Human hoppers compensate for simultaneous changes in surface compression and damping

On a range of elastic and damped surfaces, human hoppers and runners adjust leg mechanics to maintain similar spring-like mechanics of the leg and surface combination. In a previous study of adaptations to damped surfaces, we changed surface damping and stiffness simultaneously to maintain constant surface compression. The current study investigated whether hoppers maintain spring-like mechanics of the leg-surface combination when surface damping alone changes (elastic and 1000-4800 N s m(-1)). We found that hoppers adjusted leg mechanics to maintain similar spring-like mechanics of the leg-surface combination and center of mass dynamics on all surfaces. Over the range of surface damping, vertical stiffness of the leg-surface combination increased by only 12% and center of mass displacement decreased by only 6% despite up to 55% less compression of more heavily damped surfaces. In contrast, a simulation predicted a 44% decrease in vertical displacement with no adjustment to leg mechanics. To compensate for the smaller and slower compression of more heavily damped surfaces, the stance legs compressed by up to 4.1 +/- 0.2 cm further and reached peak compression sooner. To replace energy lost by damped surfaces, hoppers performed additional leg work by extending the legs during takeoff by up to 3.1 +/- 0.2 cm further than they compressed during landing. We conclude that humans simultaneously adjust leg compression magnitude and timing, as well as mechanical work output, to conserve center of mass dynamics on damped surfaces. Runners may use similar strategies on natural energy-dissipating surfaces such as sand, mud and snow.     

Footfall dynamics for racewalkers and runners barefoot on compliant surfaces

The main purpose of this study is to investigate the role of footfall surface compliance on the physical parameters affecting barefoot racewalkers and runners. These parameters are identified using a new inverted pendulum body model with a forward moving foot pivot. Model correlations of footfall loads measured for four compliant surface mats showed leg–foot compression stiffness for both gaits were in the range of 10.8–12.9 kN/m, with the initial stiffness spikes in the range of 6.5–52 kN/m. The average leg damping factor was about 0.6% for racewalkers and 6% for runners. For both gaits there was negative leg damping just prior to foot lift-off. Compared to the peak reactions for the rigid surface, a mat of intermediate compliance (1020 kN/m) was effective in reducing the runners’ peak reaction spikes by as much as 17%.     

Energetics and mechanics of human running on surfaces of different stiffnesses.

Mammals use the elastic components in their legs (principally tendons, ligaments, and muscles) to run economically, while maintaining consistent support mechanics across various surfaces. To examine how leg stiffness and metabolic cost are affected by changes in substrate stiffness, we built experimental platforms with adjustable stiffness to fit on a force-plate-fitted treadmill. Eight male subjects [mean body mass: 74.4 +/- 7.1 (SD) kg; leg length: 0.96 +/- 0.05 m] ran at 3.7 m/s over five different surface stiffnesses (75.4, 97.5, 216.8, 454.2, and 945.7 kN/m). Metabolic, ground-reaction force, and kinematic data were collected. The 12.5-fold decrease in surface stiffness resulted in a 12% decrease in the runner's metabolic rate and a 29% increase in their leg stiffness. The runner's support mechanics remained essentially unchanged. These results indicate that surface stiffness affects running economy without affecting running support mechanics. We postulate that an increased energy rebound from the compliant surfaces studied contributes to the enhanced running economy.     

Gender differences in active musculoskeletal stiffness. Part II. Quantification of leg stiffness during functional hopping tasks.

