Humans running in place on water at simulated reduced gravity

Background

On Earth only a few legged species, such as water strider insects, some aquatic birds and lizards, can run on water. For most other species, including humans, this is precluded by body size and proportions, lack of appropriate appendages, and limited muscle power. However, if gravity is reduced to less than Earth’s gravity, running on water should require less muscle power. Here we use a hydrodynamic model to predict the gravity levels at which humans should be able to run on water. We test these predictions in the laboratory using a reduced gravity simulator.

Methodology/Principal Findings

We adapted a model equation, previously used by Glasheen and McMahon to explain the dynamics of Basilisk lizard, to predict the body mass, stride frequency and gravity necessary for a person to run on water. Progressive body-weight unloading of a person running in place on a wading pool confirmed the theoretical predictions that a person could run on water, at lunar (or lower) gravity levels using relatively small rigid fins. Three-dimensional motion capture of reflective markers on major joint centers showed that humans, similarly to the Basilisk Lizard and to the Western Grebe, keep the head-trunk segment at a nearly constant height, despite the high stride frequency and the intensive locomotor effort. Trunk stabilization at a nearly constant height differentiates running on water from other, more usual human gaits.

Conclusions/Significance

The results showed that a hydrodynamic model of lizards running on water can also be applied to humans, despite the enormous difference in body size and morphology.     

A gravitational impulse model predicts collision impulse and mechanical work during a step-to-step transition

The simplest walking model, which assumes an instantaneous collision with negligible gravity effect, is limited in its representation of the collision mechanics of human gaits because the actual step-to-step transition occurs over a finite duration of time with finite impulsive ground reaction forces (GRFs) that have the same order of magnitude as the gravitational force. In this study, we propose a new collision model that includes the contribution of the gravitational impulse to the momentum change of the center of mass (COM) during a step-to-step transition. To validate the model, we measured the GRFs of six subjects' over-ground walking at five different gait speeds and calculated the collision impulses and mechanical work. The data showed a significant contribution of the gravitational impulse to the momentum change during collision. To compensate for the gravity, the magnitudes of collision impulse and COM work were estimated to be much greater than in previous predictions. Consistent with the model prediction, push-off propulsion fully compensated for the collision loss, implying the step-to-step transition occurred in an energetically optimal manner. The new model predicted a moderate change in the collision mechanics with gait speed, which seems to be physiologically achievable. The gravitational collision model enables us to better understand collision dynamics during a step-to-step transition.     

Gait transitions in simulated reduced gravity

Gravity has a strong effect on gait and the speed of gait transitions. A gait has been defined as a pattern of locomotion that changes discontinuously at the transition to another gait. On Earth, during gradual speed changes, humans exhibit a sudden discontinuous switch from walking to running at a specific speed. To study the effects of altered gravity on both the stance and swing legs, we developed a novel unloading exoskeleton that allows a person to step in simulated reduced gravity by tilting the body relative to the vertical. Using different simulation techniques, we confirmed that at lower gravity levels the transition speed is slower (in accordance with the previously reported Froude number ～0.5). Surprisingly, however, we found that at lower levels of simulated gravity the transition between walking and running was generally gradual, without any noticeable abrupt change in gait parameters. This was associated with a significant prolongation of the swing phase, whose duration became virtually equal to that of stance in the vicinity of the walk-run transition speed, and with a gradual shift from inverted-pendulum gait (walking) to bouncing gait (running).     

Muscle mechanical advantage of human walking and running: implications for energy cost.

Muscular forces generated during locomotion depend on an animal's speed, gait, and size and underlie the energy demand to power locomotion. Changes in limb posture affect muscle forces by altering the mechanical advantage of the ground reaction force (R) and therefore the effective mechanical advantage (EMA = r/R, where r is the muscle mechanical advantage) for muscle force production. We used inverse dynamics based on force plate and kinematic recordings of humans as they walked and ran at steady speeds to examine how changes in muscle EMA affect muscle force-generating requirements at these gaits. We found a 68% decrease in knee extensor EMA when humans changed gait from a walk to a run compared with an 18% increase in hip extensor EMA and a 23% increase in ankle extensor EMA. Whereas the knee joint was extended (154-176 degrees) during much of the support phase of walking, its flexed position (134-164 degrees) during running resulted in a 5.2-fold increase in quadriceps impulse (time-integrated force during stance) needed to support body weight on the ground. This increase was associated with a 4.9-fold increase in the ground reaction force moment about the knee. In contrast, extensor impulse decreased 37% (P < 0.05) at the hip and did not change at the ankle when subjects switched from a walk to a run. We conclude that the decrease in limb mechanical advantage (mean limb extensor EMA) and increase in knee extensor impulse during running likely contribute to the higher metabolic cost of transport in running than in walking. The low mechanical advantage in running humans may also explain previous observations of a greater metabolic cost of transport for running humans compared with trotting and galloping quadrupeds of similar size.     

