Kinematics and mechanical changes with step frequency at different running speeds

PURPOSE

Running at a given speed can be achieved by taking large steps at a low frequency or on the contrary by taking small steps at a high frequency. The consequences of a change in step frequency, at a fixed speed, affects the stiffness of the lower limb differently. In this study, we compared the running mechanics and kinematics at different imposed step frequencies (from 2 step s-1 to 3.6 step s-1) to understand the relationship between kinematic and kinetic parameters.

METHODS

Eight recreational male runners ran on a treadmill at 5 different speeds and 5 different step frequencies. The lower-limb segment motion and the ground reaction forces were recorded. Mechanical powers, general gait parameters, lower-limb movements and coordination were investigated.

RESULTS

At low step frequencies, in order to limit the magnitude of the ground reaction force, the vertical stiffness is reduced and thus runners deviate from an elastic rebound. At high step frequencies, the stiffness is increased and the elastic rebound is optimised in its ability to absorb and restore energy during the contact phase.

CONCLUSION

We studied the consequences of a change in step frequency on the bouncing mechanics of running. We showed that the lower limb stiffness and the intersegmental coordination of the lower-limb segments are affected by running step frequency rather than speed. The runner rather adapts their lower limb stiffness to match a step frequency for a given speed than the opposite.

Postural control in the elephant

As the largest extant legged animals, elephants arguably face the most extreme challenge for stable standing. In this study, we investigated the displacement of the centre of pressure of 12 elephants during quiet standing. We found that the average amplitude of the oscillations in the lateral and fore-aft directions was less than 1.5 cm. Such amplitudes for postural oscillation are comparable with those of dogs and other species, suggesting that some aspects of sensorimotor postural control do not scale with size.

Differential activation of lumbar and sacral motor pools during walking at different speeds and slopes

Organization of spinal motor output has become of interest for investigating differential activation of lumbar and sacral motor pools during locomotor tasks. Motor pools are associated with functional grouping of motoneurons of the lower limb muscles. Here we examined how the spatiotemporal organization of lumbar and sacral motor pool activity during walking is orchestrated with slope of terrain and speed of progression. Ten subjects walked on an instrumented treadmill at different slopes and imposed speeds. Kinetics, kinematics, and electromyography of 16 lower limb muscles were recorded. The spinal locomotor output was assessed by decomposing the coordinated muscle activation profiles into a small set of common factors and by mapping them onto the rostrocaudal location of the motoneuron pools. Our results show that lumbar and sacral motor pool activity depend on slope and speed. Compared with level walking, sacral motor pools decrease their activity at negative slopes and increase at positive slopes, whereas lumbar motor pools increase their engagement when both positive and negative slope increase. These findings are consistent with a differential involvement of the lumbar and the sacral motor pools in relation to changes in positive and negative center of body mass mechanical power production due to slope and speed.NEW & NOTEWORTHY In this study, the spatiotemporal maps of motoneuron activity in the spinal cord were assessed during walking at different slopes and speeds. We found differential involvement of lumbar and sacral motor pools in relation to changes in positive and negative center of body mass power production due to slope and speed. The results are consistent with recent findings about the specialization of neuronal networks located at different segments of the spinal cord for performing specific locomotor tasks.

Effect of walking speed on the intersegmental coordination of lower-limb segments in elderly adults

BACKGROUND

Ageing brings profound changes in walking gait. For example, older adults reduce the modification of pelvic and trunk kinematics with walking speed. However, the modification of the coordination between lower-limb segments with age has never been investigated across various controlled speeds.

RESEARCH QUESTION

Is the effect of speed on the intersegmental coordination different between elderly and young adults?

METHODS

Nineteen senior and eight young adults walked on a treadmill at speeds ranging from 0.56 to 1.94 m s^-1. The motion of the lower-limb segments in the sagittal plane was recorded by cinematography. When the angles of the thigh, shank and foot during a stride are plotted one versus the other, they describe loops constraint on a plane. The coordination between lower-limb segments was thus evaluated by performing a principal component analysis between the thigh, shank and foot elevation angles. The effect of speed and age on the intersegmental coordination was examined using a two-level linear mixed model ANOVA.