Leg stiffness was compared between age-matched males and females during hopping at preferred and controlled frequencies. Stiffness was defined as the linear regression slope between the vertical center of mass (COM) displacement and ground-reaction forces recorded from a force plate during the stance phase of the hopping task. Results demonstrate that subjects modulated the vertical displacement of the COM during ground contact in relation to the square of hopping frequency. This supports the accuracy of the spring-mass oscillator as a representative model of hopping. It also maintained peak vertical ground-reaction load at approximately three times body weight. Leg stiffness values in males (33.9+/-8.7 kN/m) were significantly (p<0.01) greater than in females (26.3+/-6.5 kN/m) at each of three hopping frequencies, 3.0, 2.5 Hz, and a preferred hopping rate. In the spring-mass oscillator model leg stiffness and body mass are related to the frequency of motion. Thus male subjects necessarily recruited greater leg stiffness to drive their heavier body mass at the same frequency as the lighter female subjects during the controlled frequency trials. However, in the preferred hopping condition the stiffness was not constrained by the task because frequency was self-selected. Nonetheless, both male and female subjects hopped at statistically similar preferred frequencies (2.34+/-0.22 Hz), therefore, the females continued to demonstrate less leg stiffness. Recognizing the active muscle stiffness contributes to biomechanical stability as well as leg stiffness, these results may provide insight into the gender bias in risk of musculoskeletal knee injury.     

Biomechanical analysis of the stance phase during barefoot and shod running

This study investigated spatio-temporal variables, ground reaction forces and sagittal and frontal plane kinematics during the stance phase of nine trained subjects running barefoot and shod at three different velocities (3.5, 4.5, 5.5 m s(-1)). Differences between conditions were detected with the general linear method (factorial model). Barefoot running is characterized by a significantly larger external loading rate than the shod condition. The flatter foot placement at touchdown is prepared in free flight, implying an actively induced adaptation strategy. In the barefoot condition, plantar pressure measurements reveal a flatter foot placement to correlate with lower peak heel pressures. Therefore, it is assumed that runners adopt this different touchdown geometry in barefoot running in an attempt to limit the local pressure underneath the heel. A significantly higher leg stiffness during the stance phase was found for the barefoot condition. The sagittal kinematic adaptations between conditions were found in the same way for all subjects and at the three running velocities. However, large individual variations were observed between the runners for the rearfoot kinematics.     

Positive force feedback in bouncing gaits?

During bouncing gaits (running, hopping, trotting), passive compliant structures (e.g. tendons, ligaments) store and release part of the stride energy. Here, active muscles must provide the required force to withstand the developing tendon strain and to compensate for the inevitable energy losses. This requires an appropriate control of muscle activation. In this study, for hopping, the potential involvement of afferent information from muscle receptors (muscle spindles, Golgi tendon organs) is investigated using a two-segment leg model with one extensor muscle. It is found that: (i) positive feedbacks of muscle-fibre length and muscle force can result in periodic bouncing; (ii) positive force feedback (F+) stabilizes bouncing patterns within a large range of stride energies (maximum hopping height of 16.3 cm, almost twofold higher than the length feedback); and (iii) when employing this reflex scheme, for moderate hopping heights (up to 8.8 cm), an overall elastic leg behaviour is predicted (hopping frequency of 1.4-3 Hz, leg stiffness of 9-27 kN m(-1)). Furthermore, F+ could stabilize running. It is suggested that, during the stance phase of bouncing tasks, the reflex-generated motor control based on feedbacks might be an efficient and reliable alternative to central motor commands.     

A simple method for measuring stiffness during running

The spring-mass model, representing a runner as a point mass supported by a single linear leg spring, has been a widely used concept in studies on running and bouncing mechanics. However, the measurement of leg and vertical stiffness has previously required force platforms and high-speed kinematic measurement systems that are costly and difficult to handle in field conditions. We propose a new "sine-wave" method for measuring stiffness during running. Based on the modeling of the force-time curve by a sine function,this method allows leg and vertical stiffness to be estimated from just a few simple mechanical parameters: body mass, forward velocity, leg length, flight time, and contact time. We compared this method to force-platform-derived stiffness measurements for treadmill dynamometer and overground running conditions, at velocities ranging from 3.33 m.s-1 to maximal running velocity in both recreational and highly trained runners. Stiffness values calculated with the proposed method ranged from 0.67 % to 6.93 % less than the force platform method, and thus were judged to be acceptable. Furthermore, significant linear regressions (p < 0.01) close to the identity line were obtained between force platform and sine-wave model values of stiffness. Given the limits inherent in the use of the spring-mass model, it was concluded that this sine-wave method allows leg and stiffness estimates in running on the basis of a few mechanical parameters, and could be useful in further field measurements.     

