An analysis of the rebound of the body in backward human running.

Step frequency and energy expenditure are greater in backward running than in forward running. The differences in the motion of the centre of mass of the body associated with these findings are not known. These differences were measured here on nine trained subjects during backward and forward running steps on a force platform at 3-17 km h(-1). In contrast to previous reports, we found that the maximal upward acceleration of the centre of mass and the aerial phase, averaged over the whole speed range, are greater in backward running than in forward running (15.7 versus 13.2 m s(-2), P=1.9×10(-6) and 0.098 versus 0.072 s, P=2.4×10(-5), respectively). Opposite to forward running, the impulse on the ground is directed more vertically during the push at the end of stance than during the brake at the beginning of stance. The higher step frequency in backward running is explained by a greater mass-specific vertical stiffness of the bouncing system (499 versus 352 s(-2), P=2.3×10(-11)) resulting in a shorter duration of the lower part of the vertical oscillation of the centre of mass when the force is greater than body weight, with a similar duration of the upper part when the force is lower than body weight. As in a catapult, muscle-tendon units are stretched more slowly during the brake at the beginning of stance and shorten more rapidly during the push at the end of stance. We suggest that the catapult-like mechanism of backward running, although requiring greater energy expenditure and not providing a smoother ride, may allow a safer stretch-shorten cycle of muscle-tendon units.

Running backwards: soft landing-hard takeoff, a less efficient rebound.

Human running at low and intermediate speeds is characterized by a greater average force exerted after 'landing', when muscle-tendon units are stretched ('hard landing'), and a lower average force exerted before 'takeoff', when muscle-tendon units shorten ('soft takeoff'). This landing-takeoff asymmetry is consistent with the force-velocity relation of the 'motor' (i.e. with the basic property of muscle to resist stretching with a force greater than that developed during shortening), but it may also be due to the 'machine' (e.g. to the asymmetric lever system of the foot operating during stance). Hard landing and soft takeoff-never the reverse-were found in running, hopping and trotting animals using diverse lever systems, suggesting that the different machines evolved to comply with the basic force-velocity relation of the motor. Here we measure the mechanical energy of the centre of mass of the body in backward running, an exercise where the normal coupling between motor and machine is voluntarily disrupted, in order to see the relevance of the motor-machine interplay in human running. We find that the landing-takeoff asymmetry is reversed. The resulting 'soft landing' and 'hard takeoff' are associated with a reduced efficiency of positive work production. We conclude that the landing-takeoff asymmetry found in running, hopping and trotting is the expression of a convenient interplay between motor and machine. More metabolic energy must be spent in the opposite case when muscle is forced to work against its basic property (i.e. when it must exert a greater force during shortening and a lower force during stretching).

Biomechanics of locomotion in Asian elephants.

Elephants are the biggest living terrestrial animal, weighing up to five tons and measuring up to three metres at the withers. These exceptional dimensions provide certain advantages (e.g. the mass-specific energetic cost of locomotion is decreased) but also disadvantages (e.g. forces are proportional to body volume while supportive tissue strength depends on their cross-sectional area, which makes elephants relatively more fragile than smaller animals). In order to understand better how body size affects gait mechanics the movement of the centre of mass (COM) of 34 Asian elephants (Elephas maximus) was studied over their entire speed range of 0.4-5.0 m s(-1) with force platforms. The mass-specific mechanical work required to maintain the movements of the COM per unit distance is approximately 0.2 J kg(-1) m(-1) (about 1/3 of the average of other animals ranging in size from a 35 g kangaroo rat to a 70 kg human). At low speeds this work is reduced by a pendulum-like exchange between the kinetic and potential energies of the COM, with a maximum energy exchange of approximately 60% at 1.4 m s(-1). At high speeds, elephants use a bouncing mechanism with little exchange between kinetic and potential energies of the COM, although without an aerial phase. Elephants increase speed while reducing the vertical oscillation of the COM from about 3 cm to 1 cm.

The bounce of the body in hopping, running and trotting: different machines with the same motor.