RESULTS

In both age groups the orientation of the plane changes with speed, due to a more in-phase shank and foot motion. However, the effect of speed on the covariation plane is lessened with age.

SIGNIFICANCE

Our results demonstrate that there is an age-related specific adjustment of the intersegmental coordination to speed. In particular, older adults restrict their repertoire of angular segment motion. These differences in coordination are mainly related to different foot-shank coordination.

Kinematic patterns while walking on a slope at different speeds

During walking, the elevation angles of the thigh, shank, and foot (i.e., the angle between the segment and the vertical) covary along a characteristic loop constrained on a plane. Here, we investigate how the shape of the loop and the orientation of the plane, which reflect the intersegmental coordination, change with the slope of the terrain and the speed of progression. Ten subjects walked on an inclined treadmill at different slopes (between -9° and +9°) and speeds (from 0.56 to 2.22 m/s). A principal component analysis was performed on the covariance matrix of the thigh, shank, and foot elevation angles. At each slope and speed, the variance accounted for by the two principal components was >99%, indicating that the planar covariation is maintained. The two principal components can be associated to the limb orientation (PC1*) and the limb length (PC2*). At low walking speeds, changes in the intersegmental coordination across slopes are characterized mainly by a change in the orientation of the covariation plane and in PC2* and to a lesser extent, by a change in PC1*. As speed increases, changes in the intersegmental coordination across slopes are more related to a change in PC1 *, with limited changes in the orientation of the plane and in PC 2*. Our results show that the kinematic patterns highly depend on both slope and speed. NEW & NOTEWORTHY In this paper, changes in the lower-limb intersegmental coordination during walking with slope and speed are linked to changes in the trajectory of the body center of mass. Modifications in the kinematic pattern with slope depend on speed: at slow speeds, the net vertical displacement of the body during each step is related to changes in limb length and orientation. When speed increases, the vertical displacement is mostly related to a change in limb orientation.

The mechanics of head-supported load carriage by Nepalese porters

In the Everest valley of Nepal, because of the rugged mountain terrain, roads are nothing more than dirt paths and all material must be conveyed on foot. The Nepalese porters routinely carry head-supported loads, which often exceed their body mass, over long distances up and down the steep mountain footpaths. In Africa, women transport their loads economically thanks to an energy-saving gait adaptation. We hypothesized that the Nepalese porters may have developed a corresponding mechanism. To investigate this proposition, we measured the mechanical work done during level walking in Nepalese porters while carrying different loads at several speeds. Our results show that the Nepalese porters do not use an equivalent mechanism as the African women to reduce work. In contrast, the Nepalese porters develop an equal amount of total mechanical work as Western control subjects while carrying loads of 0 to 120% of their body mass at all speeds measured (0.5–1.7 m s−1), making even more impressive their ability to carry loads without any apparent mechanically determined tricks. Nevertheless, our results show that the Nepalese porters have a higher efficiency, at least at slow speeds and high loads.

Human motor control of landing from a drop in simulated microgravity

Landing on the ground on one's feet implies that the energy gained during the fall be dissipated. The aim of this study is to assess human motor control of landing in different conditions of fall initiation, simulated gravity, and sensory neural input. Six participants performed drop landings using a trapdoor system and landings from self-initiated counter-movement jumps in microgravity conditions simulated in a weightlessness environment by different pull-down forces of 1-, 0.6-, 0.4-, and 0.2 g External forces applied to the body, orientation of the lower limb segments, and muscular activity of 6 lower limb muscles were recorded synchronously. Our results show that 1) subjects are able to land and stabilize in all experimental conditions; 2) prelanding muscular activity is always present, emphasizing the capacity of the central nervous system to approximate the instant of touchdown; 3) the kinetics and muscular activity are adjusted to the amount of energy gained during the fall; 4) the control of landing seems less finely controlled in drop landings as suggested by higher impact forces and loading rates, plus lower mechanical work done during landing for a given amount of energy to be dissipated. In conclusion, humans seem able to adapt the control of landing according to the amount of energy to be dissipated in an environment where sensory information is altered, even under conditions of non-self-initiated falls.