Body mass distribution and gait mechanics in fat-tailed dwarf lemurs (Cheirogaleus medius) and patas monkeys (Erythrocebus patas)

Most quadrupeds walk with lateral sequence (LS) gaits, where hind limb touchdowns are followed by ipsilateral forelimb touchdowns. Primates, however, typically walk with diagonal sequence (DS) gaits, where hind limb touchdowns are followed by contralateral forelimb touchdowns. Because the use of DS gaits is nearly ubiquitous among primates, understanding gait selection in primates is critical to understanding primate locomotor evolution. The Support Polygon Model [Tomita, M., 1967. A study on the movement pattern of four limbs in walking. J. Anthropol. Soc. Nippon 75, 120-146; Rollinson, J., Martin, R.D., 1981. Comparative aspects of primate locomotion, with special reference to arboreal cercopithecines. Symp. Zool. Soc. Lond. 48, 377-427] argues that primates' use of DS gaits stems from a more caudal position of the whole-body center of mass (COM) relative to other mammals. We tested the predictions of the Support Polygon Model by examining the effects of natural and experimental variations in COM position on gait mechanics in two distantly related primates: fat-tailed dwarf lemurs (Cheirogaleus medius) and patas monkeys (Erythrocebus patas). Dwarf lemur experiments compared individuals with and without a greatly enlarged tail (a feature associated with torpor that can be expected to shift the COM caudally). During patas monkey experiments, we experimentally shifted the COM cranially with the use of a weighted belt (7-12% of body mass) positioned above the scapulae. Examination of limb kinematics revealed changes consistent with systematic deviations in COM position. Nevertheless, footfall patterns changed in a direction contrary to the predictions of the Support Polygon Model in the dwarf lemurs and did not change at all in the patas monkey. These results suggest that body mass distribution is unlikely to be the sole determinant of footfall pattern in primates and other mammals.     

Locomotion in degus on terrestrial substrates varying in orientation – implications for biomechanical constraints and gait selection

To gain new insights into running gaits on sloped terrestrial substrates, metric and selected kinematic parameters of the common degu (Octodon degus) were examined. Individuals were filmed at their maximum voluntary running speed using a high-speed camera placed laterally to the terrestrial substrate varying in orientations from −30° to +30°, at 10° increments. Degus used trotting, lateral-sequence (LS) and diagonal-sequence (DS) running gaits at all substrate orientations. Trotting was observed across the whole speed range whereas DS running gaits occurred at significantly higher speeds than LS running gaits. Metric and kinematic changes on sloped substrates in degus paralleled those noted for most other mammals. However, the timing of metric and kinematic locomotor adjustments differed significantly between individual degus. In addition, most of these adjustments took place at 10° rather than 30° inclines and declines, indicating significant biomechanical demands even on slightly sloped terrestrial substrates. The results of this study suggest that DS and LS running gaits may represent an advantage in small to medium-sized mammals for counteracting some level of locomotor instability. Finally, changes in locomotor parameters of the forelimbs rather than the hindlimbs seem to play an important role in gait selection in small to medium-sized mammals.     

Stance leg control: variation of leg parameters supports stable hopping

The spring-loaded inverted pendulum describes the planar center-of-mass dynamics of legged locomotion. This model features linear springs with constant parameters as legs. In biological systems, however, spring-like properties of limbs can change over time. Therefore, in this study, it is asked how variation of spring parameters during ground contact would affect the dynamics of the spring-mass model. Neglecting damping initially, it is found that decreasing stiffness and increasing rest length of the leg during a stance phase are required for orbitally stable hopping. With damping, stable hopping is found for a larger region of rest-length rates and stiffness rates. Here, also increasing stiffness and decreasing rest length can result in stable hopping. Within the predicted range of leg parameter variations for stable hopping, there is no need for precise parameter tuning. Since hopping gaits form a subset of the running gaits (with vanishing horizontal velocity), these results may help to improve leg design in robots and prostheses.     