The bouncing mechanism of human running is characterized by a shorter duration of the brake after 'landing' compared with a longer duration of the push before 'takeoff'. This landing-takeoff asymmetry has been thought to be a consequence of the force-velocity relation of the muscle, resulting in a greater force exerted during stretching after landing and a lower force developed during shortening before takeoff. However, the asymmetric lever system of the human foot during stance may also be the cause. Here, we measure the landing-takeoff asymmetry in bouncing steps of running, hopping and trotting animals using diverse lever systems. We find that the duration of the push exceeds that of the brake in all the animals, indicating that the different lever systems comply with the basic property of muscle to resist stretching with a force greater than that developed during shortening. In addition, results show both the landing-takeoff asymmetry and the mass-specific vertical stiffness to be greater in small animals than in large animals. We suggest that the landing-takeoff asymmetry is an index of a lack of elasticity, which increases with increasing the role of muscle relative to that of tendon within muscle-tendon units.

The landing-take-off asymmetry of human running is enhanced in old age.

The landing-take-off asymmetry of running was thought to derive from, or at least to be consistent with, the physiological property of muscle to resist stretching (after landing) with a force greater than it can develop during shortening (before take-off). In old age, muscular force is reduced, but the deficit in force is less during stretching than during shortening. The greater loss in concentric versus eccentric strength with aging led us to hypothesize that older versus younger adults would increase the landing-take-off asymmetry in running. To test this hypothesis, we measured the within-step changes in mechanical energy of the centre of mass of the body in old and young subjects. The difference between the peaks in kinetic energy attained during the fall and during the lift of the centre of mass is greater in the old subjects. The difference between the time to lift and accelerate the centre of mass (positive work) and to absorb the same amount of energy during the downward displacement (negative work) is also greater in the old subjects. Both these findings imply a difference in force between stretching and shortening during the bounce, which is greater in the old subjects than in the young subjects. This is qualitatively consistent with the more asymmetric force-velocity relation found in aged muscle and supports, even if does not prove, the hypothesis that the landing-take-off asymmetry in running derives from the different response of muscle to stretching and shortening.

Old men running: mechanical work and elastic bounce.

It is known that muscular force is reduced in old age. We investigate what are the effects of this phenomenon on the mechanics of running. We hypothesized that the deficit in force would result in a lower push, causing reduced amplitude of the vertical oscillation, with smaller elastic energy storage and increased step frequency. To test this hypothesis, we measured the mechanical energy of the centre of mass of the body during running in old and young subjects. The amplitude of the oscillation is indeed reduced in the old subjects, resulting in an approximately 20% smaller elastic recovery and a greater step frequency (3.7 versus 2.8 Hz, p=1.9x10(-5), at 15-17 km h(-1)). Interestingly, the greater step frequency is due to a lower aerial time, and not to a greater natural frequency of the system, which is similar in old and young subjects (3.6 versus 3.4 Hz, p=0.2). Moreover, we find that in the old subjects, the step frequency is always similar to the natural frequency, even at the highest speeds. This is at variance with young subjects who adopt a step frequency lower than the natural frequency at high speeds, to contain the aerobic energy expenditure. Finally, the external work to maintain the motion of the centre of mass is reduced in the old subjects (0.9 versus 1.2 J kg(-1) m(-1), p=5.1x10(-6)) due to the lower work done against gravity, but the higher step frequency involves a greater internal work to reset the limbs at each step. The net result is that the total work increases with speed more steeply in the old subjects than in young subjects.

The landing-take-off asymmetry in human running.

In the elastic-like bounce of the body at each running step the muscle-tendon units are stretched after landing and recoil before take-off. For convenience, both the velocity of the centre of mass of the body at landing and take-off, and the characteristics of the muscle-tendon units during stretching and recoil, are usually assumed to be the same. The deviation from this symmetrical model has been determined here by measuring the mechanical energy changes of the centre of mass of the body within the running step using a force platform. During the aerial phase the fall is greater than the lift, and also in the absence of an aerial phase the transduction between gravitational potential energy and kinetic energy is greater during the downward displacement than during the lift. The peak of kinetic energy in the sagittal plane is attained thanks to gravity just prior to when the body starts to decelerate downwards during the negative work phase. In contrast, a lower peak of kinetic energy is attained, during the positive work phase, due to the muscular push continuing to accelerate the body forwards after the end of the acceleration upwards. Up to a speed of 14 km h(-1) the positive external work duration is greater than the negative external work duration, suggesting a contribution of muscle fibres to the length change of the muscle-tendon units. Above this speed, the two durations (<0.1 s) are similar, suggesting that the length change is almost totally due to stretch-recoil of the tendons with nearly isometrically contracting fibres.

