Mechanism of leg stiffness adjustment for hopping on surfaces of different stiffnesses

When humans hopin place or run forward, leg stiffness is increased to offsetreductions in surface stiffness, allowing the global kinematics andmechanics to remain the same on all surfaces. The purpose of thepresent study was to determine the mechanism for adjusting legstiffness. Seven subjects hopped in place on surfaces of differentstiffnesses (23-35,000 kN/m) while force platform, kinematic, andelectromyographic data were collected. Leg stiffness approximatelydoubled between the most stiff surface and the least stiff surface.Over the same range of surfaces, ankle torsional stiffness increased1.75-fold, and the knee became more extended at the time of touchdown(2.81 vs. 2.65 rad). We used a computer simulation to examine thesensitivity of leg stiffness to the observed changes in ankle stiffnessand touchdown knee angle. Our model consisted of four segments (foot,shank, thigh, head-arms-trunk) interconnected by three torsionalsprings (ankle, knee, hip). In the model, an increase in anklestiffness 1.75-fold caused leg stiffness to increase 1.7-fold. A changein touchdown knee angle as observed in the subjects caused legstiffness to increase 1.3-fold. Thus both joint stiffness and limbgeometry adjustments are important in adjusting leg stiffness to allow similar hopping on different surfaces.

     

Knee stiffness is a major determinant of leg stiffness during maximal hopping

Understanding stiffness of the lower extremities during human movement may provide important information for developing more effective training methods during sports activities. It has been reported that leg stiffness during submaximal hopping depends primarily on ankle stiffness, but the way stiffness is regulated in maximal hopping is unknown. The goal of this study was to examine the hypothesis that knee stiffness is a major determinant of leg stiffness during the maximal hopping. Ten well-trained male athletes performed two-legged hopping in place with a maximal effort. We determined leg and joint stiffness of the hip, knee, and ankle from kinetic and kinematic data. Knee stiffness was significantly higher than ankle and hip stiffness. Further, the regression model revealed that only knee stiffness was significantly correlated with leg stiffness. The results of the present study suggest that the knee stiffness, rather than those of the ankle or hip, is the major determinant of leg stiffness during maximal hopping.     

Leg stiffness adjustment for a range of hopping frequencies in humans

The purpose of the present study was to determine how humans adjust leg stiffness over a range of hopping frequencies. Ten male subjects performed in place hopping on two legs, at three frequencies (1.5, 2.2, and 3.0 Hz). Leg stiffness, joint stiffness and touchdown joint angles were calculated from kinetic and/or kinematics data. Electromyographic activity (EMG) was recorded from six leg muscles. Leg stiffness increased with an increase in hopping frequency. Hip and knee stiffnesses were significantly greater at 3.0 Hz than at 1.5 Hz. There was no significant difference in ankle stiffness among the three hopping frequencies. Although there were significant differences in EMG activity among the three hopping frequencies, the largest was the 1.5 Hz, followed by the 2.2 Hz and then 3.0 Hz. The subjects landed with a straighter leg (both hip and knee were extended more) with increased hopping frequency. These results suggest that over the range of hopping frequencies we evaluated, humans adjust leg stiffness by altering hip and knee stiffness. This is accomplished by extending the touchdown joint angles rather than by altering neural activity.     

Comparison of whole-body vertical stiffness and leg stiffness during single-leg hopping in place in children and adults

In the hopping literature, whole-body vertical stiffness and leg stiffness are used interchangeably, due to most of the movement occurring in the vertical direction. However, there is some anterior/posterior movement of the center of mass and displacements of the foot during hopping in place in both children and adults. Further it is not understood if leg stiffness show a similar pattern as whole-body vertical stiffness when increasing hopping frequency. The purpose of this study was to test if whole-body vertical stiffness and leg stiffness are different during single-leg hopping in-place in children and adults, across a range of frequencies. Seventeen children aged 5–11 years and 16 young adults participated in this study. The subjects hopped at their preferred frequency as well as 20% below, 20% above and 40% above preferred frequency. Our results demonstrate that both whole-body vertical stiffness and leg stiffness increase when increasing hopping frequency for children and adults. However, whole-body vertical stiffness consistently overestimates leg stiffness due to a similar peak force but a greater leg length change compared to vertical COM displacement. This suggests a considerable horizontal COM movement from landing to mid-stance during hopping. Children aged 5–11 years old showed lower absolute values but higher normalized values of two stiffness measures than adults. This suggests somewhat adult-like stiffness control in children, but a reduced ability to manipulate the horizontal movement during single-leg hopping in place when compared to adults.     