Influence of body segment parameters and modeling assumptions on the estimate of center of mass trajectory

This study sought to determine the effect of inaccuracies in body segment parameters and modeling assumptions on the estimate of antero-posterior center of mass (COM) trajectory. Four different methods, one based on segmental kinematics, and three methods based on kinetic recordings were compared via simulation. Kinematic patterns (quiet stance, ankle-related sway, hip-ankle-related sway, sit-up and sit-up-sit-down) were tested with a 2D four-link model of the body and the ground reaction force vector was obtained by inverse dynamics. Errors in the estimation of body segment parameters were simulated by applying a +/-10% variation to one or more parameters at a time. These errors propagated differently to the COM estimated location between methods, between parameters within the same method, and between tasks. The kinematics-based method was the most sensitive to body segment parameters, with special regards to segment lengths and head-arms-trunk parameters. Root mean square error between estimated and simulated COM location reached 19mm in balance-related tasks and 38.3mm in sit-up-sit-down. The kinetics-based methods were largely less sensitive to inaccuracies in body segment parameters. In particular, the technique proposed by Zatsiorsky and King (J. Biomech. 31 (1998) 161), was completely insensitive to segment parameters. On the other hand the kinetics-based methods showed an intrinsic estimation error, due to the underlying model assumptions. The methods based on the double integration of horizontal force had better outcomes with tasks challenging such assumptions, with a maximal error in COM location of 15mm in the sit-up-sit-down. The method proposed by Shimba (J. Biomech. 17 (1984) 53) showed the best trade-off between sensitivity to body segment parameters and estimation performances given the ideal test conditions.     

Consequences of forward translation of the point of force application for the mechanics of running

In running humans, the point of force application between the foot and the ground moves forwards during the stance phase. Our aim was to determine the mechanical consequences of this 'point of force translation' (POFT). We modified the planar spring-mass model of locomotion to incorporate POFT, and then compared spring-mass simulations with and without POFT. We found that, if leg stiffness is adjusted appropriately, it is possible to maintain very similar values of peak vertical ground reaction force (GRF), stance time, contact length and vertical centre of mass displacement, whether or not POFT occurs. The leg stiffness required to achieve this increased as the distance of POFT increased. Peak horizontal GRF and mechanical work per step were lower when POFT occurred. The results indicate that the lack of POFT in the traditional spring-mass model should not prevent it from providing good predictions of peak vertical GRF, stance time, contact length and vertical centre of mass displacement in running humans, if an appropriate spring stiffness is used. However, the model can be expected to overestimate peak horizontal GRF and mechanical work per step. When POFT occurs, the spring stiffness in the traditional spring-mass model is not equivalent to leg stiffness. Therefore, caution should be exercised when using spring stiffness to understand how the musculoskeletal system adapts to different running conditions. This can explain the contradictory results in the literature regarding the effect of running speed on leg stiffness.     

Criteria for dynamic similarity in bouncing gaits

Animals of different sizes tend to move in a dynamically similar manner when travelling at speeds corresponding to equal values of a dimensionless parameter (DP) called the Froude number. Consequently, the Froude number has been widely used for defining equivalent speeds and predicting speeds of locomotion by extinct species and on other planets. However, experiments using simulated reduced gravity have demonstrated that equality of the Froude number does not guarantee dynamic similarity. This has cast doubt upon the usefulness of the Froude number in locomotion research. Here we use dimensional analysis of the planar spring-mass model, combined with Buckingham's Pi-Theorem, to demonstrate that four DPs must be equal for dynamic similarity in bouncing gaits such as trotting, hopping and bipedal running. This can be reduced to three DPs by applying the constraint of maintaining a constant average speed of locomotion. Sensitivity analysis indicates that all of these DPs are important for predicting dynamic similarity. We show that the reason humans do not run in a dynamically similar manner at equal Froude number in different levels of simulated reduced gravity is that dimensionless leg stiffness decreases as gravity increases. The reason that the Froude number can predict dynamic similarity in Earth gravity is that dimensionless leg stiffness and dimensionless vertical landing speed are both independent of size. In conclusion, although equal Froude number is not sufficient for dynamic similarity, it is a necessary condition. Therefore, to detect fundamental differences in locomotion, animals of different sizes should be compared at equal Froude number, so that they can be as close to dynamic similarity as possible. More generally, the concept of dynamic similarity provides a powerful framework within which similarities and differences in locomotion can be interpreted.     