Effect of an increase in gravity on the power output and the rebound of the body in human running.

The effect of an increase in gravity on the mechanics of running has been studied by using a force platform fixed to the floor of an aircraft undergoing flight profiles, resulting in a simulated gravity of 1.3 g. The power spent to maintain the motion of the centre of mass of the body is approximately 1.3 times greater than on Earth, due to a similar increase of both the power spent against gravity and to sustain the forward speed changes. This indicates that the average vertical displacement per unit distance and the average direction of the push are unchanged. The increase in power is mainly due to an increase in step frequency rather than to an increase in the work done at each step. The increase in step frequency in turn is mainly due to a decreased duration of the effective aerial phase (when the vertical force is less than body weight), rather than an increase in the stiffness of the bouncing system. The maximal speed where step frequency can match the resonant frequency of the bouncing system is increased by approximately 5 km h(-1) at 1.3 g. These results suggest a similar running mechanics at higher gravity, maintained at the expense of greater energy expenditure.

Pendular energy transduction within the step in human walking.

During walking, the centre of mass of the body moves like that of a 'square wheel': with each step cycle, some of its kinetic energy, E(k), is converted into gravitational potential energy, E(p), and then back into kinetic energy. To move the centre of mass, the locomotory muscles must supply only the power required to overcome the losses occurring during this energy transduction. African women carry loads of up to 20% of their body weight on the head without increasing their energy expenditure. This occurs as a result of an unexplained, more effective energy transduction between E(k) and E(p) than that of Europeans. In this study we measured the value of the E(k) to E(p) transduction at each instant in time during the step in African women and European subjects during level walking at 3.5-5.5 km h(-1), both unloaded and carrying loads spanning 20-30% of their body weight. A simulation of the changes in E(k) and E(p) during the step by sinusoidal curves was used for comparison. It was found that loading improves the transduction of E(p) to E(k) during the descent of the centre of mass. The improvement is not significant in European subjects, whereas it is highly significant in African women.

Energy transfer during stress relaxation of contracting frog muscle fibres.

1. A contracting muscle resists stretching with a force greater than the force it can exert at a constant length, T(o). If the muscle is kept active at the stretched length, the excess tension disappears, at first rapidly and then more slowly (stress relaxation). The present study is concerned with the first, fast tension decay. In particular, it is still debated if and to what extent the fast tension decay after a ramp stretch involves a conservation of the elastic energy stored during stretching into cross-bridge states of higher chemical energy. 2. Single muscle fibres of Rana temporaria and Rana esculenta were subjected to a short ramp stretch (approximately 15 nm per half-sarcomere at either 1.4 or 0.04 sarcomere lengths s(-1)) on the plateau of the force-length relation at temperatures of 4 and 14 degrees C. Immediately after the end of the stretch, or after discrete time intervals of fixed-end contraction and stress relaxation at the stretched length (Delta t(isom) = 0.5-300 ms), the fibre was released against a force ~T(o). Fibre and sarcomere stiffness during the elastic recoil to T(o) (phase 1) and the subsequent transient shortening against T(o) (phase 2), which is expression of the work enhancement by stretch, were measured after different Delta t(isom) and compared with the corresponding fast tension decay during Delta t(isom). 3. The amplitude of fast tension decay is large after the fast stretch, and small or nil after the slow stretch. Two exponential terms are necessary to fit the fast tension decay after the fast stretch at 4 degrees C, whereas one is sufficient in the other cases. The rate constant of the dominant exponential term (0.1-0.2 ms(-1) at 4 degrees C) increases with temperature with a temperature coefficient (Q(10)) of approximately 3. 4. After fast stretch, the fast tension decay during Delta t(isom) is accompanied in both species and at both temperatures by a corresponding increase in the amplitude of phase 2 shortening against T(o) after Delta t(isom): a maximum of approximately 5 nm per half-sarcomere is attained when the fast tension decay is almost complete, i.e. 30 ms after the stretch at 4 degrees C and 10 ms after the stretch at 14 degrees C. After slow stretch, when fast tension decay is small or nil, the increase in phase 2 shortening is negligible. 5. The increase in phase 2 work during fast tension decay (Delta W(out)) is a constant fraction of the elastic energy simultaneously set free by the recoil of the undamped elastic elements. 6. Delta W(out) is accompanied by a decrease in stiffness, indicating that it is not due to a greater number of cross-bridges. 7. It is concluded that, during the fast tension decay following a fast ramp stretch, a transfer of energy occurs from the undamped elastic elements to damped elements within the sarcomeres by a temperature-dependent mechanism with a dominant rate constant consistent with the theory proposed by A. F. Huxley and R. M. Simmons in 1971.

