Order ◽  
Primary Model

ABSTRACT A new primary model based on a thermodynamically consistent first-order kinetic approach was constructed to describe non-log-linear inactivation kinetics of pressure-treated bacteria. The model assumes a first-order process in which the specific inactivation rate changes inversely with the square root of time. The model gave reasonable fits to experimental data over six to seven orders of magnitude. It was also tested on 138 published data sets and provided good fits in about 70% of cases in which the shape of the curve followed the typical convex upward form. In the remainder of published examples, curves contained additional shoulder regions or extended tail regions. Curves with shoulders could be accommodated by including an additional time delay parameter and curves with tails shoulders could be accommodated by omitting points in the tail beyond the point at which survival levels remained more or less constant. The model parameters varied regularly with pressure, which may reflect a genuine mechanistic basis for the model. This property also allowed the calculation of (a) parameters analogous to the decimal reduction time D and z, the temperature increase needed to change the D value by a factor of 10, in thermal processing, and hence the processing conditions needed to attain a desired level of inactivation; and (b) the apparent thermodynamic volumes of activation associated with the lethal events. The hypothesis that inactivation rates changed as a function of the square root of time would be consistent with a diffusion-limited process.

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