Evaluating the 'cost of generating force' hypothesis across frequency in human running and hopping.

The volume of active muscle and duration of extensor muscle force well explain the associated metabolic energy expenditure across body mass and velocity during level-ground running and hopping. However, if these parameters fundamentally drive metabolic energy expenditure, then they should pertain to multiple modes of locomotion and provide a simple framework for relating biomechanics to metabolic energy expenditure in bouncing gaits. Therefore, we evaluated the ability of the 'cost of generating force' hypothesis to link biomechanics and metabolic energy expenditure during human running and hopping across step frequencies. We asked participants to run and hop at 85%, 92%, 100%, 108% and 115% of preferred running step frequency. We calculated changes in active muscle volume, duration of force production and metabolic energy expenditure. Overall, as step frequency increased, active muscle volume decreased as a result of postural changes via effective mechanical advantage (EMA) or duty factor. Accounting for changes in EMA and muscle volume better related to metabolic energy expenditure during running and hopping at different step frequencies than assuming a constant EMA and muscle volume. Thus, to ultimately develop muscle mechanics models that can explain metabolic energy expenditure across different modes of locomotion, we suggest more precise measures of muscle force production that include the effects of EMA.

Models for resonant acoustic metasurfaces with application to moth wing ultrasound absorption.

Taking as bioinspiration the remarkable acoustic absorption properties of moth wings, we develop a simple analytical model that describes the interaction between acoustic pressure fields, and thin elastic plates incorporating resonant sub-structures. The moth wing is an exemplar of a natural acoustic metamaterial; the wings are deeply subwavelength in thickness at the frequencies of interest, the absorption is broadband and the tiny scales resonate on the moth wing acting in concert. The simplified model incorporates only the essential physics and the scales are idealized to flat rigid rectangular plates coupled via a spring to an elastic plate that forms the wing; all the components are deep-subwavelength at desired frequencies. Based on Fourier analysis, complemented by phenomenological modelling, our theory shows excellent agreement with simulation mimicking the moth-wing structure. Moth wings operate as broadband sound absorbers employing a range of scale sizes. We demonstrate that a random distribution of scale sizes generates a broadband absorption spectrum. To further illustrate the potential of the model, we design a deeply sub-wavelength acoustic counterpart of electromagnetically induced reflectance. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Influence of footwear, foot-strike pattern and step frequency on spatiotemporal parameters and lower-body stiffness in running.

This study aimed to determine the influence of footwear condition, foot-strike pattern and step frequency on running spatiotemporal parameters and lower-body stiffness during treadmill running. Thirty-one amateur endurance runners performed a two-session protocol (shod and barefoot). Each session consisted of two trials at 12 km · h-1 over 5 minutes altering step frequency every minute (150, 160, 170, 180 and 190 spm). First, participants were instructed to land with the heel first; after completion, the same protocol was repeated landing with the forefoot first. Repeated measures ANOVAs showed significant differences for footwear condition, foot-strike pattern and step frequency for each variable: percent contact time, percent flight time, vertical stiffness and leg stiffness (all p < 0.001). The results demonstrate greater estimated vertical and leg stiffness when running barefoot for both foot-strike patterns showing the largest values for barefoot+forefoot condition. Likewise, both vertical and leg stiffness became greater as step frequency increased. The proper manipulation of these variables facilitates our understanding of running performance and assist in training programmes design and injury management.

The influence of sagittal trunk lean on uneven running mechanics.