Mechanical power and efficiency in running children.

The effect of age and body size on the total mechanical power output (Wtot) during running was studied in children of 3-12 years of age and in adults. Wtot was measured as the sum of the power required to move the body's centre-of-mass relative to the surroundings (the "external power", Wext) plus the power required to move the limbs relative to the body's centre-of-mass (the "internal power", Wint). At low and intermediate speeds (less than about 13 km h-1) the higher step frequency used by young children resulted in a decrease of up to 40-50% in the mass-specific external power and an equal increase in the mass-specific internal power relative to adults. Due to this crossed effect, the mass-specific Wtot is nearly independent of age. At high speeds the mass-specific Wtot is 20-30% larger in young children than in adults, due to a greater forward deceleration of the centre-of-mass at each step. The efficiency of positive work production, calculated as the positive mechanical power divided by the net energy consumption rate, appears to be similar in children and adults (i.e. 0.40-0.55).

The role of gravity in human walking: pendular energy exchange, external work and optimal speed.

During walking on Earth, at 1.0 g of gravity, the work done by the muscles to maintain the motion of the centre of mass of the body (W(ext)) is reduced by a pendulum-like exchange between gravitational potential energy and kinetic energy. The weight-specific W(ext) per unit distance attains a minimum of 0.3 J x kg(-1) x m(-1) at about 4.5 km x h(-1) in adults. The effect of a gravity change has been studied during walking on a force platform fixed to the floor of an aircraft undergoing flight profiles which resulted in a simulated gravity of 0.4 and 1.5 times that on Earth. At 0.4 g, such as on Mars, the minimum W(ext) was 0.15 J x kg(-1) x m(-1), half that on Earth and occurred at a slower speed, about 2.5 km x h(-1). The range of walking speeds is about half that on Earth. At 1.5 g, the lowest value of W(ext) was 0.60 J x kg(-1) x m(-1), twice that on Earth; it was nearly constant up to about 4.3 km x h(-1) and then increased with speed. The range of walking speeds is probably greater than that on Earth. A model is presented in which the speed for an optimum exchange between potential and kinetic energy, the 'optimal speed', is predicted by the balance between the forward deceleration due to the lift of the body against gravity and the forward deceleration due to the impact against the ground. In conclusion, over the range studied, gravity increases the work required to walk, but it also increases the range of walking speeds.

Effect of stretching on undamped elasticity in muscle fibres from Rana temporaria.

