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.     

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.     

The effect on conventional gait model kinematics and kinetics of hip joint centre equations in adult healthy gait

The Conventional Gait Model (CGM) needs to benefit from large investigations on localization of the hip joint centre (HJC). Incorrect positions from the native equations were demonstrated (Sangeux et al., 2014; Harrington et al., 2007). More accurate equations were proposed but their impact on kinematics and kinetic CGM outputs was never evaluated. This short communication aims at examining if adoption of new HJC equations would alter standard CGM outputs. Sixteen able bodied participants underwent a full 3-D optoelectronic gait analysis followed by a 3-D ultrasound localization of their hips. Data were processed through the open source python package pyCGM2 replicating kinematic and kinetic processing of the native CGM. Compared with 3D ultrasound location, Hara equations improved the accuracy of sagittal plane kinematics (0.6°) and kinetics (0.02 N m kg⁻¹) for the hip. The worst case participant exhibited Harrington’s equations reached a deviation of 3° for the sagittal kinematics. In the coronal plane, Hara and Harrington equations presented similar differences (1°) for the hip whilst Davis equations had the largest deviation for hip abduction (2.7°) and hip abductor moment (0.10 N m kg⁻¹).Both Harrington and Hara equations improved the CGM location of the HJC. Hara equations improved results in the sagittal plane, plus utilise a single anthropometrics measurement, leg length, that may be more robust. However, neither set of equations had significant effect on kinematics. We reported some effects on kinetics, particularly in the coronal plane, which warrant caution in interpreting outputs using different sets of equations.     

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     

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.     

Effective leg stiffness in running

Leg stiffness is a common parameter used to characterize leg function during bouncing gaits, like running and hopping. In the literature, different methods to approximate leg stiffness based on kinetic and kinematic parameters are described. A challenging point in estimating leg stiffness is the definition of leg compression during contact. In this paper four methods (methods A–D) based on ground reaction forces (GRF) and one method (method E) relying on temporal parameters are described. Leg stiffness calculated by these five methods is compared with running patterns, predicted by the spring mass model.The best and simplest approximation of leg stiffness is method E. It requires only easily accessible parameters (contact time, flight time, resting leg length, body mass and the leg's touch down angle). Method D is of similar quality but additionally requires the time-dependent progression of the GRF. The other three methods show clear differences from the model predictions by over- or underestimating leg stiffness, especially at slow speeds.Leg stiffness is derived from a conceptual model of legged locomotion and does not exist without this model. Therefore, it is important to prove which experimental method is suited best for approximating the stiffness in a specific task. This will help to interpret the predictions of the conceptual model in comparison with experimental data.     

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.     

Mechanical model for theoretical determination of maximum running speed in mammals

A mechanical model for the determination of maximum speed in terrestrial tetrapods, designed for application to extinct species, is proposed. Only external bone measures and average body mass estimations are used as input data, and the hypothesis is made that leg bones are strong enough to endure the stress of running at maximum speed at a certain universal safety factor. The model is applied to a broad sample of living mammalian species to test its predictive power, and it is found to provide very good estimates of maximum running speed.     

Mechanical energy contribution of the metatarsophalangeal joint to running and sprinting

Despite the fact that a number of studies have investigated lower extremity energy generation during locomotion, the influence of the metatarsophalangeal (MP) joint remained unknown. The purpose of this study was to determine the relative contribution of the MP joint to the total mechanical energy in running and sprinting. A sagittal plane analysis was performed on data collected from 10 trained male athletes (five runners and five sprinters). The MP moment was assumed to be negligible until the ground reaction force acted distal to the joint. During running, once the ground reaction force crossed the MP joint, the MP moment was plantarflexor for the remainder of ground contact with average peak values of 59.9 Nm. The MP joint moment was plantarflexor throughout the stance phase for sprinting with average peak values of 112.4 Nm. Since the MP joint was dorsiflexing throughout the majority of the stance phase the joint absorbed large amounts of energy, on average 20.9 J during running and 47.8 J during sprinting. A lack of plantarflexion of the MP joint resulted in a lack of energy generation during take-off. Thus, the energy that was absorbed at the joint was dissipated in the shoe and foot structures.     

