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.     

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.     

Linear center-of-mass dynamics emerge from non-linear leg-spring properties in human hopping

Given the almost linear relationship between ground-reaction force and leg length, bouncy gaits are commonly described using spring–mass models with constant leg-spring parameters. In biological systems, however, spring-like properties of limbs may change over time. Therefore, it was investigated how much variation of leg-spring parameters is present during vertical human hopping. In order to do so, rest-length and stiffness profiles were estimated from ground-reaction forces and center-of-mass dynamics measured in human hopping. Trials included five hopping frequencies ranging from 1.2 to 3.6 Hz. Results show that, even though stiffness and rest length vary during stance, for most frequencies the center-of-mass dynamics still resemble those of a linear spring–mass hopper. Rest-length and stiffness profiles differ for slow and fast hopping. Furthermore, at 1.2 Hz two distinct control schemes were observed.     

Influence of leg stiffness and its effect on myodynamic jumping performance.

The purposes of this study are: a) to examine the possibility of influencing the leg stiffness through instructions given to the subjects and b) to determine the effect of the leg stiffness on the mechanical power and take-off velocity during the drop jumps. A total of 15 athletes performed a series of drop jumps from heights of 20, 40 and 60 cm. The instructions given to the subjects were a) "jump as high as you can" and b) "jump high a little faster than your previous jump". The jumps were performed at each height until the athlete could not achieve a shorter ground contact time. The ground reaction forces were measured using a "Kistler" force plate (1000 Hz). The athletes body positions were recorded using a high speed (250 Hz) video camera. EMG was used to measure muscle activity in five leg muscles. The data was divided into 5 groups where group 1 was made up of the longest ground contact times of each athlete and group 5 the shortest. The leg and ankle stiffness values were higher when the contact times were shorter. This means that by influencing contact time through verbal instructions it is possible to control leg stiffness. Maximum center of mass take-off velocity the can be achieved with different levels of leg stiffness. The mechanical power acting on the human body during the positive phase of the drop jumps had the highest values in group 3. This means that there is an optimum stiffness value for the lower extremities to maximize mechanical power.     

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.     

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.     

Leg stiffness in unilateral transfemoral amputees across a range of running speeds

Carbon fiber running-specific prostheses have allowed lower extremity amputees to participate in running activity by providing spring-like properties in their affected limb. It has been established that as running speed increases, stiffness of the leg spring (leg stiffness; k_leg) remains constant in non-amputees. Although a better understanding of k_leg regulation may be helpful for the development of spring-based prostheses, little is known about stiffness regulation in unilateral transfemoral amputees. The aim of this study was to investigate stiffness regulation at different running speeds in unilateral transfemoral amputees wearing a running-specific prosthesis. Nine unilateral transfemoral amputees performed running on an instrumented treadmill across a range of speeds (30, 40, 50, 60, and 70% of their maximum running speed). Using a spring-mass model, k_leg was calculated as the ratio of maximal vertical ground reaction force to maximum leg compression during the stance phase in both affected and unaffected limbs. We found a decrease in k_leg from the slower speed to 70% speed for the affected limb, whereas no change was present in the unaffected limb. Specifically, there was a significant differences in the k_leg between 30% and 70%, 40% and 70%, and 50% and 70%, and the magnitude of the k_leg difference between affected and unaffected limbs varied with variations in running speeds in unilateral TFAs with an RSP. These results suggest the k_leg regulation strategy of unilateral transfemoral amputees is not the same in the affected and unaffected limbs across a range of running speeds.     

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.     

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.     