Muscle stiffness was measured from the undamped elastic recoil taking place when the force attained during ramp stretches of muscle fibres, tetanized on the plateau of the tension-length relation, was suddenly reduced to the isometric value developed before the stretch, T0. Sarcomere elastic recoil was measured on a tendon-free segment of the fibre by means of a striation follower. After small ramp stretches, stiffness increases to a value 1.33x greater than that measured during release from a state of isometric contraction to 0.9 T0. While the relative increase in stiffness is equal to that reported for fibres of Rana esculenta (Piazzesi et al., 1992), the absolute value of stiffness measured during release from isometric contraction is just over half. As stretch amplitude is increased, on the plateau of the force-length relation, stiffness decreases toward the isometric value. This finding shows that the decrease in stiffness with large stretches cannot be due to a decrease in myofilament overlap (as may be the case when stretching occurs on the descending limb of the tension-length relation, Sugi & Tsuchiya, 1988), but must be due to an effect of the ramp stretch per se. For a given stretch amplitude, the after-stretch transient shortening against T0 taking place after the elastic recoil (which is expression of the work enhancement induced by stretching, Cavagna et al., 1986, 1994) is similar in fibres with very different stiffness of their undamped elastic elements. This suggests that this work enhancement is not due to the recoil of damped elastic structures recruited during stretching because of sarcomere length inhomogenity, a condition which would result in a decrease in stiffness (Morgan et al., 1996).

The mechanics of running in children.

1. The effect of age and body size on the bouncing mechanism of running was studied in children aged 2-16 years. 2. The natural frequency of the bouncing system (fs) and the external work required to move the centre of mass of the body were measured using a force platform. 3. At all ages, during running below approximately 11 km h-1, the freely chosen step frequency (f) is about equal to fs (symmetric rebound), independent of speed, although it decreases with age from 4 Hz at 2 years to 2.5 Hz above 12 years. 4. The decrease of step frequency with age is associated with a decrease in the mass-specific vertical stiffness of the bouncing system (k/m) due to an increase of the body mass (m) with a constant stiffness (k). Above 12 years, k/m and f remain approximately constant due to a parallel increase in both k and m with age. 5. Above the critical speed of approximately 11 km h-1, independent of age, the rebound becomes asymmetric, i.e. f < fs. 6. The maximum running speed (Vf, max) increases with age while the step frequency at remains constant (approximately 4 Hz), independent of age. 7. At a given speed, the higher step frequency in preteens results in a mass-specific power against gravity less than that in adults. The external power required to move the centre of mass of the body is correspondingly reduced.

Muscle work enhancement by stretch. Passive visco-elasticity or cross-bridges?

Tetanized frog muscle fibres subjected to ramp stretches on the plateau of the tension-length relation, followed by an isotonic release against a load equal to the maximum isometric tension (T0), exhibit a well defined transient shortening against T0 which was attributed to the release of mechanical energy stored during stretching within the damped element of the cross-bridges. However, this interpretation has recently been challenged, and 'transient shortening against T0' has instead been attributed to elastic elements strained because of non-uniform distribution of lengthening within the fibre volume. The 'excess length change', resulting from the recoil of these elastic elements, was found i) to increase continuously with stretch amplitude up to 50 nm per h.s. with a 100 nm per h.s. strain, ii) to decrease steadily with the decrease in force during stress relaxation after the ramp stretch, and iii) to increase on the descending limb of the tension-length relation where sarcomere inhomogeneity is greater. In contrast, the transient shortening against T0: i) reaches a plateau at 8 nm per half sarcomere after about 50 nm per half sarcomere strain, ii) remains constant during the temperature dependent, fast phase of stress relaxation, when the excess in force above isometric reduces to about one half, iii) also occurs on the ascending limb of the tension-length relation where sarcomere inhomogeneity is drastically reduced. As a consequence of these differences we conclude that transient shortening and 'excess length change' do not "reflect the same underlying process".

The resonant step frequency in human running.

At running speeds less than about 13 km h-1 the freely chosen step frequency (ffree) is lower than the frequency at which the mechanical power is minimized (fmin). This dissociation between ffree and fmin was investigated by measuring mechanical power, metabolic energy expenditure and apparent natural frequency of the body's bouncing system (fsist) during running at three given speeds with different step frequencies. The ffree requires a mechanical power greater than that at fmin mainly due to a larger vertical oscillation of the body at each step. Energy expenditure is minimal and the mechanical efficiency is maximal at ffree. At a given speed, an increase in step frequency above ffree results in an increase in energy expenditure despite a decrease in mechanical power. On the other hand, a decrease in step frequency below ffree results in a larger increase in energy expenditure associated with an increase in mechanical power. When the step frequency is forced to values above or below ffree, fsist is forced to change similarly by adjusting the stiffness of the bouncing system. However the best match between fsist and step frequency takes place only in proximity of ffree (2. 6-2.8 Hz). It is concluded that during running at speeds less than 13 km h-1 energy is saved by tuning step frequency to fsist, even if this requires a mechanical power larger than necessary.