Motor control of landing from a countermovement jump in simulated microgravity

Landing from a jump implies proper positioning of the lower limb segments and the generation of an adequate muscular force to cope with the imminent collision with the ground. This study assesses how a hypogravitational environment affects the control of landing after a countermovement jump (CMJ). Eight participants performed submaximal CMJs on Earth (1- g condition) and in a weightlessness environment with simulated gravity conditions generated by a pull-down force (1-, 0.6-, 0.4-, and 0.2- g0 conditions). External forces applied to the body, movements of the lower limb segments, and muscular activity of six lower limb muscles were recorded. 1) All subjects were able to jump and stabilize their landing in all experimental conditions, except one subject in 0.2- g0 condition. 2) The mechanical behavior of lower limb muscles switches during landing from a stiff spring to a compliant spring associated with a damper. This is true whatever the environment, on Earth as well as in environments where sensory inputs are altered. 3) The motor control of landing in simulated 1 g0 reveals an increased “safety margin” strategy, illustrated by increased stiffness and damping coefficient compared with landing on Earth. 4) The motor command is adjusted to the task constraints: muscular activity of lower limb extensors and flexors, stiffness and damping coefficient decrease according to the decreased gravity level. Our results show that even if in daily living gravity can be perceived as a constant factor, subjects can cope with altered sensory signals, taking advantage of the remaining information (visual and/or decreased proprioceptive inputs).

Observation of Gravitational Waves from a Binary Black Hole Merger

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

The rebound of the body during uphill and downhill running at different speeds

When running on the level, muscles perform as much positive as negative external work. On a slope, the external positive and negative works performed are not equal. The present study is intended to analyse how the ratio between positive and negative work modifies the bouncing mechanism of running. Our goals are (i) to identify the changes in motion of the centre of mass of the body associated with the slope of the terrain and the speed of progression, (ii) to study the effect of these changes on the storage and release of elastic energy during contact and (iii) to propose a model that predicts the change in the bouncing mechanism with slope and speed. Therefore, the ground reaction forces were measured on ten subjects running on an instrumented treadmill at different slopes (from −9° to +9°) and different speeds (between 2.2 and 5.6 m s−1). The movements of the centre of mass of the body and its external mechanical energy were then evaluated. Our results suggest that the increase in the muscular power is contained (1) on a positive slope: by decreasing the step period and the downward movements of the body, and by increasing the duration of the push, and (2) on a negative slope: by increasing the step period and the duration of the brake, and by decreasing the upward movement of the body. Finally the spring-mass model of running was adapted to take into account the energy added or dissipated each step on a slope.

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.

The mechanics of jumping over an obstacle during running: a comparison between athletes trained to hurdling and recreational runners

PURPOSE

This study compares the mechanism of running in trained athletes (TA) experienced in hurdling and in recreational runners (RR), as they approach and jump over an obstacle.

METHODS

The movements of the centre of mass of the body (COM), the external muscular work (W ext) and the leg-spring stiffness (k leg) were evaluated in athletes approaching an obstacle at 18 km h(-1), from the ground reaction forces (measured by force-platforms) and the orientation of the lower-limb segments (measured by camera). These results were compared to those obtained in RR.

RESULTS

Two steps before the obstacle, k leg is reduced by 10-20 %; so, the COM is lowered and accelerated forward. During the step preceding the obstacle, k leg is increased by 40-60 %; so the COM is raised and accelerated upwards, whereas its forward velocity is reduced. This change in the running pattern is similar to the one observed in RR while leaping an obstacle. However, in TA, the change in stiffness is less pronounced. As a result, the orientation of the velocity vector at the beginning of the aerial phase over the obstacle is more horizontal than in RR, which involves a 10-20 % greater horizontal velocity and a 40-60 % smaller vertical excursion of the COM when crossing the obstacle; subsequently, W ext during contact before the obstacle is 10-20 % less.

CONCLUSION

Athletes use the same mechanisms as non-specialists to cross an obstacle. However, athletes adapt the mechanism of jumping to reduce the loss in the velocity of progression when crossing an obstacle.