Regulation of step frequency in transtibial amputee endurance athletes using a running-specific prosthesis

Running specific prostheses (RSP) are designed to replicate the spring-like behaviour of the human leg during running, by incorporating a real physical spring in the prosthesis. Leg stiffness is an important parameter in running as it is strongly related to step frequency and running economy. To be able to select a prosthesis that contributes to the required leg stiffness of the athlete, it needs to be known to what extent the behaviour of the prosthetic leg during running is dominated by the stiffness of the prosthesis or whether it can be regulated by adaptations of the residual joints. The aim of this study was to investigate whether and how athletes with an RSP could regulate leg stiffness during distance running at different step frequencies.Seven endurance runners with an unilateral transtibial amputation performed five running trials on a treadmill at a fixed speed, while different step frequencies were imposed (preferred step frequency (PSF) and −15%, −7.5%, +7.5% and +15% of PSF). Among others, step time, ground contact time, flight time, leg stiffness and joint kinetics were measured for both legs.In the intact leg, increasing step frequency was accompanied by a decrease in both contact and flight time, while in the prosthetic leg contact time remained constant and only flight time decreased. In accordance, leg stiffness increased in the intact leg, but not in the prosthetic leg. Although a substantial contribution of the residual leg to total leg stiffness was observed, this contribution did not change considerably with changing step frequency.Amputee athletes do not seem to be able to alter prosthetic leg stiffness to regulate step frequency during running. This invariant behaviour indicates that RSP stiffness has a large effect on total leg stiffness and therefore can have an important influence on running performance. Nevertheless, since prosthetic leg stiffness was considerably lower than stiffness of the RSP, compliance of the residual leg should not be ignored when selecting RSP stiffness.     

Leg stiffness primarily depends on ankle stiffness during human hopping

When humans hop in place or run forward, they adjust leg stiffness to accommodate changes in stride frequency or surface stiffness. The goal of the present study was to determine the mechanisms by which humans adjust leg stiffness during hopping in place. Five subjects hopped in place at 2.2 Hz while we collected force platform and kinematic data. Each subject completed trials in which they hopped to whatever height they chose ("preferred height hopping") and trials in which they hopped as high as possible ("maximum height hopping"). Leg stiffness was approximately twice as great for maximum height hopping as for preferred height hopping. Ankle torsional stiffness was 1.9-times greater while knee torsional stiffness was 1.7-times greater in maximum height hopping than in preferred height hopping. We used a computer simulation to examine the sensitivity of leg stiffness to the observed changes in ankle and knee stiffness. Our model consisted of four segments (foot, shank, thigh, head-arms-trunk) interconnected by three torsional springs (ankle, knee, hip). In the model, increasing ankle stiffness by 1.9-fold, as observed in the subjects, caused leg stiffness to increase by 2.0-fold. Increasing knee stiffness by 1.7-fold had virtually no effect on leg stiffness. Thus, we conclude that the primary mechanism for leg stiffness adjustment is the adjustment of ankle stiffness.     

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.     

Three-dimensional knee joint contact forces during walking in unilateral transtibial amputees

Individuals with unilateral transtibial amputations have greater prevalence of osteoarthritis in the intact knee joint relative to the residual leg and non-amputees, but the cause of this greater prevalence is unclear. The purpose of this study was to compare knee joint contact forces and the muscles contributing to these forces between amputees and non-amputees during walking using forward dynamics simulations. We predicted that the intact knee contact forces would be higher than those of the residual leg and non-amputees. In the axial and mediolateral directions, the intact and non-amputee legs had greater peak tibio-femoral contact forces and impulses relative to the residual leg. The peak axial contact force was greater in the intact leg relative to the non-amputee leg, but the stance phase impulse was greater in the non-amputee leg. The vasti and hamstrings muscles in early stance and gastrocnemius in late stance were the largest contributors to the joint contact forces in the non-amputee and intact legs. Through dynamic coupling, the soleus and gluteus medius also had large contributions, even though they do not span the knee joint. In the residual leg, the prosthesis had large contributions to the joint forces, similar to the soleus in the intact and non-amputee legs. These results identify the muscles that contribute to knee joint contact forces during transtibial amputee walking and suggest that the peak knee contact forces may be more important than the knee contact impulses in explaining the high prevalence of intact leg osteoarthritis.     