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.     

Neuromechanical adaptation to hopping with an elastic ankle-foot orthosis.

When humans hop or run on different surfaces, they adjust their effective leg stiffness to offset changes in surface stiffness. As a result, the overall stiffness of the leg-surface series combination remains independent of surface stiffness. The purpose of this study was to determine whether humans make a similar adjustment when springs are placed in parallel with the leg via a lower limb orthosis. We studied seven human subjects hopping in place on one leg while wearing an ankle-foot orthosis. We used an ankle-foot orthosis because the ankle joint is primarily responsible for leg stiffness during hopping. A spring was added to the ankle-foot orthosis so that it increased orthosis stiffness by providing plantar flexor torque during ankle dorsiflexion. We hypothesized that subjects would decrease their biological ankle stiffness when the spring was added to the orthosis, keeping total ankle stiffness constant. We collected kinematic, kinetic, and electromyographic data during hopping with and without the spring on the orthosis. We found that total ankle stiffness and leg stiffness did not change across the two orthosis conditions (ANOVA, P > 0.05). This was possible because subjects decreased their biological ankle stiffness to offset the orthosis spring stiffness (P < 0.0001). The reduction in biological ankle stiffness was accompanied by decreases in soleus, medial gastrocnemius, and lateral gastrocnemius muscle activation (P < 0.0002). These results suggest that an elastic exoskeleton might improve human running performance by reducing muscle recruitment.     

Intralimb compensation strategy depends on the nature of joint perturbation in human hopping

Due to the well-described spring-mass dynamics of bouncing gaits, human hopping is a tractable model for elucidating basic neuromuscular compensation principles. We tested whether subjects would employ a multi-joint or single-joint response to stabilize leg stiffness while wearing a spring-loaded ankle-foot orthosis (AFO) that applied localized resistive and assistive torques to the ankle. We analyzed kinematics and kinetics data from nine subjects hopping in place on one leg, at three frequencies (2.2, 2.4, and 2.8Hz) and three orthosis conditions (freely articulating AFO, AFO with plantarflexion resistance, and AFO with plantarflexion assistance). Leg stiffness was invariant across AFO conditions, however, compensation strategy depended upon the nature of the applied load. Biological ankle stiffness increased in response to a resistive load at twice the rate that it decreased with an assitive load. Ankle adjustments alone fully compensated for an assistive load with no net change in combined (biological plus applied) total ankle stiffness (p > or =0.133). In contrast, a resistive load resulted in a 7.4-9.0% increase in total ankle stiffness across frequencies and a concomitant 10-15% increase in knee joint stiffness at each frequency (p< or =0.037). The increased knee joint stiffness in response to resistive ankle load allowed subjects to maintain a more flexed knee at mid-stance, which attenuated the effect of the increased total ankle joint stiffness to preserve leg stiffness and whole limb biomechanical performance. Our findings suggest humans maintain invariant leg stiffness in bouncing gaits through different intralimb compensation strategies that are specific to the nature of the joint loading.     

Determinants of difference in leg stiffness between endurance- and power-trained athletes

Understanding the leg and joint stiffness during human movement would provide important information that could be utilized for evaluating sports performance and for injury prevention. In the present study, we examined the determinants of the difference in the leg stiffness between the endurance-trained and power-trained athletes. Seven distance runners and seven power-trained athletes performed in-place hopping, matching metronome beats at 3.0 and 1.5Hz. Leg and joint stiffness were calculated from kinetic and kinematics data. Electromyographic activity (EMG) was recorded from six leg muscles. At both hopping frequencies, the power-trained athletes demonstrated significantly higher leg stiffness than the distance runners. Hip, knee, and ankle joints were analyzed for stiffness and touchdown angles. Ankle stiffness was significantly greater in the power-trained athletes than the distance runners at 3.0Hz as was knee stiffness at 1.5Hz. There was no significant difference in touchdown angle between the DR and PT groups at either hopping frequencies. When significant difference in EMG activity existed between two groups, it was always greater in the distance runners than the power-trained athletes. These results suggest that (1) the difference in leg stiffness between endurance-trained and power-trained athletes is best attributed to increased joint stiffness, and (2) the difference in joint stiffness between the two groups may be attributed to a lack of similarity in the intrinsic stiffness of the muscle-tendon complex rather than in altered neural activity.     