Running in the real world: adjusting leg stiffness for different surfaces.

A running animal coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a single mechanical spring during ground contact. Experimental observations have revealed that an animal''s leg stiffness is independent of both speed and gravity level, suggesting that it is dictated by inherent musculoskeletal properties. However, if leg stiffness was invariant, the biomechanics of running (e.g. peak ground reaction force and ground contact time) would change when an animal encountered different surfaces in the natural world. We found that human runners adjust their leg stiffness to accommodate changes in surface stiffness, allowing them to maintain similar running mechanics on different surfaces. These results provide important insight into mechanics and control of animal locomotion and suggest that incorporating an adjustable leg stiffness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.     

Stiffness adaptations in shod running

When mechanical parameters of running are measured, runners have to be accustomed to testing conditions. Nevertheless, habituated runners could still show slight evolutions of their patterns at the beginning of each new running bout. This study investigated runners' stiffness adjustments during shoe and barefoot running and stiffness evolutions of shoes. Twenty-two runners performed two 4-minute bouts at 3.61 m.s-1 shod and barefoot after a 4-min warm-up period. Vertical and leg stiffness decreased during the shoe condition but remained stable in the barefoot condition, p < 0.001. Moreover, an impactor test showed that shoe stiffness increased significantly during the first 4 minutes, p < 0.001. Beyond the 4th minute, shoe properties remained stable. Even if runners were accustomed to the testing condition, as running pattern remained stable during barefoot running, they adjusted their leg and vertical stiffness during shoe running. Moreover, as measurements were taken after a 4-min warm-up period, it could be assumed that shoe properties were stable. Then the stiffness adjustment observed during shoe running might be due to further habituations of the runners to the shod condition. To conclude, it makes sense to run at least 4 minutes before taking measurements in order to avoid runners' stiffness alteration due to shoe property modifications. However, runners could still adapt to the shoe.     

A comparison and update of direct kinematic-kinetic models of leg stiffness in human running

Direct kinematic-kinetic modelling currently represents the “Gold-standard” in leg stiffness quantification during three-dimensional (3D) motion capture experiments. However, the medial-lateral components of ground reaction force and leg length have been neglected in current leg stiffness formulations. It is unknown if accounting for all 3D would alter healthy biologic estimates of leg stiffness, compared to present direct modelling methods. This study compared running leg stiffness derived from a new method (multiplanar method) which includes all three Cartesian axes, against current methods which either only include the vertical axis (line method) or only the plane of progression (uniplanar method). Twenty healthy female runners performed shod overground running at 5.0 m/s. Three-dimensional motion capture and synchronised in-ground force plates were used to track the change in length of the leg vector (hip joint centre to centre of pressure) and resultant projected ground reaction force. Leg stiffness was expressed as dimensionless units, as a percentage of an individual’s bodyweight divided by standing leg length (BW/LL). Leg stiffness using the line method was larger than the uniplanar method by 15.6%BW/LL (P < .001), and multiplanar method by 24.2%BW/LL (P < .001). Leg stiffness from the uniplanar method was larger than the multiplanar method by 8.5%BW/LL (6.5 kN/m) (P < .001). The inclusion of medial-lateral components significantly increased leg deformation magnitude, accounting for the reduction in leg stiffness estimate with the multiplanar method. Given that limb movements typically occur in 3D, the new multiplanar method provides the most complete accounting of all force and length components in leg stiffness calculation.     