Lower limb joint stiffness and muscle co-contraction adaptations to instability footwear during locomotion

Unstable shoes (US) continually perturb gait which can train the lower limb musculature, but muscle co-contraction and potential joint stiffness strategies are not well understood. A shoe with a randomly perturbing midsole (IM) may enhance these adaptations. This study compares ankle and knee joint stiffness, and ankle muscle co-contraction during walking and running in US, IM and a control shoe in 18 healthy females. Ground reaction forces, three-dimensional kinematics and electromyography of the gastrocnemius medialis and tibialis anterior were recorded. Stiffness was calculated during loading and propulsion, derived from the sagittal joint angle-moment curves. Ankle co-contraction was analysed during pre-activation and stiffness phases. Ankle stiffness reduced and knee stiffness increased during loading in IM and US whilst walking (ankle, knee: p = 0.008, 0.005) and running (p < 0.001; p = 0.002). During propulsion, the opposite joint stiffness re-organisation was found in IM whilst walking (both joints p < 0.001). Ankle co-contraction increased in IM during pre-activation (walking: p = 0.001; running: p < 0.001), and loading whilst walking (p = 0.003), not relating to ankle stiffness. Results identified relative levels of joint stiffness change in unstable shoes, providing new evidence of how stability is maintained at the joint level.     

Active and passive contributions to joint kinetics during walking in older adults

The objectives of this study were to characterize the active and passive contributions to joint kinetics during walking in healthy young and older adults, and assess whether isokinetic ankle strength is associated with ankle power output during walking. Twenty healthy young (18–35 years) and 20 healthy older (65–85 years) adults participated in this study. We measured subject-specific passive-elastic joint moment–angle relationships in the lower extremity and tested maximum isokinetic ankle strength at 30 deg/s. Passive moment–angle relationships were used to estimate active and passive joint moment, power, and work quantities during walking at 80%, 100% and 120% of preferred walking speed. There were no significant differences in walking speed, step length, or cadence between the older and young adults. However, the older adults produced significantly more net positive work at the hip but less net positive work at the ankle at all walking speeds. Passive contributions to hip and ankle work did not significantly differ between groups, inferring that the older adults generated the additional hip work actively. Maximum isokinetic ankle strength was significantly less in the older adults, and correlated with peak positive plantar-flexor power at both the preferred and fast walking speeds. The results of this study suggest that age-related shifts in joint kinetics do not arise as a result of increased passive hip joint stiffness, but seem to be reflected in plantar-flexor weakness.     

Dependence of elbow joint stiffness measurements on speed,angle, and muscle contraction level

Elbow joint stiffness is critical to positioning the hand. Abnormal elbow joint stiffness may affect a person's ability to participate in activities of daily living. In this work, elbow joint stiffness was measured in ten healthy young adults with a device adapted from one previously used to measure stiffness in other joints. Measurements of elbow stiffness involved applying a constant-velocity rotational movement to the elbow and measuring the resultant displacement, torque, and acceleration. Elbow stiffness was then computed using a previously-established model for joint stiffness. Measurements were made at two unique elbow joint angles, two speeds, and two forearm muscle contraction levels. The results indicate that the elbow joint stiffness is significantly affected by both rotational speed and forearm muscle contraction level.     

Effects of low-pass filter combinations on lower extremity joint moments in distance running

Inverse dynamics is a standard tool in biomechanics, which requires low-pass filtering of external force and kinematic signals. Unmatched filtering procedures are reported to affect joint moment amplitudes in high impact movements, like landing or cutting, but are also common in the analysis of distance running. We analyzed the effects of cut-off frequencies in 94 rearfoot runners at a speed of 3.5 m/s. Additionally, we investigated whether the evaluation of footwear interventions is affected by the choice of cut-off frequencies. We performed 3D inverse dynamics for the hip, knee and ankle joints using different low-pass filter cut-off frequency combinations for a recursive fourth-order Butterworth filter. We observed fluctuations of joint moment curves in the first half of stance, which were most pronounced for the most unmatched cut-off frequency combination (kinematics: 10 Hz; ground reaction forces (GRFs): 100 Hz) and for more proximal joints. Peak sagittal plane hip joint moments were altered by 94% on average. We observed a change in the ranking of subjects based on joint moment amplitude. We found significant (p < 0.001) footwear by cut-off frequency combination interaction effects for most peak joint moments. These findings highlight the importance of cut-off frequency choice in the analysis of joint moments and the assessment of footwear interventions in distance running. Based on our results, we propose to use matched cut-off frequencies around 20 Hz in order to avoid large artificial fluctuations in joint moment curves while at the same time avoiding a severe removal of physiological high-frequency signal content from the GRF signals.     