Energy-saving gait mechanics with head-supported loads.

In many areas of the world that lack a transportation infrastructure, people routinely carry extraordinary loads supported by their heads, for example the Sherpa of the Himalayas and the women of East Africa. It has previously been shown that African women from the Kikuyu and Luo tribes can carry loads substantially more cheaply than army recruits; however, the mechanism for their economy has remained unknown. Here we investigate, using a force platform, the mechanics of carrying head-supported loads by Kikuyu and Luo women. The weight-specific mechanical work, required to maintain the motion of the common centre of mass of the body and load, decreases with load in the African women, whereas it increases in control subjects. The decrease in work by the African women is a result of a greater conservation of mechanical energy resulting from an improved pendulum-like transfer of energy during each step, back and forth between gravitational potential energy and kinetic energy of the centre of mass.

External, internal and total work in human locomotion.

The muscle-tendon work performed during locomotion can, in principle, be measured from the mechanical energy of the centre of mass of the whole body and the kinetic energy due to the movements of the body segments relative to the centre of mass of the body. Problems arise when calculating the muscle-tendon work from increases in mechanical energy, largely in correctly attributing these increases either to energy transfer or to muscle-tendon work. In this study, the kinetic and gravitational potential energy of the centre of mass of the whole human body was measured (using a force platform) simultaneously with calculation of the kinetic and potential energy of the body segments due to their movements relative to the body centre of mass (using cinematography) at different speeds of walking and running. Upper and lower boundaries to the total work were determined by including or excluding possible energy transfers between the segments of each limb, between the limbs and between the centre of mass of the body and the limbs. It appears that the muscle-tendon work of locomotion is most accurately measured when energy transfers are only included between segments of the same limb, but not among the limbs or between the limbs and the centre of mass of the whole body.

Storage and release of mechanical energy by contracting frog muscle fibres.

1. Stretching a contracting muscle leads to greater mechanical work being done during subsequent shortening by its contractile component; the mechanism of this enhancement is not known. 2. This mechanism has been investigated here by subjecting tetanized frog muscle fibres to ramp stretches followed by an isotonic release against a load equal to the maximum isometric tension, T(o). Shortening against T(o) was taken as direct evidence of an absolute increase in the ability to do work as a consequence of the previous stretch. 3. Ramp stretches (0.5-8.6% sarcomere strain, confined to the plateau of the isometric tension-length relationship) were given at different velocities of lengthening (0.03-1.8 sarcomere lengths s-1). Isotonic release to T(o) took place immediately after the end of the ramp, or 5-800 ms after the end of the largest ramp stretches. The length changes taking place after release were measured both at the fibre end and on a tendon-free segment of the fibre. The experiments were carried out at 4 and 14 degrees C. 4. After the elastic recoil of the undamped elastic elements, taking place during the fall in tension at the instant of the isotonic release, a well-defined shortening took place against T(o) (transient shortening against T(o)). 5. The amplitude and time course of transient shortening against T(o) were similar at the fibre end and in the segment, indicating that it is due to a properly of the sarcomeres and not due to stress relaxation of the tendons. 6. Transient shortening against T(o) increased with sarcomere stretch amplitude up to about 8 nm per half-sarcomere independent of stretch velocity. 7. When a short delay (5-20 ms) was introduced between the end of the stretch and the isotonic release, the transient shortening against T(o) did not change; after longer time delays, the transient shortening against T(o) decreased in amplitude. 8. The velocity of transient shortening against T(o) increased with temperature with a temperature coefficient, Q10, of approximately 2.5. 9. It is suggested that transient shortening against T(o) results from the release of mechanical energy stored within the damped element of the cross-bridges. The cross-bridges are brought into a state of greater potential energy not only during the ramp stretch, but also immediately afterwards, during the first phase of stress relaxation.