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.     

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.     

Muscle pre-activation strategies play a role in modulating Kvert for change of direction manoeuvres: An observational study

The aim of the study presented in this paper was to establish if a relationship existed between lower limb muscle pre-activation strategies and vertical stiffness (K_vert). Participants from a professional rugby union club all performed a multidirectional hopping task on a force platform which measured K_vert. Muscle activity was concurrently measured for the gluteus maximus, vastus lateralis, vastus medialis, biceps femoris, semimembranosus, and medial gastrocnemius using electromyography and the activity of those muscles in the 100 ms prior to foot contact (pre-activation) was analysed. Moderate to strong positive relationships were typically seen for K_vert and muscle pre-activation for each muscle when normalized to maximum voluntary contraction. Pre-activation cocontraction of the muscles surrounding the knee joint also showed a typically moderate relationship with K_vert and peak muscle activation of antagonist muscles at the knee joint were typically similar. Results suggest that muscle pre-activation strategies play a role in modulating K_vert for change of direction manoeuvre.     

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.     

Running-specific prostheses reduce lower-limb muscle activity compared to daily-use prostheses in people with unilateral transtibial amputations

People with unilateral transtibial amputation (TTA) have biomechanical differences between the amputated and intact legs and compared to people without TTA during running. Additional biomechanical differences emerge between running with running-specific (RSPs) and daily-use prostheses (DUPs), but the associated underlying muscle activity is unclear. We collected surface electromyography from the biceps femoris long head, rectus femoris, vastus lateralis, and gastrocnemius as well as body kinematics and ground reaction forces in six people with and six people without TTA. We compared stance phase muscle activity and peak activation timing in people with and without TTA and between people using RSPs compared to DUPs during running at 3.5 m/s. Peak amputated leg hamstring activity occurred 34% (RSP) and 31% (DUP) earlier in stance phase compared to the intact leg. Peak amputated leg rectus femoris activity of people wearing DUPs occurred 8% and 9% later in stance phase than the intact leg of people wearing DUPs and amputated leg of people wearing RSPs, respectively. People with TTA had 45% (DUP) and 61% (RSP) smaller peak amputated leg knee extension moments compared to people without TTA, consistent with observations of quadriceps muscle activity. Using RSPs decreased overall muscle activity compared to DUPs.     

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.     

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.     

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.     

Biomechanical analysis of the stance phase during barefoot and shod running

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

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.     

Amputee locomotion: Frequency content of prosthetic vs. intact limb vertical ground reaction forces during running and the effects of filter cut-off frequency

Compared to intact limbs, running-specific prostheses have high resonance non-biologic materials and lack active tissues to damp high frequencies. These differences may lead to ground reaction forces (GRFs) with high frequency content. If so, ubiquitously applying low-pass filters to prosthetic and intact limb GRFs may attenuate veridical high frequency content and mask important and ecologically valid data from prostheses. To explore differences in frequency content between prosthetic and intact limbs we divided signal power from transtibial unilateral amputees and controls running at 2.5, 3.0, and 3.5 m/s into Low (<10 Hz), High (10–25 Hz), and Non-biologic (>25 Hz) frequency bandwidths. Faster speeds tended to reduce the proportion of signal power in the Low bandwidth while increasing it in the High and Non-biologic bandwidths. Further, prostheses had lower proportions of signal power at the High frequency bandwidth but greater proportions at the Non-biologic bandwidth. To evaluate whether these differences in frequency content interact with filter cut-offs and alter results, we filtered GRFs with cut-offs from 1 to 100 Hz and calculated vertical impact peak (VIP). Changing cut-off had inconsistent effects on VIP across speeds and limbs: Faster speeds had significantly larger changes in VIP per change in cut-off while, compared to controls, prosthetic limbs had significantly smaller changes in VIP per change in cut-off. These findings reveal differences in GRF frequency content between prosthetic and intact limbs and suggest that a cut-off frequency that is appropriate for one limb or speed may be inappropriate for another.     

Stiffness adaptations in shod running

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

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.

     

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.     

Dynamic balance during running using running-specific prostheses

Running is beneficial for physical, social, and emotional health, and participating in physical activity, including running, is becoming more popular for people with an amputation. However, this population has a greater risk of falling relative to people without an amputation, which may be a barrier to running. Understanding how dynamic balance is maintained during running is important for removing this barrier. To investigate dynamic balance, we quantified whole-body angular momentum in eight people with a unilateral transtibial amputation (TTA) using running-specific prostheses (RSPs) compared to eight people without TTA during running at 2.5, 3.0, and 3.5 m/s. People with TTA had greater ranges of whole-body angular momentum compared to people without TTA in the frontal and sagittal planes (p < 0.01). These greater ranges resulted from smaller peak medial, lateral, and braking ground reaction forces from the amputated leg compared to the intact leg and people without TTA. Reduced RSP mass relative to the biological leg also influenced whole-body angular momentum as evidenced by smaller ranges of amputated leg angular momentum compared to the intact leg in the frontal and sagittal planes. Smaller amputated leg angular momentum corresponded with smaller contralateral arm angular momentum in the sagittal plane (p < 0.01). People with TTA maintain balance during running with altered muscle coordination and prosthesis characteristics. Restoring mediolateral force generation through prosthetic design advances may help in regulating the frontal plane component of whole-body angular momentum for people with TTA, with potential to improve their ability to maintain balance during running.     

