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.     

Active stiffness of the ankle in response to inertial and elastic loads.

Effective stiffness of the musculoskeletal system was examined as a function of the characteristics of an external load. Thirteen healthy subjects provided active contraction of the ankle plantarflexion musculature in a neutral ankle posture to support an external load. Musculoskeletal stiffness was computed from kinetic data recorded in response to dorsiflexion/plantarflexion perturbations. Ankle dynamics were recorded while supporting external loads of 19 and 38 kg with and without antagonistic co-contraction. External loads were applied using pure gravitational mass. In separate trials external loads were applied from stretch of steel springs in parallel with the plantarflexion musculature that also provided added parallel stiffness to the system. Adding external stiffness of 4.9 and 8.1 kN/m surprisingly failed to significantly change the stiffness of the ankle-plus-spring system. This suggests contributions from intrinsic muscle stiffness and reflex stiffness declined in response to added external stiffness. This could not be explained by load magnitudes, ankle postures, or co-activation as these were similar between the inertial and elastic loading conditions. However, non-linear parametric analyses suggest mean intrinsic stiffness of 35.5 kN/m and reflex gain of 11.6 kN/m with a constant reflex delay of 70 ms accurately described the empirical results. The phase response between the mechanical dynamics of the musculoskeletal system and delayed neuromotor feedback combine to provide robust control of system behavior.     

The inverted pendulum model of bipedal standing cannot be stabilized through direct feedback of force and contractile element length and velocity at realistic series elastic element stiffness

Control of bipedal standing is typically analyzed in the context of a single-segment inverted pendulum model. The stiffness K (SE) of the series elastic element that transmits the force generated by the contractile elements of the ankle plantarflexors to the skeletal system has been reported to be smaller in magnitude than the destabilizing gravitational stiffness K ( g ). In this study, we assess, in case K (SE) + K ( g ) < 0, if bipedal standing can be locally stable under direct feedback of contractile element length, contractile element velocity (both sensed by muscle spindles) and muscle force (sensed by Golgi tendon organs) to alpha-motoneuron activity. A theoretical analysis reveals that even though positive feedback of force may increase the stiffness of the muscle-tendon complex to values well over the destabilizing gravitational stiffness, dynamic instability makes it impossible to obtain locally stable standing under the conditions assumed.     

Invariance of ankle dynamic stiffness during fatiguing muscle contractions

Our objective was to determine the effect of muscle fatigue on the dynamic stiffness of the human ankle. Four subjects were required to maintain constant-force contractions of tibialis anterior until the required force could no longer be maintained. Repeated pseudo-random displacements of ankle angular position were applied throughout each contraction. The dynamic relation between ankle angular position and ankle torque was identified by determining non-parametric compliance impulse response functions (CIRFs). The CIRFs were redetermined every 2.55s throughout the sustained contractions to provide a quantitative measure of changes in ankle stiffness dynamics. Inspection of these CIRFs revealed little change in shape or magnitude throughout the contractions, despite large increases in tibialis anterior EMG. The dynamics were further quantified by estimating the equivalent joint inertia, viscosity and elasticity associated with each CIRF. As each contraction progressed, the inertial and elastic terms remained constant whereas the viscous term decreased slightly. These findings demonstrate that fatigue of tibialis anterior during sustained constant mean force contractions results in little change in the mechanical dynamics of the human ankle.     

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.

     

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.     

Prestress revealed by passive co-tension at the ankle joint

This study was designed to test the assumption that elastic tissues of the ankle are prestressed, by investigating the presence of simultaneous opposite passive elastic moments and thus, passive co-tension, at the ankle joint. A prestressed two-spring model used to generate qualitative predictions of the effects of stretching the posterior elastic structures of the ankle on the net passive moment of this joint was used. Twenty-seven healthy individuals were subjected to passive evaluation of the net elastic moment of the ankle in the sagittal plane, with the knee positioned at 90°, 60°, 30° and 0° of flexion, in order to change the length of the posterior biarticular elastic structures. The placement of the knee in the more extended positions caused changes in the net passive moment as predicted by the prestressed model. The ankle position in which the net passive moment was equal to zero was shifted to more plantar flexed positions (p<0.001) and there was a global increase in ankle stiffness since both passive dorsiflexion stiffness (p≤0.037) and passive plantar flexion stiffness (p≤0.029) increased. The normalized terminal plantar flexion stiffness also increased (p≤0.047), suggesting that biarticular posterior elastic structures are pre-strained and still under tension when the ankle is maximally plantar flexed and the knee is positioned at 60° of flexion. Resting positions were indicative of equilibrium between opposite passive elastic moments. The results revealed that there is passive co-tension at the ankle, demonstrating the existence of prestress in elastic structures of this joint.     