Muscle dynamics differences between legs in healthy adults

Differences in muscle dynamics between the preferred and nonpreferred jumping legs of subjects in maximal, explosive exercise were examined. Eight subjects performed nonfatiguing bouts of single-legged drop jumps and rebound jumps on a force sledge apparatus. Measures of flight time, reactive strength index, peak vertical force, and vertical leg-spring stiffness were obtained for 3 drop jumps and 3 rebound jumps on both legs. Subjects utilized a stiffer leg spring and a more explosive jumping action in the nonpreferred leg when performing a cyclical rebound jumping task in comparison to a single drop jump task (observed through differences in vertical leg-spring stiffness, peak vertical force, and reactive strength index, p < 0.05). The preferred leg performed equally well in both tasks. Between-leg analysis showed no differences in dependent variables between the preferred and the nonpreferred leg in the rebound jumping protocol. However, the drop jump protocol showed significant performance differences, with flight time and reactive strength index greater in the preferred leg than the nonpreferred leg (p < 0.05). We hypothesize that, throughout the lifespan, both legs are equally trained in cyclical rebound jumping tasks through running. However, because a preferred leg must be selected when performing any one-off, single-legged jump, imbalances in this specific task develop over time with consistent selection of a preferred jumping leg. The data demonstrate that the rebound jump protocol is representative of the symmetrical mechanics of forward running and that leg-spring stiffness is modulated depending on the demands of the specific task involved. Strength and conditioning practitioners should give careful consideration to appropriate jump protocol selection and should exercise caution when comparing laboratory results to data gathered in field testing.     

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.     

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.     

Long-term training adaptations in elite male volleyball players

Several investigations have demonstrated differences in anthropometry, jump performance, and strength variables between developmental and elite-level volleyball players. However, within the elite level of play, the magnitude of change that can occur with training is unclear. The purpose of this investigation was to examine the anthropometric, vertical jump, and strength quality changes over 2 years in a group of national team volleyball players. Fourteen national team volleyball players (age, 23.0 ± 4.1 years; height, 1.98 ± 0.07 m; weight, 91.7 ± 7.9 kg) began and completed this study. Participants had all played international matches (representing Australia) before the examination time period and continued to do so during the international season. Anthropometry (stature, mass, and sum of 7 skinfolds), vertical jump measures (countermovement vertical jump; depth jump from 0.35 m, DJ; spike jump, SPJ, all including arm swing), and lower-body power (jump squat at body mass, and jump squat + 50% body weight, JS50) measures were tested before and at the conclusion of the investigation period. Significant (p < 0.05) improvements were observed in sum of 7 skinfolds, DJ, SPJ, and JS50 performance, with large magnitude changes (d > 0.70) in the sum of 7 skinfolds reduction, SPJ, and leg extensor power. This study has demonstrated that elite male volleyball players can improve leanness and power, which contribute to improvements in vertical jump.     

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.     

Comparison between kinematic and kinetic methods for computing the vertical displacement of the center of mass during human hopping at different frequencies

Kinematic and kinetic methods (sacral marker, reconstructed pelvis, segmental analysis, and force platform methods) have been used to calculate the vertical excursion of the center of mass (COM) during movement. In this study we compared the measurement of vertical COM displacement yielded by different methods during able-bodied subjects' hopping at different frequencies (varying between 1.2 and 3.2 Hz). ANOVA revealed a significant interaction between hopping frequency and method (p < 0.001), showing that increasing hopping frequency reduced the differences between methods. A post hoc analysis revealed a significant difference between all methods at the lowest hopping frequency and between the force platform and both the sacral marker and reconstructed pelvis methods at the intermediate hopping frequencies, with differences ranging from 16 to 67 millimeters (all p < 0.05). Results are discussed in view of each methods' limits. We conclude that the segmental analysis and force platform methods can be considered to provide the most accurate results for COM vertical excursion during human hopping in a large range of hopping frequency.