Positive force feedback in bouncing gaits?

During bouncing gaits (running, hopping, trotting), passive compliant structures (e.g. tendons, ligaments) store and release part of the stride energy. Here, active muscles must provide the required force to withstand the developing tendon strain and to compensate for the inevitable energy losses. This requires an appropriate control of muscle activation. In this study, for hopping, the potential involvement of afferent information from muscle receptors (muscle spindles, Golgi tendon organs) is investigated using a two-segment leg model with one extensor muscle. It is found that: (i) positive feedbacks of muscle-fibre length and muscle force can result in periodic bouncing; (ii) positive force feedback (F+) stabilizes bouncing patterns within a large range of stride energies (maximum hopping height of 16.3 cm, almost twofold higher than the length feedback); and (iii) when employing this reflex scheme, for moderate hopping heights (up to 8.8 cm), an overall elastic leg behaviour is predicted (hopping frequency of 1.4-3 Hz, leg stiffness of 9-27 kN m(-1)). Furthermore, F+ could stabilize running. It is suggested that, during the stance phase of bouncing tasks, the reflex-generated motor control based on feedbacks might be an efficient and reliable alternative to central motor commands.     

Gender differences in active musculoskeletal stiffness. Part II. Quantification of leg stiffness during functional hopping tasks.

Leg stiffness was compared between age-matched males and females during hopping at preferred and controlled frequencies. Stiffness was defined as the linear regression slope between the vertical center of mass (COM) displacement and ground-reaction forces recorded from a force plate during the stance phase of the hopping task. Results demonstrate that subjects modulated the vertical displacement of the COM during ground contact in relation to the square of hopping frequency. This supports the accuracy of the spring-mass oscillator as a representative model of hopping. It also maintained peak vertical ground-reaction load at approximately three times body weight. Leg stiffness values in males (33.9+/-8.7 kN/m) were significantly (p<0.01) greater than in females (26.3+/-6.5 kN/m) at each of three hopping frequencies, 3.0, 2.5 Hz, and a preferred hopping rate. In the spring-mass oscillator model leg stiffness and body mass are related to the frequency of motion. Thus male subjects necessarily recruited greater leg stiffness to drive their heavier body mass at the same frequency as the lighter female subjects during the controlled frequency trials. However, in the preferred hopping condition the stiffness was not constrained by the task because frequency was self-selected. Nonetheless, both male and female subjects hopped at statistically similar preferred frequencies (2.34+/-0.22 Hz), therefore, the females continued to demonstrate less leg stiffness. Recognizing the active muscle stiffness contributes to biomechanical stability as well as leg stiffness, these results may provide insight into the gender bias in risk of musculoskeletal knee injury.     

Leg stiffness 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.     

Energy absorption as a predictor of leg impedance in highly trained females

Although leg spring stiffness represents active muscular recruitment of the lower extremity during dynamic tasks such as hopping and running, the joint-specific characteristics comprising the damping portion of this measure, leg impedance, are uncertain. The purpose of this investigation was to assess the relationship between leg impedance and energy absorption at the ankle, knee, and hip during early (impact) and late (stabilization) phases of landing. Twenty highly trained female dancers (age = 20.3 +/- 1.4 years, height = 163.7 +/- 6.0 cm, mass = 62.1 +/- 8.1 kg) were instrumented for biomechanical analysis. Subjects performed three sets of double-leg landings from under preferred, stiff, and soft landing conditions. A stepwise linear regression analysis revealed that ankle and knee energy absorption at impact, and knee and hip energy absorption during the stabilization phases of landing explained 75.5% of the variance in leg impedance. The primary predictor of leg impedance was knee energy absorption during the stabilization phase, independently accounting for 55% of the variance. Future validation studies applying this regression model to other groups of individuals are warranted.     