Vertical stiffness during one-legged hopping with and without using a running-specific prosthesis

Although athletes with unilateral below-the-knee amputations (BKAs) generally use their affected leg, including their prosthesis, as their take-off leg for the long jump, little is known about the spring-like leg behavior and stiffness regulation of the affected leg. The purpose of this study was to investigate vertical stiffness during one-legged hopping in an elite-level long jump athlete with a unilateral BKA. We used the spring-mass model to calculate vertical stiffness, which equals the ratio of maximum vertical ground reaction force to maximum center of mass displacement, while the athlete with a BKA hopped on one leg at a range of frequencies. Then, we compared the vertical stiffness of this athlete to seven non-amputee elite-level long-jumpers. We found that from 1.8 to 3.4 Hz, the vertical stiffness of the unaffected leg for an athlete with a BKA increases with faster hopping frequencies, but the vertical stiffness of the affected leg remains nearly constant across frequencies. The athlete with a BKA attained the desired hopping frequencies at 2.2 and 2.6 Hz, but was unable to match the lowest (1.8 Hz) and two highest frequencies (3.0 and 3.4 Hz) using his affected leg. We also found that at 2.5 Hz, unaffected leg vertical stiffness was 15% greater than affected leg vertical stiffness, and the vertical stiffness of non-amputee long-jumpers was 32% greater than the affected leg vertical stiffness of an athlete with a BKA. The results of the present study suggest that the vertical stiffness regulation strategy of an athlete with a unilateral BKA is not the same in the unaffected versus affected legs, and compared to non-amputees.     

Energy absorption as a predictor of leg impedance in highly trained females

Although leg spring stiffness represents active muscular recruitment of the lower extremity during dynamic tasks such as hopping and running, the joint-specific characteristics comprising the damping portion of this measure, leg impedance, are uncertain. The purpose of this investigation was to assess the relationship between leg impedance and energy absorption at the ankle, knee, and hip during early (impact) and late (stabilization) phases of landing. Twenty highly trained female dancers (age = 20.3 +/- 1.4 years, height = 163.7 +/- 6.0 cm, mass = 62.1 +/- 8.1 kg) were instrumented for biomechanical analysis. Subjects performed three sets of double-leg landings from under preferred, stiff, and soft landing conditions. A stepwise linear regression analysis revealed that ankle and knee energy absorption at impact, and knee and hip energy absorption during the stabilization phases of landing explained 75.5% of the variance in leg impedance. The primary predictor of leg impedance was knee energy absorption during the stabilization phase, independently accounting for 55% of the variance. Future validation studies applying this regression model to other groups of individuals are warranted.     

Neuromuscular changes for hopping on a range of damped surfaces.

Humans hopping and running on elastic and damped surfaces maintain similar center-of-mass dynamics by adjusting stance leg mechanics. We tested the hypothesis that the leg transitions from acting like an energy-conserving spring on elastic surfaces to a power-producing actuator on damped surfaces during hopping due to changes in ankle mechanics. To test this hypothesis, we collected surface electromyography, video kinematics, and ground reaction force while eight male subjects (body mass: 76.2 +/- 1.7 kg) hopped in place on a range of damped surfaces. On the most damped surface, most of the mechanical work done by the leg appeared at the ankle (52%), whereas 23 and 25% appeared at the knee and hip, respectively. Hoppers extended all three joints during takeoff further than they flexed during landing and thereby did more net positive work on more heavily damped surfaces. Also, all three joints reached peak flexion sooner after touchdown on more heavily damped surfaces. Consequently, peak moment occurred during joint extension rather than at peak flexion as on elastic surfaces. These strategies caused the positive work during extension to exceed the negative work during flexion to a greater extent on more heavily damped surfaces. At the muscle level, surface EMG increased by 50-440% in ankle and knee extensors as surface damping increased to compensate for greater surface energy dissipation. Our findings, and those of previous studies of hopping on elastic surfaces, show that the ankle joint is the key determinant of both springlike and actuator-like leg mechanics during hopping in place.     