Changes in running mechanics and spring-mass behavior induced by a mountain ultra-marathon race

Changes in running mechanics and spring-mass behavior due to fatigue induced by a mountain ultra-marathon race (MUM, 166km, total positive and negative elevation of 9500m) were studied in 18 ultra-marathon runners. Mechanical measurements were undertaken pre- and 3h post-MUM at 12km h(-1) on a 7m long pressure walkway: contact (t(c)), aerial (t(a)) times, step frequency (f), and running velocity (v) were sampled and averaged over 5-8 steps. From these variables, spring-mass parameters of peak vertical ground reaction force (F(max)), vertical downward displacement of the center of mass (Δz), leg length change (ΔL), vertical (k(vert)) and leg (k(leg)) stiffness were computed. After the MUM, there was a significant increase in f (5.9±5.5%; P<0.001) associated with reduced t(a) (-18.5±17.4%; P<0.001) with no change in t(c), and a significant decrease in both Δz and F(max) (-11.6±10.5 and -6.3±7.3%, respectively; P<0.001). k(vert) increased by 5.6±11.7% (P=0.053), and k(leg) remained unchanged. These results show that 3h post-MUM, subjects ran with a reduced vertical oscillation of their spring-mass system. This is consistent with (i) previous studies concerning muscular structure/function impairment in running and (ii) the hypothesis that these changes in the running pattern could be associated with lower overall impact (especially during the braking phase) supported by the locomotor system at each step, potentially leading to reduced pain during running.     

Passive dynamics change leg mechanics for an unexpected surface during human hopping.

Humans running and hopping maintain similar center-of-mass motions, despite large changes in surface stiffness and damping. The goal of this study was to determine the contributions of anticipation and reaction when human hoppers encounter surprise, expected, and random changes from a soft elastic surface (27 kN/m) to a hard surface (411 kN/m). Subjects encountered the expected hard surface on every fourth hop and the random hard surface on an average of 25% of the hops in a trial. When hoppers on a soft surface were surprised by a hard surface, the ankle and knee joints were forced into greater flexion by passive interaction with the hard surface. Within 52 ms after subjects landed on the surprise hard surface, joint flexion increased, and the legs became less stiff than on the soft surface. These mechanical changes occurred before electromyography (EMG) first changed 68-188 ms after landing. Due to the fast mechanical reaction to the surprise hard surface, center-of-mass displacement and average leg stiffness were the same as on expected and random hard surfaces. This similarity is striking because subjects anticipated the expected and random hard surfaces by landing with their knees more flexed. Subjects also anticipated the expected hard surface by increasing the level of EMG by 24-76% during the 50 ms before landing. These results show that passive mechanisms alter leg stiffness for unexpected surface changes before muscle EMG changes and may be critical for adjustments to variable terrain encountered during locomotion in the natural world.     

Interaction of leg stiffness and surface stiffness during human hopping

Ferris, Daniel P., and Claire T. Farley. Interaction ofleg stiffness and surface stiffness during human hopping.J. Appl.Physiol. 82(1): 15-22, 1997.When mammals run,the overall musculoskeletal system behaves as a single linear "legspring." We used force platform and kinematic measurements todetermine whether leg spring stiffness(k_leg) isadjusted to accommodate changes in surface stiffness(k_surf) whenhumans hop in place, a good experimental model for examiningadjustments tok_leg in bouncinggaits. We found thatk_leg was greatlyincreased to accommodate surfaces of lower stiffnesses. The seriescombination ofk_leg andk_surf[total stiffness(k_tot)]was independent ofk_surf at a givenhopping frequency. For example, when humans hopped at a frequency of 2 Hz, they tripled theirk_leg on the leaststiff surface(k_surf = 26.1 kN/m; k_leg = 53.3 kN/m) compared with the most stiff surface(k_surf = 35,000 kN/m; k_leg = 17.8 kN/m). Values fork_tot were notsignificantly different on the least stiff surface (16.7 kN/m) and themost stiff surface (17.8 kN/m). Because of thek_leg adjustment,many aspects of the hopping mechanics (e.g., ground-contact time andcenter of mass vertical displacement) remained remarkably similardespite a >1,000-fold change ink_surf. This studyprovides insight into howk_leg adjustmentscan allow similar locomotion mechanics on the variety of terrainsencountered by runners in the natural world.