Age-related differences in the neural regulation of stretch-shortening cycle activities in male youths during maximal and sub-maximal hopping

The aim of the current study was to investigate potential age-related differences in neural regulation strategies during maximal and sub-maximal hopping. Thirty-two boys from three different age groups (9-, 12- and 15-years), completed trials of both maximal and sub maximal hopping, and based on contact and flight times, measures of reactive strength index (RSI = jump height/contact time) and leg stiffness (peak ground reaction force/peak displacement of centre of mass) were collected respectively. During all trials, surface electromyograms (EMG) were recorded from four different muscle sites of the dominant lower limb, during 100 ms pre-ground contact, and then four subsequent stretch reflex phases: background muscle activity (0-30 ms), short-latency stretch reflex (31-60 ms), intermediate15 latency stretch reflex 61-90 ms and long-latency stretch reflex (91-120 ms). Reactive strength index and leg stiffness were measured during the hopping trials. During maximal hopping, both 12- and 15-year olds produced significantly greater RSI (P < 0.02) than 9-year olds, with 15-year olds utilising significantly greater soleus muscle activity during the 100 ms prior to ground contact than the younger age groups (P < 0.01). During sub-maximal hopping, 15-year olds produced significantly greater absolute leg stiffness than both 12- and 9-year olds (P < 0.01), with 9-year olds producing significantly less soleus muscle activity during the 31-60 ms time phase. For all age groups, sub-maximal hopping was associated with significantly greater background muscle activity and short-latency stretch reflex activity in the soleus and vastus lateralis, when compared to maximal hopping (P < 0.001). Results suggest that as children mature, they become more reliant on supra-spinal feed forward input and short latency stretch reflexes to regulate greater levels of leg stiffness and RSI when hopping.     

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

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

Muscle pre- and coactivity during downward stepping are associated with leg stiffness in aging.

We have previously reported that elderly compared to young women executed downward stepping with substantially greater leg stiffness. Because antagonist muscle coactivity increases joint stiffness we hypothesized that increased leg stiffness in aging is associated with increased muscle coactivity. We also explored the possibility that the magnitude of the preparatory muscle activity preceding impact also differed between young and old subjects. Young (n=11, 20. 8 yr) and old (n=12, 69 yr) women performed downward stepping from a platform set at 20% body height. The leg was modeled as a simple mass-spring system. From video and ground reaction force data leg stiffness was computed as the ratio of force under the foot and the linear shortening of the limb. EMG activity of the vastus lateralis, biceps femoris, gastrocnemius lateralis, and tibialis anterior were recorded with a telemetric system. Elders compared to young subjects had 64% greater leg stiffness during downward stepping. Muscle activity over a 200-ms period preceding touch down was 136% greater in elderly than in young subjects. Biceps femoris and tibialis anterior coactivity during ground contact was 120% greater in the elders. Muscle pre- and coactivity, respectively, accounted for about 50% of the variance in leg stiffness. In conclusion, elderly people elevate muscle pre- and coactivity during downward stepping to stiffen the leg in compensation for impaired neuromotor functions.     

Muscle force and power in obese and overweight children

The study investigated differences in skeletal muscle function between obese and non-obese children using a force platform. Forty obese children and adolescents (age range 8 to 18 years; 21 girls) and 40 age- and sex-matched controls performed two tests: (1) single two-legged jump, a countermovement jump for maximal height; (2) multiple one-legged hopping on the forefoot, a test of maximal force. In the single two-legged jump, obese subjects had higher absolute peak force (1.62 kN vs 1.09 kN) and peak power (2.46 kW vs 2.06 kW), but lower body weight-related peak force (2.10 vs 2.33) and lower peak power per body mass (30.9 W/kg vs 41.6 W/kg). Jump height (29.3 cm vs 37.5 cm) and maximal vertical velocity (1.92 ms(-1) vs 2.31 ms(-1)) were reduced in obese children. In multiple one-legged hopping, obese subjects had 72% and 84% higher absolute peak force on the left and right foot, respectively. However, forces relative to body weight were 24% and 23% lower in the obese group than in the control group. In conclusion, obese children and adolescents have increased muscle force and power. This partly compensates for the effect of high body weight on muscle performance.     