Spring-mass running: simple approximate solution and application to gait stability

The planar spring-mass model is frequently used to describe bouncing gaits (running, hopping, trotting, galloping) in animal and human locomotion and robotics. Although this model represents a rather simple mechanical system, an analytical solution predicting the center of mass trajectory during stance remains open. We derive an approximate solution in elementary functions assuming a small angular sweep and a small spring compression during stance. The predictive power and quality of this solution is investigated for model parameters relevant to human locomotion. The analysis shows that (i), for spring compressions of up to 20% (angle of attack > or = 60 degree, angular sweep < or = 60 degree) the approximate solution describes the stance dynamics of the center of mass within a 1% tolerance of spring compression and 0.6 degree tolerance of angular motion compared to numerical calculations, and (ii), despite its relative simplicity, the approximate solution accurately predicts stable locomotion well extending into the physiologically reasonable parameter domain. (iii) Furthermore, in a particular case, an explicit parametric dependency required for gait stability can be revealed extending an earlier, empirically found relationship. It is suggested that this approximation of the planar spring-mass dynamics may serve as an analytical tool for application in robotics and further research on legged locomotion.     

Energetics of walking and running: insights from simulated reduced-gravity experiments.

On Earth, a person uses about one-half as much energy to walk a mile as to run a mile. On another planet with lower gravity, would walking still be more economical than running? When people carry weights while they walk or run, energetic cost increases in proportion to the added load. It would seem to follow that if gravity were reduced, energetic cost would decrease in proportion to body weight in both gaits. However, we find that under simulated reduced gravity, the rate of energy consumption decreases in proportion to body weight during running but not during walking. When gravity is reduced by 75%, the rate of energy consumption is reduced by 72% during running but only by 33% during walking. Because reducing gravity decreases the energetic cost much more for running than for walking, walking is not the cheapest way to travel a mile at low levels of gravity. These results suggest that the link between the mechanics of locomotion and energetic cost is fundamentally different for walking and for running.     

Early development of locomotor behavior in vervet monkeys

The locomotor development of three vervet infants across approximately the first 2 months of life is described. Fairly normal-looking walking movements (as compared to adults) were seen in all the animals by approximately 1 month of age and galloping was observed by 2 months. Early locomotor footfall patterns were often aberrant and bounding-type gaits were sometimes exhibited. Most of the symmetrical gaits observed were classifiable as lateral sequence. Across the 2-month period the animals showed decreased three- and four-foot support and improvements in joint angular displacement patterns. From their earliest locomotor movements the infants showed significant linear relationship between both cycle duration and swing and stance durations of the limbs. We suggest that locomotor control mechanisms are probably fairly mature at birth but that weight support and postural control problems explain the initial locomotor difficulties exhibited by these infants.     

Gait selection in the ostrich: mechanical and metabolic characteristics of walking and running with and without an aerial phase

It has been argued that minimization of metabolic-energy costs is a primary determinant of gait selection in terrestrial animals. This view is based predominantly on data from humans and horses, which have been shown to choose the most economical gait (walking, running, galloping) for any given speed. It is not certain whether a minimization of metabolic costs is associated with the selection of other prevalent forms of terrestrial gaits, such as grounded running (a widespread gait in birds). Using biomechanical and metabolic measurements of four ostriches moving on a treadmill over a range of speeds from 0.8 to 6.7 m s(-1), we reveal here that the selection of walking or grounded running at intermediate speeds also favours a reduction in the metabolic cost of locomotion. This gait transition is characterized by a shift in locomotor kinetics from an inverted-pendulum gait to a bouncing gait that lacks an aerial phase. By contrast, when the ostrich adopts an aerial-running gait at faster speeds, there are no abrupt transitions in mechanical parameters or in the metabolic cost of locomotion. These data suggest a continuum between grounded and aerial running, indicating that they belong to the same locomotor paradigm.     