The role of trunk orientation during uneven running is not well understood. This study compared the running mechanics during the approach step to and the step down for a 10 cm expected drop, positioned halfway through a 15 m runway, with that of the level step in 12 participants at a speed of 3.5 m s-1 while maintaining self-selected (17.7±4.2 deg; mean±s.d.), posterior (1.8±7.4 deg) and anterior (26.6±5.6 deg) trunk leans from the vertical. Our findings reveal that the global (i.e. the spring-mass model dynamics and centre-of-mass height) and local (i.e. knee and ankle kinematics and kinetics) biomechanical adjustments during uneven running are specific to the step nature and trunk posture. Unlike the anterior-leaning posture, running with a posterior trunk lean is characterized by increases in leg angle, leg compression, knee flexion angle and moment, resulting in a stiffer knee and a more compliant spring-leg compared with the self-selected condition. In the approach step versus the level step, reductions in leg length and stiffness through the ankle stiffness yield lower leg force and centre-of-mass position. Contrariwise, significant increases in leg length, angle and force, and ankle moment, reflect in a higher centre-of-mass position during the step down. Plus, ankle stiffness significantly decreases, owing to a substantially increased leg compression. Overall, the step down appears to be dominated by centre-of-mass height changes, regardless of having a trunk lean. Observed adjustments during uneven running can be attributed to anticipation of changes to running posture and height. These findings highlight the role of trunk posture in human perturbed locomotion relevant for the design and development of exoskeleton or humanoid bipedal robots.

The Influence of Age and Maturation on Trajectories of Stretch-Shortening Cycle Capability in Male Youth Team Sports.

PURPOSE: To examine the influence of growth and maturation in the trajectory of stretch-shortening cycle capability. METHOD: Using a mixed-longitudinal design, absolute and relative leg stiffness and reactive strength index (RSI) were measured 3 times over a 3-year period in 44 youth team-sport players. Maturation was determined as maturity offset and included within the Bayesian inference analysis as a covariate alongside chronological age. RESULTS: Irrespective of age and maturation, there was no change in absolute leg stiffness, however relative leg stiffness decreased over time. Maturation and age reduced this decline, but the decline remained significant (Bayesian factor [10] = 5097, model averaged R2 = .61). The RSI increased over time and more so in older more mature youth players (Bayesian factor [10] = 9.29e8, model averaged R2 = .657). CONCLUSION: In youth players who are at/post peak height velocity, relative leg stiffness appears to decline, which could have an impact on both performance and injury risk. However, RSI increases during this period, and these data reinforce that leg stiffness and RSI reflect different components of stretch-shortening cycle capability. Practitioners should consider these differences when planning training to maximize stretch-shortening cycle capability during growth and maturation in athletes on the developmental performance pathway.

Relationship between split-step timing and leg stiffness in world-class tennis players when returning fast serves.

This study investigated split-step timing when returning serves and whether this timing is related to neuromechanical capabilities in world-class tennis players. In Experiment 1, the split-step timing of four groups of world-class players (male and female ATP/WTA seniors, and ITF juniors) was measured on court when returning serves of the same level players. The four groups initiated the split-step at a similar time, starting around the time ball-racket contact in the serve stroke and landed when early ball-flight information was available. In Experiment 2, the neuromechanical capabilities (leg stiffness and vertical jump performance) of a group of world-class players and three groups of less-skilled tennis players were examined. The results showed an increase in leg stiffness with an increase in the level of expertise. A cross-experiment analysis in world-class male players (ATP/ITF, n = 10) revealed that the timing of initial foot movement was significantly correlated with the leg stiffness (r2 = 0.54), with later lateral step after the serve in the players who had higher stiffness. The findings support the hypothesis that world-class tennis players adapt perceptual-motor control on the basis of their neuromechanical capabilities and maximise the time before initiating their interceptive action to rely on more reliable information.

Relationship between vertical stiffness and soft-tissue injuries in professional Australian football.

Soft-tissue injuries are common in Australian football. Recently, literature has identified non-modifiable and modifiable risk factors, including vertical stiffness (Kvert). However, limitations regarding measurement frequency and duration exist; thus, further information is required about the role of Kvert as a modifiable risk factor for injury. This study examined the seasonal variation in Kvert and its relationship to soft-tissue injuries in professional Australian football. The mean Kvert and bilateral asymmetry were assessed and compared between injured and non-injured players. For the seasonal analysis, 56 players were tested across two seasons with no variation in bilateral asymmetry evident (p= 0.33). While there were generally no changes in Kvert, the value from the end of the second pre-season revealed 5% lower values than the mean of two seasons (p= 0.02). Considering the injury analysis, 21 lower-body soft-tissue injuries were recorded from 18 participants. No differences were recorded for mean Kvert between the injured and non-injured groups (p= 0.16-0.76). When assessing Kvert asymmetry, the injured group displayed a 4.5% higher value than the non-injured group at the end of the pre-season test (p= 0.03) but not at other time-points (p= 0.16-0.99). Higher Kvert bilateral asymmetry measures after the pre-season appear to be related to lower-body soft-tissue injury in professional Australian footballers. Medical and conditioning staff should consider this measure when trying to mitigate the onset of injury or identify at-risk players.