The mechanics of hopping by kangaroos (Macropodidae)

Force platform records and films have been made of kangaroos and a wallaby hopping.
The maximum forces exerted on the ground were about six times body weight. The force exerted on the ground changes direction, throughout the period when the feet are on the ground, so that it is always more or less in line with the centre of mass. Consequently the animal decelerates a little and then accelerates again, during the contact phase.
The fluctuations of potential energy which occur in each hop are slightly smaller at high speeds than at low ones. Fluctuations of external kinetic energy increase with speed and account for most of the energy cost of hopping at high speeds. Fluctuations of internal kinetic energy (due to acceleration and deceleration of the limbs) are relatively small. While the feet are on the ground the extensor muscles of the hip do positive work, those of the knee negative work and those of the ankle negative work followed by positive work. The energy cost of hopping is reduced substantially by elastic storage of energy in the Achilles tendon. In the case of a wallaby hopping at moderate speed the calculated saving was 40%. The maximum stresses developed in leg muscles, tendons and the tibia have been calculated and are discussed in relation to the known properties of muscle, tendon and bone. The trunk pitches as the animal hops because the two legs swing forwards and back simultaneously. Appropriate tail movements reduce, but do not eliminate, this effect. A mathematical theory of hopping is presented and used to investigate the merits of different hopping techniques.
Dawson & Taylor's (1973) discovery that the rate of oxygen consumption of kangaroos decreases a little, as hopping speed increases, is probably to be explained by the increased role of elastic storage of energy at high speeds.     

Neuromuscular changes for hopping on a range of damped surfaces.

Humans hopping and running on elastic and damped surfaces maintain similar center-of-mass dynamics by adjusting stance leg mechanics. We tested the hypothesis that the leg transitions from acting like an energy-conserving spring on elastic surfaces to a power-producing actuator on damped surfaces during hopping due to changes in ankle mechanics. To test this hypothesis, we collected surface electromyography, video kinematics, and ground reaction force while eight male subjects (body mass: 76.2 +/- 1.7 kg) hopped in place on a range of damped surfaces. On the most damped surface, most of the mechanical work done by the leg appeared at the ankle (52%), whereas 23 and 25% appeared at the knee and hip, respectively. Hoppers extended all three joints during takeoff further than they flexed during landing and thereby did more net positive work on more heavily damped surfaces. Also, all three joints reached peak flexion sooner after touchdown on more heavily damped surfaces. Consequently, peak moment occurred during joint extension rather than at peak flexion as on elastic surfaces. These strategies caused the positive work during extension to exceed the negative work during flexion to a greater extent on more heavily damped surfaces. At the muscle level, surface EMG increased by 50-440% in ankle and knee extensors as surface damping increased to compensate for greater surface energy dissipation. Our findings, and those of previous studies of hopping on elastic surfaces, show that the ankle joint is the key determinant of both springlike and actuator-like leg mechanics during hopping in place.     

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.     

Energy management that generates terrain following versus apex-preserving hopping in man and machine

While hopping, 12 subjects experienced a sudden step down of 5 or 10 cm. Results revealed that the hopping style was “terrain following”. It means that the subjects pursued to keep the distance between maximum hopping height (apex) and ground profile constant. The spring-loaded inverse pendulum (SLIP) model, however, which is currently considered as template for stable legged locomotion would predict apex-preserving hopping, by which the absolute maximal hopping height is kept constant regardless of changes of the ground level. To get more insight into the physics of hopping, we outlined two concepts of energy management: “constant energy supply”, by which in each bounce—regardless of perturbations—the same amount of mechanical energy is injected, and “lost energy supply”, by which the mechanical energy that is going to be dissipated in the current cycle is assessed and replenished. When tested by simulations and on a robot testbed capable of hopping, constant energy supply generated stable and robust terrain following hopping, whereas lost energy supply led to something like apex-preserving hopping, which, however, lacks stability as well as robustness. Comparing simulated and machine hopping with human hopping suggests that constant energy supply has a good chance to be used by humans to generate hopping.     

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.     

Positive work as a function of eccentric load in maximal leg extension movements

Negative and positive work performed during leg extension movements of 53 well trained subjects was measured with the help of a special dynamometer. The subjects performed four maximal push off trials against five different loads (25-105 kg): two two-legged extensions from a squatting position (SM) with a knee angle of 70 degrees and two trials with a preliminary counter movement (CM) but with the same extension range as in the SM. Positive work differed only by about 4% between CM and SM in spite of large differences in initial forces at the onset of concentric contraction. Based on simulations, it is suggested that in CM the advantage of stored elastic energy can almost completely be nullified by the disadvantage of a limited shortening distance of the contractile elements. It is hypothesised that elastic energy in CM can only cause considerable extra work during concentric contraction compared to the maximal positive work done in SM if the total range of lengthening and shortening of the muscle(s) involved is larger in CM than in SM.     