Leg stiffness can be maintained during reactive hopping despite modified acceleration conditions

AimThe aim of the present study was to evaluate reactive hops under systematically modified acceleration conditions. It was hypothesized that a high preactivity of the leg extensors and phase-specific adjustments of the leg muscle activation would compensate the alterations caused by the various acceleration levels in order to maintain a high leg stiffness, thus enabling the jumper to perform truly reactive jumps with short ground contact times despite the unaccustomed acceleration conditions.MethodsGround reaction forces (GRF), kinematic and electromyographic data of 20 healthy subjects were recorded during reactive hopping in a special sledge jump system for seven different acceleration levels: three acceleration levels with lower than normal gravity (0.7g, 0.8g, 0.9g), one with gravitational acceleration (1g) and three with higher acceleration (1.1g, 1.2g, 1.3g).ResultsThe increase of the acceleration from 0.7g to 1.3g had no significant effect on the preactivity of the leg extensors, the leg stiffness and the rate of force development. However, it resulted in increased peak GRF (+15%), longer ground contact time (+10%) and increased angular excursion at the ankle and knee joints (+3°).DiscussionThroughout a wide acceleration range, the subjects were able to maintain a high leg stiffness and perform reactive hops by keeping the preactivity constantly high and adjusting the muscle activity in the later phases. In consequence, it can be concluded that the neuromuscular system can cope with different acceleration levels, at least in the acceleration range used in this study.     

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.     

Walking and running at resonance

Humans and other animals can temporarily store mechanical energy in elastic oscillations, f(el), of body parts and in pendulum oscillations, f(p) = const sq.rt (g/L), of legs, length L, or other appendages, and thereby reduce the energy consumption of locomotion. However, energy saving only occurs if these oscillations are tuned to the leg propagation frequency f. It has long been known that f is tuned to the pendulum frequency of the free-swinging leg of walkers. During running the leg frequency increases to some new value f = f(r). We propose that in order to maintain resonance the animal, mass M, actively increases its leg pendulum frequency to the new value f(p,r) =const sq.rt (a(y)/L)=f(r), by giving its hips a vertical acceleration a(y)= F(y)/M. The pendulum frequency is increased if the impact force F(y) of the stance foot is larger than Mg, explaining the observation by Alexander and Bennet-Clark (1976) that F(v) becomes larger than Mg when animals start to run. Our model predictions of the running velocity U(r) as function of L, F(v), are in agreement with measurements of these quantities (Farley et al. 1993). The leg's longitudinal elastic oscillation frequency scales as f(el) = const sq.rt (k/M). Experiments by Ferris et al., (1998) show that runners adjust their leg's stiffness, k, when running on surfaces of different elasticity so that the total stiffness k remains constant. Our analysis of their data suggests that the longitudinal oscillations of the stance leg are indeed kept in tune with the running frequency. Therefore we conclude that humans, and by extension all animals, maintain resonance during running. Our model also predicts the Froude number of walking-running transitions, Fr = U(2)/gL approximately 0.5 in good agreement with measurements.     

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.     

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.     

Motor mechanisms of balance during quiet standing.

The purpose of this paper is to highlight the motor mechanisms involved in balance as the human, as a biped, continuously defends against gravitational and internal forces to maintain a safe posture. The search for these mechanisms needs precise and valid 3D measurements including both limbs plus valid biomechanical models. The literature shows the need for two force platforms to separate the mechanisms at the ankle and hip (load/unload mechanism). Also, precise measures ( approximately 0.03 mm) of markers on a multi-segment 3D bilateral model are required to record the minute trajectories of all segments and joints. The controlled variable, center-of-mass, is seen to be virtually in phase with the controlling variable, the center-of-pressure, which suggests a 0th order system where a simple series elastic spring could maintain balance. The first model involves a mass/spring/damper of medial/lateral balance: the stiffness was varied with stance width and the predicted sway from a spring controlled inverted pendulum closely matched the experimentally measured stiffness and sway. The second was a non-linear model of the plantarflexor series elastic elements which resulted in three closely validated predictions of anterior/posterior balance: the locus of the gravitational load line, the predicted ankle moment and the ankle stiffness at the operating point.     