The bending stiffness of shoes is beneficial to running energetics if it does not disturb the natural MTP joint flexion

A local minimum for running energetics has been reported for a specific bending stiffness, implying that shoe stiffness assists in running propulsion. However, the determinant of the metabolic optimum remains unknown. Highly stiff shoes significantly increase the moment arm of the ground reaction force (GRF) and reduce the leverage effect of joint torque at ground push-off. Inspired by previous findings, we hypothesized that the restriction of the natural metatarsophalangeal (MTP) flexion caused by stiffened shoes and the corresponding joint torque changes may reduce the benefit of shoe bending stiffness to running energetics. We proposed the critical stiffness, k_cr, which is defined as the ratio of the MTP joint (MTPJ) torque to the maximal MTPJ flexion angle, as a possible threshold of the elastic benefit of shoe stiffness. 19 subjects participated in a running test while wearing insoles with five different bending stiffness levels. Joint angles, GRFs, and metabolic costs were measured and analyzed as functions of the shoe stiffness. No significant changes were found in the take-off velocity of the center of mass (CoM), but the horizontal ground push-offs were significantly reduced at different shoe stiffness levels, indicating that complementary changes in the lower-limb joint torques were introduced to maintain steady running. Slight increases in the ankle, knee, and hip joint angular impulses were observed at stiffness levels exceeding the critical stiffness, whereas the angular impulse at the MTPJ was significantly reduced. These results indicate that the shoe bending stiffness is beneficial to running energetics if it does not disturb the natural MTPJ flexion.     

The effect of stride length on the dynamics of barefoot and shod running

A number of interventions and technique changes have been proposed to attempt to improve performance and reduce the number of running related injuries. Running shoes, barefoot running and alterations in spatio-temporal parameters (stride frequency and stride length) have been associated with significant kinematic and kinetic changes, which may have implications for performance and injury prevention. However, because footwear interventions have been shown to also affect spatio-temporal parameters, there is uncertainty regarding the origin of the kinematic and kinetic alterations. Therefore, the purpose of this study was to independently evaluate the effects of shoes and changes in stride length on lower extremity kinetics. Eleven individuals ran over-ground at stride lengths ±5 and 10% of their preferred stride length, in both the barefoot and shod condition. Three-dimensional motion capture and force plate data were captured synchronously and used to compute lower extremity joint moments. We found a significant main effect of stride length on anterior–posterior and vertical GRFs, and sagittal plane knee and ankle moments in both barefoot and shod running. When subjects ran at identical stride lengths in the barefoot and shod conditions we did not observe differences for any of the kinetic variables that were measured. These findings suggest that barefoot running triggers a decrease in stride length, which could lead to a decrease in GRFs and sagittal plane joint moments. When evaluating barefoot running as a potential option to reduce injury, it is important to consider the associated change in stride length.     

The effects of squatting footwear on three-dimensional lower limb and spine kinetics

Altering footwear worn during performance of the barbell back squat has been shown to change motion patterns, but it is not completely understood how this affects biomechanical loading demands. The primary objective was to compare lower back and extremity net joint moments in 24 experienced weightlifters (12M, 12F) who performed 80% one-repetition maximum back squats under three different footwear conditions (barefoot, running shoes, weightlifting shoes). Results showed that there was a significant main effect of footwear condition on the knee extension moment (p = 0.001), where the running and weightlifting shoes produced significantly larger moments than the barefoot condition. There was also a main effect of footwear condition on knee external rotation moments (p = 0.002), where the weightlifting shoe produced significantly larger moments than both other conditions. At the hip, there was also a main effect of footwear condition on the extension moment (p = 0.004), where the barefoot condition produced significantly larger moments than either the running shoe or weightlifting shoe condition. Lastly, there was also a significant main effect of footwear condition on both hip external (p = 0.005) and internal (p = 0.003) rotation moments, where the barefoot condition produced greater internal rotation and less external rotation moments than either shod condition. This study indicates that altering footwear conditions while performing the barbell back squat may redistribute the internal biomechanical loading patterns amongst the lower extremity joints and perhaps alter the musculoskeletal adaptations elicited.     

The effect of perturbing body segment parameters on calculated joint moments and muscle forces during gait

This study examined the effect of body segment parameter (BSP) perturbations on joint moments calculated using an inverse dynamics procedure and muscle forces calculated using computed muscle control (CMC) during gait. BSP (i.e. segment mass, center of mass location (com) and inertia tensor) of the left thigh, shank and foot of a scaled musculoskeletal model were perturbed. These perturbations started from their nominal value and were adjusted to ±40% in steps of 10%, for both individual as well as combined perturbations in BSP. For all perturbations, an inverse dynamics procedure calculated the ankle, knee and hip moments based on an identical inverse kinematics solution. Furthermore, the effect of applying a residual reduction algorithm (RRA) was investigated. Muscle excitations and resulting muscle forces were calculated using CMC. The results show only a limited effect of an individual parameter perturbation on the calculated moments, where the largest effect is found when perturbing the shank com (MS_com,shank, the ratio of absolute difference in torque and relative parameter perturbation, is maximally −7.81 N m for hip flexion moment). The additional influence of perturbing two parameters simultaneously is small (MS_{mass+com,thigh} is maximally 15.2 N m for hip flexion moment). RRA made small changes to the model to increase the dynamic consistency of the simulation (after RRA MS_com,shank is maximally 5.01 N m). CMC results show large differences in muscle forces when BSP are perturbed. These result from the underlying forward integration of the dynamic equations.     

