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.     

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.     

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.     

Bipedal walking and running with spring-like biarticular muscles

Compliant elements in the leg musculoskeletal system appear to be important not only for running but also for walking in human locomotion as shown in the energetics and kinematics studies of spring-mass model. While the spring-mass model assumes a whole leg as a linear spring, it is still not clear how the compliant elements of muscle-tendon systems behave in a human-like segmented leg structure. This study presents a minimalistic model of compliant leg structure that exploits dynamics of biarticular tension springs. In the proposed bipedal model, each leg consists of three leg segments with passive knee and ankle joints that are constrained by four linear tension springs. We found that biarticular arrangements of the springs that correspond to rectus femoris, biceps femoris and gastrocnemius in human legs provide self-stabilizing characteristics for both walking and running gaits. Through the experiments in simulation and a real-world robotic platform, we show how behavioral characteristics of the proposed model agree with basic patterns of human locomotion including joint kinematics and ground reaction force, which could not be explained in the previous models.     

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.     

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.     

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 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.     

Modeling the stance leg in two-dimensional analyses of sprinting: inclusion of the MTP joint affects joint kinetics

Two-dimensional analyses of sprint kinetics are commonly undertaken but often ignore the metatarsalphalangeal (MTP) joint and model the foot as a single segment. Due to the linked-segment nature of inverse dynamics analyses, the aim of this study was to investigate the effect of ignoring the MTP joint on the calculated joint kinetics at the other stance leg joints during sprinting. High-speed video and force platform data were collected from four to five trials for each of three international athletes. Resultant joint moments, powers, and net work at the stance leg joints during the first stance phase after block clearance were calculated using three different foot models. By ignoring the MTP joint, peak extensor moments at the ankle, knee, and hip were on average 35% higher (p < .05 for each athlete), 40% lower (p < .05), and 9% higher (p > .05), respectively, than those calculated with the MTP joint included. Peak ankle and knee joint powers and net work at all joints were also significantly (p < .05) different. By ignoring a genuine MTP joint plantar flexor moment, artificially high peak ankle joint moments are calculated, and these also affect the calculated joint kinetics at the knee.     

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.     

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.

     

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.     

Assessing the Relative Contributions of Active Ankle and Knee Assistance to the Walking Mechanics of Transfemoral Amputees Using a Powered Prosthesis

Powered knee-ankle prostheses are capable of providing net-positive mechanical energy to amputees. Yet, there are limitless ways to deliver this energy throughout the gait cycle. It remains largely unknown how different combinations of active knee and ankle assistance affect the walking mechanics of transfemoral amputees. This study assessed the relative contributions of stance phase knee swing initiation, increasing ankle stiffness and powered plantarflexion as three unilateral transfemoral amputees walked overground at their self-selected walking speed. Five combinations of knee and ankle conditions were evaluated regarding the kinematics and kinetics of the amputated and intact legs using repeated measures analyses of variance. We found eliminating active knee swing initiation or powered plantarflexion was linked to increased compensations of the ipsilateral hip joint during the subsequent swing phase. The elimination of knee swing initiation or powered plantarflexion also led to reduced braking ground reaction forces of the amputated and intact legs, and influenced both sagittal and frontal plane loading of the intact knee joint. Gradually increasing prosthetic ankle stiffness influenced the shape of the prosthetic ankle plantarflexion moment, more closely mirroring the intact ankle moment. Increasing ankle stiffness also corresponded to increased prosthetic ankle power generation (despite a similar maximum stiffness value across conditions) and increased braking ground reaction forces of the amputated leg. These findings further our understanding of how to deliver assistance with powered knee-ankle prostheses and the compensations that occur when specific aspects of assistance are added/removed.     

Leg and Joint Stiffness in Children with Spastic Diplegic Cerebral Palsy during Level Walking