Female Athletes With Varying Levels of Vertical Stiffness Display Kinematic and Kinetic Differences During Single-Leg Hopping.

Vertical stiffness may contribute to lower-extremity injury risk; however, it is unknown whether athletes with different stiffness levels display differences in biomechanics. This study compared differences in biomechanics between female athletes (n = 99) with varying stiffness levels during a repetitive, single-leg, vertical hopping task. Vertical stiffness was calculated as the ratio of peak vertical ground-reaction force to maximum center-of-mass displacement. Tertiles were established using stiffness values, and separate 1-way ANOVAs were used to evaluate between-group differences. Stance times decreased, and flight times, ground-reaction force, and stiffness increased, from the low- to high-stiffness group (P < .050). The high-stiffness group displayed: (1) greater lateral trunk flexion (P = .009) and lesser hip adduction (P = .022) at initial ground contact compared to the low- and moderate-stiffness groups, respectively; (2) lesser peak hip adduction compared to the low-stiffness group (P = .040); (3) lesser lateral trunk-flexion (P = .046) and knee-flexion (P = .010) excursion compared to the moderate- and low-stiffness groups, respectively; and (4) greater peak hip-flexion (P = .001), ankle-dorsiflexion (P = .002), and ankle-eversion (P = .038) moments compared to the low-stiffness group. A wide range of variability in stiffness exists within a relatively homogenous population. Athletes with varying stiffness levels display biomechanical differences that may help identify the potential mechanism(s) by which stiffness contributes to injury risk.

A Comparison of Bilateral and Unilateral Drop Jumping Tasks in the Assessment of Vertical Stiffness.

This study sought to compare vertical stiffness during bilateral and unilateral drop jumping. Specifically, the intersession reliabilities and force-deformation profiles associated with each task were to be examined. On 3 occasions, following familiarization, 14 healthy males (age: 22 [2] y; height: 1.77 [0.08] m; and body mass: 73.5 [8.0] kg) performed 3 bilateral, left leg and right leg drop jumps. All jumps were performed from a drop height of 0.18 m on to a dual force plate system. Vertical stiffness was calculated as the ratio of peak ground reaction force (GRF) to the peak center of mass (COM) displacement. Unilateral drop jumping was associated with higher GRF and greater COM displacement (both Ps < .001), but vertical stiffness was not different between tasks when considering individual limbs (P = .98). A coefficient of variation of 14.6% was observed for bilateral vertical stiffness during bilateral drop jumping; values of 6.7% and 7.6% were observed for left and right limb vertical stiffness during unilateral drop jumping. These findings suggest that unilateral drop jumps may exhibit greater reliability than bilateral drop jumps while eliciting similar vertical stiffness. It is also apparent that higher GRFs during unilateral drop jumping are mitigated by increased COM displacement.

A general relationship links gait mechanics and running ground reaction forces.

The relationship between gait mechanics and running ground reaction forces is widely regarded as complex. This viewpoint has evolved primarily via efforts to explain the rising edge of vertical force-time waveforms observed during slow human running. Existing theoretical models do provide good rising-edge fits, but require more than a dozen input variables to sum the force contributions of four or more vague components of the body's total mass (mb). Here, we hypothesized that the force contributions of two discrete body mass components are sufficient to account for vertical ground reaction force-time waveform patterns in full (stance foot and shank, m1=0.08mb; remaining mass, m2=0.92mb). We tested this hypothesis directly by acquiring simultaneous limb motion and ground reaction force data across a broad range of running speeds (3.0-11.1 m s-1) from 42 subjects who differed in body mass (range: 43-105 kg) and foot-strike mechanics. Predicted waveforms were generated from our two-mass model using body mass and three stride-specific measures: contact time, aerial time and lower limb vertical acceleration during impact. Measured waveforms (N=500) differed in shape and varied by more than twofold in amplitude and duration. Nonetheless, the overall agreement between the 500 measured waveforms and those generated independently by the model approached unity (R2=0.95±0.04, mean±s.d.), with minimal variation across the slow, medium and fast running speeds tested (ΔR2≤0.04), and between rear-foot (R2=0.94±0.04, N=177) versus fore-foot (R2=0.95±0.04, N=323) strike mechanics. We conclude that the motion of two anatomically discrete components of the body's mass is sufficient to explain the vertical ground reaction force-time waveform patterns observed during human running.