The mechanics of running while approaching and jumping over an obstacle

When leaping an obstacle, the runner increases the vertical velocity of his/her centre of mass (COM) at takeoff to augment the amplitude and duration of the aerial phase over it. This study analyses the modification of the bouncing mechanism of running when approaching a barrier. The forces exerted by the feet on the ground are measured by a 13-m-long force platform during the four to nine running steps preceding the jump over a 0.45- to 0.85-m-high barrier, at an approaching speed between 9 and 21 km h(-1). The movements of the COM are evaluated by time-integration of the forces and the stiffness of the bouncing system by computer simulation. The running mechanism is modified during the two steps preceding the barrier. During the contact period, two steps before the barrier, the leg-spring stiffness decreases; consequently, the COM is lowered and accelerated forward. Then during the contact period preceding the obstacle, the leg-spring stiffness increases and the COM is raised and accelerated upwards, whereas its forward velocity is reduced. During this phase, the leg-spring acts like a pole, which stores elastic energy and changes the direction of the velocity vector to release this energy in a vertical direction. At high speeds, this storage-release mechanism of elastic energy is sufficient to provide the energy necessary to leap the obstacle. On the contrary, at low speeds, the amount of elastic energy stored and released in the leg-spring is not sufficient to jump over the obstacle and additional positive muscular work must be done.

Directional limits on persistent gravitational waves using LIGO S5 science data

The gravitational-wave (GW) sky may include nearby pointlike sources as well as stochastic backgrounds. We perform two directional searches for persistent GWs using data from the LIGO S5 science run: one optimized for pointlike sources and one for arbitrary extended sources. Finding no evidence to support the detection of GWs, we present 90% confidence level (C.L.) upper-limit maps of GW strain power with typical values between 2-20×10(-50)  strain(2) Hz(-1) and 5-35×10(-49)  strain(2) Hz(-1) sr(-1) for pointlike and extended sources, respectively. The latter result is the first of its kind. We also set 90% C.L. limits on the narrow-band root-mean-square GW strain from interesting targets including Sco X-1, SN 1987A and the Galactic center as low as ≈7×10(-25) in the most sensitive frequency range near 160 Hz.

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.

All-sky LIGO search for periodic gravitational waves in the early fifth-science-run data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1100 Hz and with the frequency's time derivative in the range -5 x 10{-9}-0 Hz s{-1}. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semicoherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 10{-24} are obtained over a 200-Hz band, and the sensitivity improvement over previous searches increases the spatial volume sampled by an average factor of about 100 over the entire search band. For a neutron star with nominal equatorial ellipticity of 10{-6}, the search is sensitive to distances as great as 500 pc.

All-sky LIGO search for periodic gravitational waves in the early fifth-science-run data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1100 Hz and with the frequency's time derivative in the range -5 x 10{-9}-0 Hz s{-1}. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semicoherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 10{-24} are obtained over a 200-Hz band, and the sensitivity improvement over previous searches increases the spatial volume sampled by an average factor of about 100 over the entire search band. For a neutron star with nominal equatorial ellipticity of 10{-6}, the search is sensitive to distances as great as 500 pc.

All-sky LIGO search for periodic gravitational waves in the early fifth-science-run data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1100 Hz and with the frequency's time derivative in the range -5 x 10{-9}-0 Hz s{-1}. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semicoherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 10{-24} are obtained over a 200-Hz band, and the sensitivity improvement over previous searches increases the spatial volume sampled by an average factor of about 100 over the entire search band. For a neutron star with nominal equatorial ellipticity of 10{-6}, the search is sensitive to distances as great as 500 pc.

All-sky LIGO search for periodic gravitational waves in the early fifth-science-run data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1100 Hz and with the frequency's time derivative in the range -5 x 10{-9}-0 Hz s{-1}. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semicoherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 10{-24} are obtained over a 200-Hz band, and the sensitivity improvement over previous searches increases the spatial volume sampled by an average factor of about 100 over the entire search band. For a neutron star with nominal equatorial ellipticity of 10{-6}, the search is sensitive to distances as great as 500 pc.

Search for gravitational-wave bursts from soft gamma repeaters

We present a LIGO search for short-duration gravitational waves (GWs) associated with soft gamma ray repeater (SGR) bursts. This is the first search sensitive to neutron star f modes, usually considered the most efficient GW emitting modes. We find no evidence of GWs associated with any SGR burst in a sample consisting of the 27 Dec. 2004 giant flare from SGR 1806-20 and 190 lesser events from SGR 1806-20 and SGR 1900+14. The unprecedented sensitivity of the detectors allows us to set the most stringent limits on transient GW amplitudes published to date. We find upper limit estimates on the model-dependent isotropic GW emission energies (at a nominal distance of 10 kpc) between 3x10;{45} and 9x10;{52} erg depending on waveform type, detector antenna factors and noise characteristics at the time of the burst. These upper limits are within the theoretically predicted range of some SGR models.