Spring-like leg behaviour, musculoskeletal mechanics and control in maximum and submaximum height human hopping

The purpose of this study was to understand how humans regulate their 'leg stiffness' in hopping, and to determine whether this regulation is intended to minimize energy expenditure. 'Leg stiffness' is the slope of the relationship between ground reaction force and displacement of the centre of mass (CM). Variations in leg stiffness were achieved in six subjects by having them hop at maximum and submaximum heights at a frequency of 1.7 Hz. Kinematics, ground reaction forces and electromyograms were measured. Leg stiffness decreased with hopping height, from 350 N m(-1) kg(-1) at 26 cm to 150 N m(-1) kg(-1) at 14 cm. Subjects reduced hopping height primarily by reducing the amplitude of muscle activation. Experimental results were reproduced with a model of the musculoskeletal system comprising four body segments and nine Hill-type muscles, with muscle stimulation STIM(t) as only input. Correspondence between simulated hops and experimental hops was poor when STIM(t) was optimized to minimize mechanical energy expenditure, but good when an objective function was used that penalized jerk of CM motion, suggesting that hopping subjects are not minimizing energy expenditure. Instead, we speculated, subjects are using a simple control strategy that results in smooth movements and a decrease in leg stiffness with hopping height.     

Joint stiffness of the ankle and the knee in running

The spring-mass model is a valid fundament to understand global dynamics of fast legged locomotion under gravity. The underlying concept of elasticity, implying leg stiffness as a crucial parameter, is also found on lower motor control levels, i.e. in muscle-reflex and muscle-tendon systems. Therefore, it seems reasonable that global leg stiffness emerges from local elasticity established by appropriate joint torques. A recently published model of an elastically operating, segmented leg predicts that proper adjustment of joint elasticities to the leg geometry and initial conditions of ground contact provides internal leg stability. Another recent study suggests that in turn the leg segmentation and the initial conditions may be a consequence of metabolic and bone stress constraints. In this study, the theoretical predictions were verified experimentally with respect to initial conditions and elastic joint characteristics in human running. Kinematics and kinetics were measured and the joint torques were estimated by inverse dynamics. Stiffnesses and elastic nonlinearities describing the resulting joint characteristics were extracted from parameter fits. Our results clearly support the theoretical predictions: the knee joint is always stiffer and more extended than the ankle joint. Moreover, the knee torque characteristic on the average shows the higher nonlinearity. According to literature, the leg geometry is a consequence of metabolic and material stress limitations. Adapted to this given geometry, the initial joint angle conditions in fast locomotion are a compromise between metabolic and control effort minimisation. Based on this adaptation, an appropriate joint stiffness ratio between ankle and knee passively safeguards the internal leg stability. The identified joint nonlinearities contribute to the linearisation of the leg spring.     

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.

     

The interday reliability of leg and ankle musculotendinous stiffness measures

Two popular methods of assessing lower body musculotendinous stiffness include the hopping and oscillation tests. The disparity and paucity of reliability data prompted this investigation into leg musculotendinous stiffness (Kleg) and ankle musculotendinous stiffness (Kank) measures. Kleg and Kank were assessed on three separate occasions in 20 female subjects. Kleg was determined using bilateral hopping procedures conducted at 2.2 Hz and 3.2 Hz frequencies. Kank was assessed by perturbation of the subject's ankle musculotendinous unit on an instrumented calf raise apparatus at 70% of maximum isometric force (MIF). Excellent reliability was produced for all Kleg measures between all days, whereas Kank exhibited acceptable reliability after one session of familiarization. No relationship was evident between Kleg and Kank. It was concluded that no familiarization session was required for Kleg at the test frequencies and conditions tested, whereas at least one familiarization session was needed to ensure the reliable assessment of Kank.     