Combining position and acceleration measurements for joint force estimation

The calculation of joint forces in biomechanics is usually based on the measurements of the kinematics of a given body segment, the estimation of the inertial properties of that segment and the solution of the ‘inverse dynamics problem’. Such a process results in estimates of the joint forces and moments needed to sustain the monitored motion. This paper presents a new approach that combines position and acceleration measurements for the purpose of deriving high-quality joint force estimates. An experimental system that is based on an instrumented compound pendulum was designed and tested. The joint forces necessary to maintain a swinging motion of the pendulum were measured by an array of strain gauges, and were compared to the forces estimated by the integrated kinematic segment that measured the position and acceleration of the pendulum. The joint force measurements were also compared to the force estimates that were based on the calculated segmental acceleration generated by the differentiation of the segmental position alone. The results show a high degree of correlation between the forces estimated by the integrated segment and those measured by the strain gauges. The force estimates based on the position measurements alone were less accurate and noisier. The application of the integrated segment to the study of human kinetics is discussed and illustrated by the ankle and knee forces during slow walking. The results suggest that the use of accelerometers is necessary for the estimation of transients and high-frequency components of joint forces.     

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.     

Correction of the inertial effect resulting from a plate moving under low-friction conditions

The purpose of the present study was to develop a set of equations that can be employed to remove the inertial effect introduced by the movable platform upon which a person stands during a slip induced in gait; this allows the real ground reaction force (GRF) and its center of pressure (COP) to be determined. Analyses were also performed to determine how sensitive the COP offsets were to the changes of the parameters in the equation that affected the correction of the inertial effect. In addition, the results were verified empirically using a low friction movable platform together with a stationary object, a pendulum, and human subjects during a slip induced during gait. Our analyses revealed that the amount of correction required for the inertial effect due to the movable component is affected by its mass and its center of mass (COM) position, acceleration, the friction coefficient, and the landing position of the foot relative to the COM. The maximum error in the horizontal component of the GRF was close to 0.09 (body weight) during the recovery from a slip in walking. When uncorrected, the maximum error in the COP measurement could reach as much as 4 cm. Finally, these errors were magnified in the joint-moment computation and propagated proximally, ranging from 0.2 to 1.0 Nm/body mass from the ankle to the hip.     

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.     

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

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

The effect of speed on leg stiffness and joint kinetics in human running

The goals of this study were to examine the following hypotheses: (a) there is a difference between the theoretically calculated (McMahon and Cheng, 1990. Journal of Biomechanics 23, 65-78) and the kinematically measured length changes of the spring-mass model and (b) the leg spring stiffness, the ankle spring stiffness and the knee spring stiffness are influenced by running speed. Thirteen athletes took part in this study. Force was measured using a "Kistler" force plate (1000 Hz). Kinematic data were recorded using two high-speed (120 Hz) video cameras. Each athlete completed trials running at five different velocities (approx. 2.5, 3.5, 4.5, 5.5 and 6.5 m/s). Running velocity influences the leg spring stiffness, the effective vertical spring stiffness and the spring stiffness at the knee joint. The spring stiffness at the ankle joint showed no statistical difference (p < 0.05) for the five velocities. The theoretically calculated length change of the spring-mass model significantly (p < 0.05) overestimated the actual length change. For running velocities up to 6.5 m/s the leg spring stiffness is influenced mostly by changes in stiffness at the knee joint.     

Human ankle joint stiffness over the full range of muscle activation levels

System identification techniques have been used to track changes in dynamic stiffness of the human ankle joint over a wide range of muscle contraction levels. Subjects lay supine on an experimental table with their left foot encased in a rigid, low-inertia cast which was fixed to an electro-hydraulic actuator operating as a position servo. Subjects generated tonic plantarflexor or dorsiflexor torques of different magnitudes ranging from rest to maximum voluntary contractions (MVC) during repeated presentations of a stochastic ankle angular position perturbation. Compliance impulse response functions (IRF) were determined from every 2.5 s perturbation sequence. The gain (G), natural frequency (omega n), and damping (zeta) parameters of the second-order model providing the best fit to each IRF were determined and used to compute the corresponding inertial (I), viscous (B) and elastic (K) stiffness parameters. The behaviour of these parameters with mean torque was found to follow two simple rules. First, the elastic parameter (K) increased in proportion to mean ankle torque as it was varied from rest to MVC; these changes were considerable involving increases of more than an order of magnitude. Second, the damping parameter (zeta) remained almost invariant over the entire range of contractions despite the dramatic changes in K.