Individual joint deviations are often identified in the analysis of cerebral palsy (CP) gait. However, knowledge is limited as to how these deviations affect the control of the locomotor system as a whole when striving to meet the demands of walking. The current study aimed to bridge the gap by describing the control of the locomotor system in children with diplegic CP in terms of their leg stiffness, both skeletal and muscular components, and associated joint stiffness during gait. Twelve children with spastic diplegia CP and 12 healthy controls walked at a self-selected pace in a gait laboratory while their kinematic and forceplate data were measured and analyzed during loading response, mid-stance, terminal stance and pre-swing. For calculating the leg stiffness, each of the lower limbs was modeled as a non-linear spring, connecting the hip joint center and the corresponding center of pressure, with varying stiffness that was calculated as the slope (gradient) of the axial force vs. the deformation curve. The leg stiffness was further decomposed into skeletal and muscular components considering the alignment of the lower limb. The ankle, knee and hip of the limb were modeled as revolute joints with torsional springs whose stiffness was calculated as the slope of the moment vs. the angle curve of the joint. Independent t-tests were performed for between-group comparisons of all the variables. The CP group significantly decreased the leg stiffness but increased the joint stiffness during stance phase, except during terminal stance where the leg stiffness was increased. They appeared to rely more on muscular contributions to achieve the required leg stiffness, increasing the muscular demands in maintaining the body posture against collapse. Leg stiffness plays a critical role in modulating the kinematics and kinetics of the locomotor system during gait in the diplegic CP.     

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.     

Mechanical analysis of the landing phase in heel-toe running.

Results of mechanical analyses of running may be helpful in the search for the etiology of running injuries. In this study a mechanical analysis was made of the landing phase of three trained heel-toe runners, running at their preferred speed and style. The body was modeled as a system of seven linked rigid segments, and the positions of markers defining these segments were monitored using 200 Hz video analysis. Information about the ground reaction force vector was collected using a force plate. Segment kinematics were combined with ground reaction force data for calculation of the net intersegmental forces and moments. The vertical component of the ground reaction force vector Fz was found to reach a first peak approximately 25 ms after touch-down. This peak occurs because, in the support leg, the vertical acceleration of the knee joint is not reduced relative to that of the ankle joint by rotation of the lower leg, so that the support leg segments collide with the floor. Rotation of the support upper leg, however, reduces the vertical acceleration of the hip joint relative to that of the knee joint, and thereby plays an important role in limiting the vertical forces during the first 40 ms. Between 40 and 100 ms after touch-down, the vertical forces are mainly limited by rotation of the support lower leg. At the instant that Fz reaches its first peak, net moments about ankle, knee and hip joints of the support leg are virtually zero. The net moment about the knee joint changed from -100 Nm (flexion) at touch-down to +200 Nm (extension) 50 ms after touch-down. These changes are too rapid to be explained by variations in the muscle activation levels and were ascribed to spring-like behavior of pre-activated knee flexor and knee extensor muscles. These results imply that the runners investigated had no opportunity to control the rotations of body segments during the first part of the contact phase, other than by selecting a certain geometry of the body and muscular (co-)activation levels prior to touch-down.     

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.     

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.     

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.     

Effects of altered stride frequency and contact time on leg-spring behavior in human running

Many studies have demonstrated that contact time is a key factor affecting both the energetics and mechanics of running. The purpose of the present study was to further explore the relationships between contact time (t(c)), step frequency (f) and leg stiffness (k(leg)) in human running. Since f is a compound parameter, depending on both contact and aerial time, the specific goal of this study was to independently vary f and t(c) and to investigate their respective effects on spring-mass characteristics during running, seeking to determine if the changes in k(leg) observed when running at different f are mainly due to inherent changes in t(c). We compared three types of constant 3.33 m s(-1) running conditions in 10 male subjects: normal running at the subject's freely chosen f, running with decreased and increased f, and decreased and increased t(c) at the imposed freely chosen f. The data from the varied f trials showed that the variation of t(c) was strongly correlated to that of k(leg) (r(2)=0.90), and the variation of f was also significantly correlated to that of k(leg) (r(2)=0.47). Further, changes in t(c) obtained in various t(c) conditions were significantly correlated to changes in k(leg) (r(2)=0.96). These results confirm that leg stiffness was significantly influenced by step frequency variations during constant speed running, as earlier demonstrated, but our more novel finding is that compared to step frequency, the effect of contact time variations appears to be a stronger and more direct determinant of k(leg). Indeed, 90-96% of the variance in k(leg) can be explained by contact time, whether this latter parameter is directly controlled, or indirectly controlled through its close relationship with step frequency. In conclusion, from the comparison of two experimental procedures, i.e. imposing various step frequency conditions vs. asking subjects to intentionally vary contact time at their freely chosen step frequency, it appears that changes in leg stiffness are mainly related to changes in contact time, rather than to those in step frequency. Step frequency appears to be an indirect factor influencing leg stiffness, through its effect on contact time, which could be considered a major determinant of this spring-mass characteristic of human running.