     

Changes in spring-mass model parameters and energy cost during track running to exhaustion

The purpose of this study was to determine whether exhaustion modifies the stiffness characteristics, as defined in the spring-mass model, during track running. We also investigated whether stiffer runners are also the most economical. Nine well-trained runners performed an exhaustive exercise over 2000 meters on an indoor track. This exhaustive exercise was preceded by a warm-up and was followed by an active recovery. Throughout all the exercises, the energy cost of running (Cr) was measured. Vertical and leg stiffness was measured with a force plate (Kvert and Kleg, respectively) integrated into the track. The results show that Cr increases significantly after the 2000-meter run (0.192 +/- 0.006 to 0.217 +/- 0.013 mL x kg(-1) x m(-1)). However, Kvert and Kleg remained constant (32.52 +/- 6.42 to 32.59 +/- 5.48 and 11.12 +/- 2.76 to 11.14 +/- 2.48 kN.m, respectively). An inverse correlation was observed between Cr and Kleg, but only during the 2000-meter exercise (r = -0.67; P < or = 0.05). During the warm-up or the recovery, Cr and Kleg, were not correlated (r = 0.354; P = 0.82 and r = 0.21; P = 0.59, respectively). On track, exhaustion induced by a 2000-meter run has no effect on Kleg or Kvert. The inverse correlation was only observed between Cr and Kleg during the 2000-meter run and not before or after the exercise, suggesting that the stiffness of the runner may be not associated with the Cr.     

Compliant bipedal model with the center of pressure excursion associated with oscillatory behavior of the center of mass reproduces the human gait dynamics

Although the compliant bipedal model could reproduce qualitative ground reaction force (GRF) of human walking, the model with a fixed pivot showed overestimations in stance leg rotation and the ratio of horizontal to vertical GRF. The human walking data showed a continuous forward progression of the center of pressure (CoP) during the stance phase and the suspension of the CoP near the forefoot before the onset of step transition. To better describe human gait dynamics with a minimal expense of model complexity, we proposed a compliant bipedal model with the accelerated pivot which associated the CoP excursion with the oscillatory behavior of the center of mass (CoM) with the existing simulation parameter and leg stiffness. Owing to the pivot acceleration defined to emulate human CoP profile, the arrival of the CoP at the limit of the stance foot over the single stance duration initiated the step-to-step transition. The proposed model showed an improved match of walking data. As the forward motion of CoM during single stance was partly accounted by forward pivot translation, the previously overestimated rotation of the stance leg was reduced and the corresponding horizontal GRF became closer to human data. The walking solutions of the model ranged over higher speed ranges (~1.7 m/s) than those of the fixed pivoted compliant bipedal model (~1.5 m/s) and exhibited other gait parameters, such as touchdown angle, step length and step frequency, comparable to the experimental observations. The good matches between the model and experimental GRF data imply that the continuous pivot acceleration associated with CoM oscillatory behavior could serve as a useful framework of bipedal model.     

Bone contact forces on the distal tibia during the stance phase of running

Although the tibia is a common site of stress fractures in runners, the loading of the tibia during running is not well understood. An integrated experimental and modeling approach was therefore used to estimate the bone contact forces acting on the distal end of the tibia during the stance phase of running, and the contributions of external and internal sources to these forces. Motion capture and force plate data were recorded for 10 male runners as they ran at 3.5-4 m/s. From these data, the joint reaction force (JRF), muscle forces, and bone contact force on the tibia were computed at the ankle using inverse dynamics and optimization methods. The distal end of the tibia was compressed and sheared posteriorly throughout most of stance, with respective peak forces of 9.00+/-1.13 and 0.57+/-0.18 body weights occurring during mid stance. Internal muscle forces were the primary source of tibial compression, whereas the JRF was the primary source of tibial shear due to the forward inclination of the leg relative to the external ground reaction force. The muscle forces and JRF both acted to compress the tibia, but induced tibial shear forces in opposing directions during stance, magnifying tibial compression and reducing tibial shear. The superposition of the peak compressive and posterior shear forces at mid stance may contribute to stress fractures in the posterior face of the tibia. The implications are that changes in running technique could potentially reduce stress fracture risk.     