Vertical stiffness asymmetries during drop jumping are related to ankle stiffness asymmetries.

Asymmetry in vertical stiffness has been associated with increased injury incidence and impaired performance. The determinants of vertical stiffness asymmetry have not been previously investigated. Eighteen healthy men performed three unilateral drop jumps during which vertical stiffness and joint stiffness of the ankle and knee were calculated. Reactive strength index was also determined during the jumps using the ratio of flight time to ground contact time. "Moderate" differences in vertical stiffness (t17  = 5.49; P < 0.001), "small" differences in center of mass displacement (t17  = -2.19; P = 0.043), and "trivial" differences in ankle stiffness (t17  = 2.68; P = 0.016) were observed between stiff and compliant limbs. A model including ankle stiffness and reactive strength index symmetry angles explained 79% of the variance in vertical stiffness asymmetry (R2  = 0.79; P < 0.001). None of the symmetry angles were correlated to jump height or reactive strength index. Results suggest that asymmetries in ankle stiffness may play an important role in modulating vertical stiffness asymmetry in recreationally trained men.

Do stiffness and asymmetries predict change of direction performance?

Change of direction speed (CODS) underpins performance in a wide range of sports but little is known about how stiffness and asymmetries affect CODS. Eighteen healthy males performed unilateral drop jumps to determine vertical, ankle, knee and hip stiffness, and a CODS test to evaluate left and right leg cutting performance during which ground reaction force data were sampled. A step-wise regression analysis was performed to ascertain the determinants of CODS time. A two-variable regression model explained 63% (R2 = 0.63; P = 0.001) of CODS performance. The model included the mean vertical stiffness and jump height asymmetry determined during the drop jump. Faster athletes (n = 9) exhibited greater vertical stiffness (F = 12.40; P = 0.001) and less asymmetry in drop jump height (F = 6.02; P = 0.026) than slower athletes (n  = 9); effect sizes were both "large" in magnitude. Results suggest that overall vertical stiffness and drop jump height asymmetry are the strongest predictors of CODS in a healthy, non-athletic population.

A Comparison of Vertical Stiffness Values Calculated from Different Measures of Center of Mass Displacement in Single-Leg Hopping.

This study assessed the agreement between Kvert calculated from 4 different methods of estimating vertical displacement of the center of mass (COM) during single-leg hopping. Healthy participants (N = 38) completed a 10-s single-leg hopping effort on a force plate, with 3D motion of the lower limb, pelvis, and trunk captured. Derived variables were calculated for a total of 753 hop cycles using 4 methods, including: double integration of the vertical ground reaction force, law of falling bodies, a marker cluster on the sacrum, and a segmental analysis method. Bland-Altman plots demonstrated that Kvert calculated using segmental analysis and double integration methods have a relatively small bias (0.93 kN⋅m-1) and 95% limits of agreement (-1.89 to 3.75 kN⋅m-1). In contrast, a greater bias was revealed between sacral marker cluster and segmental analysis (-2.32 kN⋅m-1), sacral marker cluster and double integration (-3.25 kN⋅m-1), and the law of falling bodies compared with all methods (17.26-20.52 kN⋅m-1). These findings suggest the segmental analysis and double integration methods can be used interchangeably for the calculation of Kvert during single-leg hopping. The authors propose the segmental analysis method to be considered the gold standard for the calculation of Kvert during single-leg, on-the-spot hopping.