Soleus muscle and Achilles tendon compressive stiffness is related to knee and ankle positioning

Changes in fascicle length and tension of the soleus (SOL) muscle have been observed in humans using B-mode ultrasound to examine the knee from different angles. An alternative technique of assessing muscle and tendon stiffness is myometry, which is non-invasive, accessible, and easy to use. This study aimed to estimate the compressive stiffness of the distal SOL and Achilles tendon (AT) using myometry in various knee and ankle joint positions. Twenty-six healthy young males were recruited. The Myoton-PRO device was used to measure the compressive stiffness of the distal SOL and AT in the dominant leg. The knee was measured in two positions (90° of flexion and 0° of flexion) and the ankle joint in three positions (10° of dorsiflexion, neutral position, and 30° of plantar flexion) in random order. A three-way repeated-measures ANOVA test was performed. Significant interactions were found for structure × ankle position, structure × knee position, and structure × ankle position × knee position (p < 0.05). The AT and SOL showed significant increases in compressive stiffness with knee extension over knee flexion for all tested ankle positions (p < 0.05). Changes in stiffness relating to knee positioning were larger in the SOL than in the AT (p < 0.05). These results indicate that knee extension increases the compressive stiffness of the distal SOL and AT under various ankle joint positions, with a greater degree of change observed for the SOL. This study highlights the relevance of knee position in passive stiffness of the SOL and AT.     

Hopping frequency in humans: a test of how springs set stride frequency in bouncing gaits.

The storage and recovery of elastic energy in muscle-tendon springs is important in running, hopping, trotting, and galloping. We hypothesized that animals select the stride frequency at which they behave most like simple spring-mass systems. If higher or lower frequencies are used, they will not behave like simple spring-mass systems, and the storage and recovery of elastic energy will be reduced. We tested the hypothesis by having humans hop forward on a treadmill over a range of speeds and hop in place over a range of frequencies. The body was modeled as a simple spring-mass system, and the properties of the spring were measured by use of a force platform. Our subjects used nearly the same frequency (the "preferred frequency," 2.2 hops/s) when they hopped forward on a treadmill and when they hopped in place. At this frequency, the body behaved like a simple spring-mass system. Contrary to our predictions, it also behaved like a simple spring-mass system when the subjects hopped at higher frequencies, up to the maximum they could achieve. However, at the higher frequencies, the time available to apply force to the ground (the ground contact time) was shorter, perhaps resulting in a higher cost of generating muscular force. At frequencies below the preferred frequency, as predicted by the hypothesis, the body did not behave in a springlike manner, and it appeared likely that the storage and recovery of elastic energy was reduced. The combination of springlike behavior and a long ground contact time at the preferred frequency should minimize the cost of generating muscular force.     

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.     

Leg stiffness and joint stiffness while running to and jumping over an obstacle

During running, muscles of the lower limb act like a linear spring bouncing on the ground. When approaching an obstacle, the overall stiffness of this leg-spring system (k_leg) is modified during the two steps preceding the jump to enhance the movement of the center of mass of the body while leaping the obstacle. The aim of the present study is to understand how k_leg is modified during the running steps preceding the jump. Since k_leg depends on the joint torsional stiffness and on the leg geometry, we analyzed the changes in these two parameters in eight subjects approaching and leaping a 0.65 m-high barrier at 15 km h⁻¹. Ground reaction force (F) was measured during 5–6 steps preceding the obstacle using force platform and the lower limb movements were recorded by camera. From these data, the net muscular moment (M_j), the angular displacement (θ_j) and the lever arm of F were evaluated at the hip, knee and ankle. At the level of the hip, the M_j–θ_j relation shows that muscles are not acting like torsional springs. At the level of the knee and ankle, the M_j–θ_j relation shows that muscles are acting like torsional springs: as compared to steady-state running, the torsional stiffness k_j decreases from ~1/3 two contacts before the obstacle, and increases from ~2/3 during the last contact. These modifications in k_j reflect in changes in the magnitude of F but also to changes in the leg geometry, i.e. in the lever arms of F.     

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.