Stance leg control: variation of leg parameters supports stable hopping

The spring-loaded inverted pendulum describes the planar center-of-mass dynamics of legged locomotion. This model features linear springs with constant parameters as legs. In biological systems, however, spring-like properties of limbs can change over time. Therefore, in this study, it is asked how variation of spring parameters during ground contact would affect the dynamics of the spring-mass model. Neglecting damping initially, it is found that decreasing stiffness and increasing rest length of the leg during a stance phase are required for orbitally stable hopping. With damping, stable hopping is found for a larger region of rest-length rates and stiffness rates. Here, also increasing stiffness and decreasing rest length can result in stable hopping. Within the predicted range of leg parameter variations for stable hopping, there is no need for precise parameter tuning. Since hopping gaits form a subset of the running gaits (with vanishing horizontal velocity), these results may help to improve leg design in robots and prostheses.     

Runners adjust leg stiffness for their first step on a new running surface.

Human runners adjust the stiffness of their stance leg to accommodate surface stiffness during steady state running. This adjustment allows runners to maintain similar center of mass movement (e.g., ground contact time and stride frequency) regardless of surface stiffness. When runners encounter abrupt transitions in the running surface, they must either make a rapid adjustment or allow the change in the surface stiffness to disrupt their running mechanics. Our goal was to determine how quickly runners adjust leg stiffness when they encounter an abrupt but expected change in surface stiffness that they have encountered previously. Six human subjects ran at 3 m s(-1) on a rubber track with two types of rubber surfaces: a compliant "soft" surface (ksurf = 21.3 kN m(-1) and a non-compliant "hard" surface (ksurf = 533 kN m(-1). We found that runners completely adjusted leg stiffness for their first step on the new surface after the transition. For example, runners decreased leg stiffness by 29% between the last step on the soft surface and the first step on the hard surface (from 10.7 kN m(-1) to 7.6 kN m(-1), respectively). As a result, the vertical displacement of the center of mass during stance ( approximately 7 cm) did not change at the transition despite a reduction in surface compression from 6 cm to less than 0.25 cm. By rapidly adjusting leg stiffness, each runner made a smooth transition between surfaces so that the path of the center of mass was unaffected by the change in surface stiffness.     

A movement criterion for running

The adjustment of the leg during running was addressed using a spring-mass model with a fixed landing angle of attack. The objective was to obtain periodic movement patterns. Spring-like running was monitored by a one-dimensional stride-to-stride mapping of the apex height to identify mechanically stable fixed points. We found that for certain angles of attack, the system becomes self-stabilized if the leg stiffness was properly adjusted and a minimum running speed was exceeded. At a given speed, running techniques fulfilling a stable movement pattern are characterized by an almost constant maximum leg force. With increasing speed, the leg adjustment becomes less critical. The techniques predicted for stable running are in agreement with experimental studies. Mechanically self-stabilized running requires a spring-like leg operation, a minimum running speed and a proper adjustment of leg stiffness and angle of attack. These conditions can be considered as a movement criterion for running.     

Hamstring muscle kinematics and activation during overground sprinting

Hamstring muscle strain injury is one of the most commonly seen injuries in sports such as track and field, soccer, football, and rugby. The purpose of this study was to advance our understanding of the mechanisms of hamstring muscle strain injuries during over ground sprinting by investigating hamstring muscle-tendon kinematics and muscle activation. Three-dimensional videographic and electromyographic (EMG) data were collected for 20 male runners, soccer or lacrosse players performing overground sprinting at their maximum effort. Hamstring muscle-tendon lengths, elongation velocities, and linear envelop EMG data were analyzed for a running gait cycle of the dominant leg. Hamstring muscles exhibited eccentric contractions during the late stance phase as well as during the late swing phase of overground sprinting. The peak eccentric contraction speeds of the hamstring muscles were significantly greater during the late swing phase than during the late stance phase (p=0.001) while the hamstring muscle-tendon lengths at the peak eccentric contraction speeds were significantly greater during the late stance phase than during the late swing phase (p=0.001). No significant differences existed in the maximum hamstring muscle-tendon lengths between the two eccentric contractions. The potential for hamstring muscle strain injury exists during the late stance phase as well as during the late swing phases of overground sprinting.     

The spring-mass model and the energy cost of treadmill running

During running, the behaviour of the support leg was studied by modelling the runner using an oscillating system composed of a spring (the leg) and of a mass (the body mass). This model was applied to eight middle-distance runners running on a level treadmill at a velocity corresponding to 90% of their maximal aerobic velocity [mean 5.10 (SD 0.33) m · s⁻¹]. Their energy cost of running (C _r ), was determined from the measurement of O₂ consumption. The work, the stiffness and the resonant frequency of both legs were computed from measurements performed with a kinematic arm. The C _r was significantly related to the stiffness (P < 0.05, r = −0.80) and the absolute difference between the resonant frequency and the step frequency (P < 0.05, r = 0.79) computed for the leg producing the highest positive work. Neither of these significant relationships were obtained when analysing data from the other leg probably because of the work asymmetry observed between legs. It was concluded that the spring-mass model is a good approach further to understand mechanisms underlying the interindividual differences in C _r . Accepted: 18 August 1997