Estimates of Running Ground Reaction Force Parameters from Motion Analysis.

We compared running mechanics parameters determined from ground reaction force (GRF) measurements with estimated forces obtained from double differentiation of kinematic (K) data from motion analysis in a broad spectrum of running speeds (1.94-5.56 m⋅s-1). Data were collected through a force-instrumented treadmill and compared at different sampling frequencies (900 and 300 Hz for GRF, 300 and 100 Hz for K). Vertical force peak, shape, and impulse were similar between K methods and GRF. Contact time, flight time, and vertical stiffness (kvert) obtained from K showed the same trend as GRF with differences < 5%, whereas leg stiffness (kleg) was not correctly computed by kinematics. The results revealed that the main vertical GRF parameters can be computed by the double differentiation of the body center of mass properly calculated by motion analysis. The present model provides an alternative accessible method for determining temporal and kinetic parameters of running without an instrumented treadmill.

Theoretical considerations on maximum running speeds for large and small animals.

Mechanical equations for fast running speeds are presented and analyzed. One of the equations and its associated model predict that animals tend to experience larger mechanical stresses in their limbs (muscles, tendons and bones) as a result of larger stride lengths, suggesting a structural restriction entailing the existence of an absolute maximum possible stride length. The consequence for big animals is that an increasingly larger body mass implies decreasing maximal speeds, given that the stride frequency generally decreases for increasingly larger animals. Another restriction, acting on small animals, is discussed only in preliminary terms, but it seems safe to assume from previous studies that for a given range of body masses of small animals, those which are bigger are faster. The difference between speed scaling trends for large and small animals implies the existence of a range of intermediate body masses corresponding to the fastest animals.

A comparison of methods to determine bilateral asymmetries in vertical leg stiffness.

Whilst the measurement and quantification of vertical leg stiffness (Kvert) asymmetry is of important practical relevance to athletic performance, literature investigating bilateral asymmetry in Kvert is limited. Moreover, how the type of task used to assess Kvert may affect the expression of asymmetry has not been properly determined. Twelve healthy males performed three types of performance tasks on a dual force plate system to determine Kvert asymmetries; the tasks were (a) bilateral hopping, (b) bilateral drop jumping and (c) unilateral drop jumping. Across all the three methods, Kvert was significantly different between compliant and stiff limbs (P < 0.001) with a significant interaction effect between limb and method (P = 0.005). Differences in Kvert between compliant and stiff limbs were -5.3% (P < 0.001), -21.8% (P = 0.007) and -15.1% (P < 0.001) for the bilateral hopping, bilateral drop jumping and unilateral drop jumping methods, respectively. All the three methods were able to detect significant differences between compliant and stiff limbs, and could be used as a diagnostic tool to assess Kvert asymmetry. Drop jumping tasks detected larger Kvert asymmetries than hopping, suggesting that asymmetries may be expressed to a greater extent in acyclic, maximal performance tasks.

Age- and gender-related development of stretch shortening cycle during a sub-maximal hopping task.

The aim of this study was to analyse the effects of age and gender (and their interaction) on a stretch shortening cycle solicited during a hopping task. For this aim, 147 girls and 148 boys aged 11 to 20 years, who were enrolled in middle school or secondary school with no experience in sport activity, or training less than three times per week, performed 3×5 hops in place. Leg-stiffness, jump-height and reactive-strength indices were assessed using an accelerometer (Myotest). The participants were selected in order to form five age groups: 11 12, 13-14, 15-16, 17-18 and 19-20 years. Regression analysis between force and centre of mass displacement revealed spring-mass behaviour for all groups (r(2)=.73-.89), meaning that beginning at the age of 11 years, children are able to perform complex inter-muscular coordination of the lower limbs, revealing efficient neural control early in childhood. Leg stiffness increased from 24.7 ± 10.6 kN · m(-1) at 11-12 years to 44.1 ± 14 kN · m(-1) in boys, with a small increase until 16 years (+17%) and a large increase between 17 and 20 years (+32.7%). In girls, leg stiffness increased from 26.6 ± 9 kN · m(-1) at 11-12 years to 39.4 ± 10.9 kN · m(-1) at 19-20 years, with a curious decrease in leg stiffness at 17-18 years, probably due to an increase in the percentage of fat at this age (25%). While no gender effect was found, the reactive-strength index revealed that, from 15-16 years onward, boys were better able to produce high levels of force in a shorter time than girls. The age of 15-16 years is a threshold of maturity and gender differentiation, where the boys investigated are more efficient in the stretch shortening cycle.