The effect of speed on leg stiffness and joint kinetics in human running

The goals of this study were to examine the following hypotheses: (a) there is a difference between the theoretically calculated (McMahon and Cheng, 1990. Journal of Biomechanics 23, 65-78) and the kinematically measured length changes of the spring-mass model and (b) the leg spring stiffness, the ankle spring stiffness and the knee spring stiffness are influenced by running speed. Thirteen athletes took part in this study. Force was measured using a "Kistler" force plate (1000 Hz). Kinematic data were recorded using two high-speed (120 Hz) video cameras. Each athlete completed trials running at five different velocities (approx. 2.5, 3.5, 4.5, 5.5 and 6.5 m/s). Running velocity influences the leg spring stiffness, the effective vertical spring stiffness and the spring stiffness at the knee joint. The spring stiffness at the ankle joint showed no statistical difference (p < 0.05) for the five velocities. The theoretically calculated length change of the spring-mass model significantly (p < 0.05) overestimated the actual length change. For running velocities up to 6.5 m/s the leg spring stiffness is influenced mostly by changes in stiffness at the knee joint.     

Leg stiffness in human running: Comparison of estimates derived from previously published models to direct kinematic-kinetic measures

It is not presently clear whether mathematical models used to estimate leg stiffness during human running are valid. Therefore, leg stiffness during the braking phase of ground contact of running was calculated directly using synchronous kinematic (high-speed motion analysis) and kinetic (force platform) analysis, and compared to stiffness calculated using four previously published kinetic models. Nineteen well-trained male middle distance runners (age=21.1±4.1yr; VO(2max)=69.5±7.5mlO(2)kg(-1)min(-1)) completed a series of runs of increasing speed from 2.5 to 6.5ms(-1). Leg stiffness was calculated directly from kinetic-kinematic analysis using both vertical and horizontal forces to obtain the resultant force in the line of leg compression (Model 1). Values were also estimated using four previously published mathematical models where only force platform derived and anthropometric measures were required (Models 2-5; Morin et al., 2005, Morin et al., 2011, Blum et al., 2009, Farley et al., 1993, respectively). The greatest statistical similarity between leg stiffness values occurred with Models 1 and 2. The poorest similarity occurred when values from Model 4 were compared with Model 1. Analyses suggest that the poor correlation between Model 1 other models may have resulted from errors in the estimation in change in leg length during the braking phase. Previously published mathematical models did not provide accurate leg stiffness estimates, although Model 2, used by Morin et al. (2005), provided reasonable estimates that could be further improved by the removal of systematic error using a correction factor (K=1.0496K(Model2)).     

Force-velocity relationship and stretch-shortening cycle function in sprint and endurance athletes

This study examined the torque-velocity and power-velocity relationships of quadriceps muscle function, stretch shortening cycle function, and leg-spring stiffness in sprint and endurance athletes. Isokinetic maximal knee extension torque was obtained from 7 sprinters and 7 endurance athletes using a Con-trex isokinetic dynamometer. Torque and power measures were corrected for lean-thigh cross-sectional area and lean-thigh volume, respectively. Stretch-shortening cycle function and muscle stiffness measurements were obtained while subjects performed single-legged squat, countermovement, and drop-rebound jumps on an inclined sledge and force-plate apparatus. The results indicated that sprinters generated, on average, 0.15 +/- 0.05 N.m.cm(-2) more torque across all velocities compared with endurance athletes. Significant differences were also found in the power-velocity relationships between the 2 groups. The sprinters performed significantly better than the endurance athletes on all jumps, but there were no differences in prestretch augmentation between the groups. The average vertical leg stiffness during drop jumps was significantly higher for sprinters (5.86 N.m(-1)) compared with endurance runners (3.38 N.m(-1)). The findings reinforce the need for power training to be carried out at fast contraction speeds but also show that SSC function remains important in endurance running.     

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.