Amputee locomotion: Spring-like leg behavior and stiffness regulation using running-specific prostheses

Carbon fiber running-specific prostheses (RSPs) have allowed individuals with lower extremity amputation (ILEA) to participate in running. It has been established that as running speed increases, leg stiffness (K_leg) remains constant while vertical stiffness (K_vert) increases in able-bodied runners. The K_vert further depends on a combination of the torsional stiffnesses of the joints (joint stiffness; K_joint) and the touchdown joint angles. Thus, an increased understanding of spring-like leg function and stiffness regulation in ILEA runners using RSPs is expected to aid in prosthetic design and rehabilitation strategies. The aim of this study was to investigate stiffness regulation to various overground running speeds in ILEA wearing RSPs. Eight ILEA performed overground running at a range of running speeds. K_leg, K_vert and K_joint were calculated from kinetic and kinematic data in both the intact and prosthetic limbs. K_leg and K_vert in both the limbs remained constant when running speed increased, while intact limbs in ILEA running with RSPs have a higher K_leg and K_vert than residual limbs. There were no significant differences in K_ankle, K_knee and touchdown knee angle between the legs at all running speeds. Hip joints in both the legs did not demonstrate spring-like function; however, distinct impact peaks were observed only in the intact leg hip extension moment at the early stance phase, indicating that differences in K_vert between limbs in ILEA are due to attenuating shock with the hip joint. Therefore, these results suggest that ILEA using RSPs has a different stiffness regulation between the intact and prosthetic limbs during running.     

The impact of adding trunk motion to the interpretation of the role of joint moments during normal walking

Biomechanical model assumptions affect the interpretation of the role of the muscle or joint moments to the segmental power estimated by induced acceleration analysis (IAA). We evaluated the effect of modeling the pelvis and trunk segments as two separate segments (8 SM) versus as a single segment (7 SM) on the segmental power, support of the body, knee and hip extension acceleration produced by the joint moments during the stance phase of normal walking. Significant differences were observed in the contribution of the stance hip abductor and extensor moments to support, ipsilateral knee and hip acceleration, and ipsilateral thigh and upper body power. The primary finding was that the role of the stance hip moment in generating ipsilateral thigh and upper body power differed based on degrees of freedom in the model. Secondarily, the magnitude of contributions also differed. For example, the hip abductor and extensor moments showed greater contribution to support, hip and knee acceleration in the 8 SM. IAA and segment power analysis are sensitive to the degrees of freedom between the pelvis and trunk. There is currently no gold standard by which to evaluate the accuracy of IAA predictions. However, modeling the pelvis and trunk as separate segments is closer to the anatomical architecture of the body. An 8 SM appears to be more appropriate for estimating the role of joint moments, particularly to motion of more proximal segments during normal walking.     

Improving joint torque calculations: optimization-based inverse dynamics to reduce the effect of motion errors

The accuracy of joint torques calculated from inverse dynamics methods is strongly dependent upon errors in body segment motion profiles, which arise from two sources of noise: the motion capture system and movement artifacts of skin-mounted markers. The current study presents a method to increase the accuracy of estimated joint torques through the optimization of the angular position data used to describe these segment motions. To compute these angular data, we formulated a constrained nonlinear optimization problem with a cost function that minimizes the difference between the known ground reaction forces (GRFs) and the GRF calculated via a top-down inverse dynamics solution. To evaluate this approach, we constructed idealized error-free reference movements (of squatting and lifting) that produced a set of known “true” motions and associated true joint torques and GRF. To simulate real-world inaccuracies in motion data, these true motions were perturbed by artificial noise. We then applied our approach to these noise-induced data to determine optimized motions and related joint torques. To evaluate the efficacy of the optimization approach compared to traditional (bottom-up or top-down) inverse dynamics approaches, we computed the root mean square error (RMSE) values of joint torques derived from each approach relative to the expected true joint torques. Compared to traditional approaches, the optimization approach reduced the RMSE by 54% to 79%. Average reduction due to our method was 65%; previous methods only achieved an overall reduction of 30%. These results suggest that significant improvement in the accuracy of joint torque calculations can be achieved using this approach.