Locomotor control of limb force switches from minimal intervention principle in early adaptation to noise reduction in late adaptation.

During movement, errors are typically corrected only if they hinder performance. Preferential correction of task-relevant deviations is described by the minimal intervention principle but has not been demonstrated in the joints during locomotor adaptation. We studied hopping as a tractable model of locomotor adaptation of the joints within the context of a limb-force-specific task space. Subjects hopped while adapting to shifted visual feedback that induced them to increase peak ground reaction force (GRF). We hypothesized subjects would preferentially reduce task-relevant joint torque deviations over task-irrelevant deviations to increase peak GRF. We employed a modified uncontrolled manifold analysis to quantify task-relevant and task-irrelevant joint torque deviations for each individual hop cycle. As would be expected by the explicit goal of the task, peak GRF errors decreased in early adaptation before reaching steady state during late adaptation. Interestingly, during the early adaptation performance improvement phase, subjects reduced GRF errors by decreasing only the task-relevant joint torque deviations. In contrast, during the late adaption performance maintenance phase, all torque deviations decreased in unison regardless of task relevance. In deadaptation, when the shift in visual feedback was removed, all torque deviations decreased in unison, possibly because performance improvement was too rapid to detect changes in only the task-relevant dimension. We conclude that limb force adaptation in hopping switches from a minimal intervention strategy during performance improvement to a noise reduction strategy during performance maintenance, which may represent a general control strategy for locomotor adaptation of limb force in other bouncing gaits, such as running.

The mechanical cost of transport of fast running animals.

Regarding running animals, algebraic expressions for the horizontal (ωx) and vertical (ωy) components of the mechanical cost of transport are deduced for a ground force pattern based on the Spring-mass model. Defining µËœ as the maximum ground forces ratio µËœ=max(Fx)/max(Fy), the analysis shows that the mechanical cost of transport ωx+ωy for fast running animals is approximately proportional to µËœ, and to the relative contact length, and positively correlated to the limb take-off angle and the collision angle. The vertical cost ωy is shown to approximate to zero for fast running animals. Sustained top running speeds are predicted to require the largest possible values of µËœ and therefore relatively large horizontal propulsive forces, as well as a minimum possible ground contact time. The equations also show that animals running relatively slow would tend to prefer certain interval of values for parameter µËœ, which would minimize both their mechanical cost of transport and their metabolic cost of transport. Very large animals are suspected to be less capable of developing large values of µËœ, which possibly renders them incapable of developing great speeds.

The contribution of lower-limb joint quasi-stiffness to theoretical leg stiffness during level, uphill and downhill running at different speeds.

Humans change joint quasi-stiffness (k joint) and leg stiffness (kleg) when running at different speeds on level ground and during uphill and downhill running. These mechanical properties can inform device designs for running such as footwear, exoskeletons and prostheses. We measured kinetics and kinematics from 17 runners (10 M; 7 F) at three speeds on 0°, ±2°, ±4° and ±6° slopes. We calculated ankle and knee k joint, the quotient of change in joint moment and angular displacement, and theoretical leg stiffness (klegT) based on the joint external moment arms and k joint. Runners increased k ankle at faster speeds (p < 0.01). Runners increased and decreased the ankle and knee contributions to klegT, respectively, by 2.89% per 1° steeper uphill slope (p < 0.01) during the first half of stance. Runners decreased and increased ankle and knee joint contributions to klegT, respectively, by 3.68% during the first half and 0.86% during the second half of stance per 1° steeper downhill slope (p < 0.01). Thus, biomimetic devices require stiffer k ankle for faster speeds, and greater ankle contributions and greater knee contributions to klegT during the first half of stance for steeper uphill and downhill slopes, respectively.