Upper limits on a stochastic background of gravitational waves

The Laser Interferometer Gravitational-Wave Observatory has performed a third science run with much improved sensitivities of all three interferometers. We present an analysis of approximately 200 hours of data acquired during this run, used to search for a stochastic background of gravitational radiation. We place upper bounds on the energy density stored as gravitational radiation for three different spectral power laws. For the flat spectrum, our limit of omega0 < 8.4 x 10(-4) in the 69-156 Hz band is approximately 10(5) times lower than the previous result in this frequency range.

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 ∼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 ∼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.

Limits on gravitational-wave emission from selected pulsars using LIGO data

We place direct upper limits on the amplitude of gravitational waves from 28 isolated radio pulsars by a coherent multidetector analysis of the data collected during the second science run of the LIGO interferometric detectors. These are the first direct upper limits for 26 of the 28 pulsars. We use coordinated radio observations for the first time to build radio-guided phase templates for the expected gravitational-wave signals. The unprecedented sensitivity of the detectors allows us to set strain upper limits as low as a few times 10(-24). These strain limits translate into limits on the equatorial ellipticities of the pulsars, which are smaller than 10(-5) for the four closest pulsars.

Effect of load and speed on the energetic cost of human walking

It is well established that the energy cost per unit distance traveled is minimal at an intermediate walking speed in humans, defining an energetically optimal walking speed. However, little is known about the optimal walking speed while carrying a load. In this work, we studied the effect of speed and load on the energy expenditure of walking. The O(2) consumption and CO(2) production were measured in ten subjects while standing or walking at different speeds from 0.5 to 1.7 m s(-1) with loads from 0 to 75% of their body mass (M(b)). The loads were carried in typical trekker's backpacks with hip support. Our results show that the mass-specific gross metabolic power increases curvilinearly with speed and is directly proportional to the load at any speed. For all loading conditions, the gross metabolic energy cost (J kg(-1) m(-1)) presents a U-shaped curve with a minimum at around 1.3 m s(-1). At that optimal speed, a load up to 1/4 M(b) seems appropriate for long-distance walks. In addition, the optimal speed for net cost minimization is around 1.06 m s(-1) and is independent of load.

Mechanical work and muscular efficiency in walking children

The effect of age and body size on the total mechanical work done during walking is studied in children of 3–12 years of age and in adults. The total mechanical work per stride (Wtot) is measured as the sum of the external work, Wext (i.e. the work required to move the centre of mass of the body relative to the surroundings), and the internal work, Wint (i.e. the work required to move the limbs relative to the centre of mass of the body, Wint,k,and the work done by one leg against the other during the double contact period, Wint,dc). Above 0.5 m s–1, both Wext and Wint,k, normalised to body mass and per unit distance (J kg–1 m–1), are greater in children than in adults; these differences are greater the higher the speed and the younger the subject. Both in children and in adults, the normalised Wint,dc shows an inverted U-shape curve as a function of speed, attaining a maximum value independent of age but occurring at higher speeds in older subjects. A higher metabolic energy input (J kg–1 m–1) is also observed in children,although in children younger than 6 years of age, the normalised mechanical work increases relatively less than the normalised energy cost of locomotion. This suggests that young children have a lower efficiency of positive muscular work production than adults during walking. Differences in normalised mechanical work, energy cost and efficiency between children and adults disappear after the age of 10.

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, Ek, is converted into gravitational potential energy, Ep, 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 Ek and Ep than that of Europeans. In this study we measured the value of the Ek to Ep 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 Ek and Ep during the step by sinusoidal curves was used for comparison. It was found that loading improves the transduction of Ep to Ek during the descent of the centre of mass. The improvement is not significant in European subjects, whereas it is highly significant in African women.