External forces on the limbs of jumping lemurs at takeoff and landing

Ground reaction forces were recorded for jumps of three individuals each of Lemur catta and Eulemur fulvus. Animals jumped back and forth between a ground-mounted force plate and a 0.5-m elevated platform, covering horizontal distances of 0.5-2 m. In total, 190 takeoffs and 263 landings were collected. Animals typically jumped from a run up and into a run out, during which they gained or into which they carried horizontal impulse. Correspondingly, vertical impulses dominated takeoffs and landings. Peak forces were moderate in magnitude and not much higher than forces reported for quadrupedal gaits. This is in contrast to the forces for standing jumps of specialized leapers that considerably exceed forces associated with quadrupedal gaits. Force magnitudes for the lemur jumps are more comparable to peak forces reported for other quadrupeds performing running jumps. Takeoffs are characterized by higher hindlimb than forelimb peak forces and impulses. L. catta typically landed with the hindlimbs making first contact, and the hindlimb forces and impulses were higher than the forelimb forces and impulses at landing. E. fulvus typically landed with the forelimbs striking first and also bearing the higher forces. This pattern does not fully conform to the paradigm of primate limb force distribution, with higher hindlimb than forelimb forces. However, the absolute highest forces in E. fulvus also occur at the hindlimbs, during acceleration for takeoff.     

Improving horizontal plane locomotion via leg angle control

The lateral leg spring model has been shown to accurately represent horizontal plane locomotion characteristics of sprawled posture insects such as the cockroach Blaberus discoidalis. While passively stable periodic gaits result from employing a constant leg touch-down angle for this model, utilizing a similar protocol for a point mass model of locomotion in three dimensions produces only unstable periodic gaits. In this work, we return to the horizontal plane model and develop a simple control law that prescribes variations in the leg touch-down angle in response to external perturbations. The resulting control law applies control once per stance phase, at the instant of leg touch-down, and depends upon previous leg angles defined in the body reference frame. As a result, our control action is consistent with the neural activity evidenced by B. discoidalis during locomotion over flat and rough terrain, and utilizes variables easily sensed by insect mechanoreceptors. Application of control in the lateral leg spring model is shown to improve stability of periodic gaits, enable stabilization of previously unstable periodic gaits, and maintain or improve the basin of stability of periodic gaits. The magnitude of leg touch-down angle variations utilized during stabilization appear consistent with the natural variations evidenced by single legs during locomotion over flat terrain.     

Symmetrical and asymmetrical gaits in the mouse: patterns to increase velocity

The gaits of the adult SWISS mice during treadmill locomotion at velocities ranging from 15 to 85 cm s^–1 have been analysed using a high-speed video camera combined with cinefluoroscopic equipment. The sequences of locomotion were analysed to determine the various space and time parameters of limb kinematics. We found that velocity adjustments are accounted for differently by the stride frequency and the stride length if the animal showed a symmetrical or an asymmetrical gait. In symmetrical gaits, the increase of velocity is provided by an equal increase in the stride length and the stride frequency. In asymmetrical gaits, the increase in velocity is mainly assured by an increase in the stride frequency in velocities ranging from 15 to 29 cm s^–1. Above 68 cm s^–1, velocity increase is achieved by stride length increase. In velocities ranging from 29 to 68 cm s^–1, the contribution of both variables is equal as in symmetrical gaits. Both stance time and swing time shortening contributed to the increase of the stride frequency in both gaits, though with a major contribution from stance time decrease. The pattern of locomotion obtained in a normal mouse should be used as a template for studying locomotor control deficits after lesions or in different mutations affecting the nervous system.     

How well can spring-mass-like telescoping leg models fit multi-pedal sagittal-plane locomotion data?

Idealized mathematical models of animals, with point-mass bodies and spring-like legs, have been used by researchers to study various aspects of terrestrial legged locomotion. Here, we fit a bipedal spring-mass model to the ground reaction forces of human running, a horse trotting, and a cockroach running. We find that, in all three cases, while the model captures center-of-mass motions and vertical force variations well, horizontal forces are less well reproduced, primarily due to variations in net force vector directions that the model cannot accommodate. The fits result in different apparent leg stiffnesses in the three animals. Assuming a simple fixed leg-angle touch-down strategy, we find that the gaits of these models are stable in different speed-step length regimes that overlap with those used by humans and horses, but not with that used by cockroaches.