Vertical stiffness during one-legged hopping with and without using a running-specific prosthesis

Although athletes with unilateral below-the-knee amputations (BKAs) generally use their affected leg, including their prosthesis, as their take-off leg for the long jump, little is known about the spring-like leg behavior and stiffness regulation of the affected leg. The purpose of this study was to investigate vertical stiffness during one-legged hopping in an elite-level long jump athlete with a unilateral BKA. We used the spring-mass model to calculate vertical stiffness, which equals the ratio of maximum vertical ground reaction force to maximum center of mass displacement, while the athlete with a BKA hopped on one leg at a range of frequencies. Then, we compared the vertical stiffness of this athlete to seven non-amputee elite-level long-jumpers. We found that from 1.8 to 3.4 Hz, the vertical stiffness of the unaffected leg for an athlete with a BKA increases with faster hopping frequencies, but the vertical stiffness of the affected leg remains nearly constant across frequencies. The athlete with a BKA attained the desired hopping frequencies at 2.2 and 2.6 Hz, but was unable to match the lowest (1.8 Hz) and two highest frequencies (3.0 and 3.4 Hz) using his affected leg. We also found that at 2.5 Hz, unaffected leg vertical stiffness was 15% greater than affected leg vertical stiffness, and the vertical stiffness of non-amputee long-jumpers was 32% greater than the affected leg vertical stiffness of an athlete with a BKA. The results of the present study suggest that the vertical stiffness regulation strategy of an athlete with a unilateral BKA is not the same in the unaffected versus affected legs, and compared to non-amputees.     

Influence of training background on jumping height

The aim of this study was to compare the pattern of force production and center of mass kinematics in maximal vertical jump performance between power athletes, recreational bodybuilders, and physically active subjects. Twenty-seven healthy male subjects (age: 24.5 +/- 4.3 years, height: 178.7 +/- 15.2 cm, and weight: 81.9 +/- 12.7 kg) with distinct training backgrounds were divided into 3 groups: power track athletes (PT, n = 10) with international experience, recreational bodybuilders (BB, n = 7) with at least 2 years of training experience, and physically active subjects (PA, n = 10). Subjects performed a 1 repetition maximum (1RM) leg press test and 5 countermovement jumps with no instructions regarding jumping technique. The power-trained group jumped significantly higher (p < 0.05) than the BB and PA groups (0.40 +/- 0.05, 0.31 +/- 0.04, and 0.30 +/- 0.05, respectively). The difference in jumping height was not produced by higher rates of force development (RFD) and shorter center of mass (CM) displacement. Instead, the PT group had greater CM excursion (p < 0.05) than the other groups. The PT and BB groups had a high correlation between jumping height and 1RM test (r = 0.93 and r = 0.89, p < 0.05, respectively). In conclusion, maximum strength seems to be important for jumping height, but RFD does not seem relevant to achieve maximum jumping heights. High RFD jumps should be performed during training only when sport skills have a time constraint for force application.     

Compensation in resting metabolism for experimentally increased activity

To study zebra finch allocation of energy to day and night at two different workloads, we assessed the daily energy turnover from: (1) metabolizable energy of the food, and (2) doubly-labeled water. In both experiments we imposed two levels of activity on captive zebra finches (Taeniopygia guttata), by applying different computer-controlled workload schedules. A low workload required 20 hops, and a high workload 40 hops to obtain 10 s access to food. In experiment 1, we further measured nocturnal energy expenditure by overnight oxygen consumption. From experiment 2 we derived an estimate of the costs of hopping activity, from inter-individual association of daily amount of hopping and daily energy expenditure. Surprisingly, the daily energy budget was, on average, reduced slightly when birds were subjected to a high workload. Since hopping activity was 50% higher during the high workload than during the low workload, the birds apparently compensated, even over-compensated, for the increased energetic demands of activity. Nocturnal energy expenditure was indeed reduced for the high workload, which was largely due to a reduction in resting metabolic rate. Economizing on energy was more than could have been accomplished by a reduction in mass alone, and we discuss the occurrence and potential mechanisms of physiological compensation. The amount of energy saved during the night did account for part of the total amount of energy saved. We surmise that the strategy of energetic compensation observed during the night was extended into the inactive hours of the day. Accepted: 10 July 1998     

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.