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 energy cost of walking in children

Size, morphology and motor skills change dramatically during growth and this probably has an effect on the cost of locomotion. In this study, the effects of age and speed on the energy expended while walking were determined during growth. The rate of oxygen consumption and carbon dioxide production were measured in 3- to 12-year-old children and in adults while standing and walking at different speeds from 0.5 m x s(-1) to near their maximum aerobic walking speed. Standing energy expenditure rate decreases with age from 3.42 +/- 0.48 W x kg(-1) (mean +/- SD, n = 6) in the 3- to 4-year-olds to 1.95 +/- 0.22 W x kg(-1) (n = 6) in young adults. At all ages the gross cost of transport has a minimum which decreases from 5.9 J x kg(-1) x m(-1) in 3- to 4-year-olds to 3.6 J x kg(-1) x m(-1) after 10 years of age. The speed at which this minimum occurs increases from 1.2 m x s(-1) to 1.5 m x s(-1) over the same age range. At low and intermediate walking speeds the net cost of transport is similar in children and adults (about 2 J x kg(-1) x m(-1)). In young children walking at their highest speeds the net cost of transport is 70% (3- to 4-year-olds) to 40% (5- to 6-year-olds) greater than in adults.

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.

Mechanics and energetics of human locomotion on sand

Moving about in nature often involves walking or running on a soft yielding substratum such as sand, which has a profound effect on the mechanics and energetics of locomotion. Force platform and cinematographic analyses were used to determine the mechanical work performed by human subjects during walking and running on sand and on a hard surface. Oxygen consumption was used to determine the energetic cost of walking and running under the same conditions. Walking on sand requires 1.6-2.5 times more mechanical work than does walking on a hard surface at the same speed. In contrast, running on sand requires only 1.15 times more mechanical work than does running on a hard surface at the same speed. Walking on sand requires 2.1-2.7 times more energy expenditure than does walking on a hard surface at the same speed; while running on sand requires 1.6 times more energy expenditure than does running on a hard surface. The increase in energy cost is due primarily to two effects: the mechanical work done on the sand, and a decrease in the efficiency of positive work done by the muscles and tendons.

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.

All-fiber zero-insertion-loss add-drop filter for wavelength-division multiplexing

We developed and fabricated an all-fiber add-drop filter by recording a Bragg grating in the waist of an asymmetric mode converter-coupler formed by adiabatic tapering and fusing of two locally dissimilar, single-mode optical fibers. The insertion loss of the device was ~0.1 dB .A narrow spectral bandwidth (<1 nm) and a large add-drop efficiency (>90%) were also demonstrated. In addition, the filter was polarization independent.

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 cost, mechanical work and muscular efficiency in swing-through gait with elbow crutches

Crutches are widely used to assist ambulation in disabled people. Many authors have shown that the use of crutches increases the energy cost as compared to normal walking. In this study we have measured the energy consumed and the mechanical work performed during swing-through crutch gait in order to assess if the greater energy expenditure is accompanied by an equivalent increase of the work done to move the body. Our results show that, depending upon the speed, the energy expenditure is 2-3 times higher in swing-through gait than in normal walking. On the other hand, the mechanical work increases only 1.3-1.5 times. Thus the extra cost of swing-through gait cannot be explained solely by an increase of the mechanical work, but is due at least in part to a reduction in the efficiency of positive work production.

Stability of the braced ankle. A biomechanical investigation

We measured the bare ankle and the braced angle-torque relationships in 12 uninjured volunteers under static and dynamic conditions within the full range of inversion motion. These relationships were measured with a specially designed mechanical device that allowed inversion movements with angular velocities up to 850 deg/sec. In testing the bare ankle under static conditions, the torque showed a 10-fold increase within the full range of motion (average, from 0.9 N-m at 7 degrees to about 8 N-m at 48 degrees of inversion). The slope of the angle-torque relationship increased under dynamic conditions giving higher torque values (up to 18 N-m on average). Both orthoses induced similar additional torques that increased linearly, up to about 6 N-m at 45 degrees, with higher angles of inversion. These additional torques are small compared with the amount of stress applied to the foot during a typical ankle sprain situation, such as recovering from a jump. Therefore, we propose that orthotic devices increase the ankle torque, counteracting the inversion movement, and also prevent the start of the inversion movement by preloading and maintaining the ankle in a proper anatomic position with optimal contact between the articular surfaces.

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.