|
| |
|
|
|
|
||||
| Home Help Feedback Subscriptions Archive Search Table of Contents | ||||
First published online May 2, 2008
Journal of Experimental Biology 211, 1571-1578 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.013805
The landing–take-off asymmetry of human running is enhanced in old age
1 Istituto di Fisiologia Umana, Università degli Studi di Milano, 20133
Milan, Italy
2 Exercise Research Laboratory, Federal University of Rio Grande do Sul,
90690-200 Porto Alegre, Brazil
* Author for correspondence (e-mail: giovanni.cavagna{at}unimi.it)
Accepted 12 March 2008
 |
Summary |
|---|
 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Key words: age, locomotion, running, muscle, force–velocity relation
|
INTRODUCTION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
;
Ochala et al., 2006) and
in vivo on humans (Vandervoort et
al., 1990; Porter et al.,
1997; Pousson et al.,
2001; Klass et al.,
2005) showed that in old age muscular force is reduced less during
stretching (negative work) than during shortening (positive work). The effect
of this change of muscle contractile properties with age on the mechanics of
locomotion is unknown.
At each running step, the muscle-tendon units are stretched after landing
and shorten before take-off. The peak in kinetic energy attained before
landing, to be absorbed by the muscle-tendon units during the negative work
phase, is higher than the peak in kinetic energy restored before take-off
during the positive work phase. On the other hand, the duration of the
positive work phase is greater than the duration of the negative work phase.
This landing–take-off asymmetry is consistent with an average force
exerted during stretching (after landing) greater than that developed during
shortening (before take-off). It has been argued that the
landing–take-off asymmetry is a consequence of the force–velocity
relation of muscle, and the greater the length change of muscle relative to
that of tendon within the muscle-tendon units the larger the
landing–take-off asymmetry (Cavagna,
2006).
We hypothesized that the increased discrepancy in old age between the greater force resisting stretching and the lower force developed during shortening, if operational during running, would increase the landing–take-off asymmetry of the apparent bounce of the body relative to that of young subjects. To test this hypothesis, we measured the mechanical energy changes of the centre of mass during the negative and positive work phases of the bounce of the body in old and young subjects running on the level at different speeds.
|
MATERIALS AND METHODS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
), similar results were obtained here by comparing
the three old trained subjects with the three male young untrained subjects
(data not shown). Informed written consent was obtained from each subject. The
experiments were carried out in accordance with the Declaration of
Helsinki. Subjects ran back and forth along a 50 m corridor that had built into it, at the level of the floor, a 4 mx0.5 m force platform sensitive to the force exerted by feet in the forward and vertical directions. A total of 124 runs by the elderly subjects at a speed of 3 to 13–17 km h–1, and 229 runs by the young subjects at a speed of 3 to 17–21 km h–1, were analyzed.
Platform records analysis
The mechanical energy of the centre of mass of the body
(Fig. 1) was determined from
the ground reaction forces as previously described
(Cavagna, 1975). Only motion in
a sagittal plane was considered when calculating the mechanical energy of the
centre of mass. Rotational kinetic energy of the body and lateral
translational energy were ignored. The only instruction given to each subject
was to run normally, trying to reach and maintain a constant step-average
speed over the section of the corridor where the platform was placed. The
average running speed was measured by two photocells placed 1–3 m apart
(depending on speed) along the side of the platform. The characteristics of
the force platform were as previously described
(Cavagna, 1975). The
experimental procedure consisted of measuring the force exerted on the ground
in the sagittal plane during running at different speeds. A microcomputer
acquired data at a rate of 500 Hz per channel from (i) the platform signal
proportional to the force exerted in the forward direction, (ii) the platform
signal proportional to the force exerted in the vertical direction, and (iii)
the signal from the photocells. Data acquisition and analysis were made
via a dedicated DAQ board and custom LabView software (version 7.1,
National Instruments, Austin, TX, USA). The platform signal from the unloaded
force platform was measured immediately before each run and subtracted from
the platform records of the vertical force, Fv, and
fore–aft force, Ff, in order to account for a
possible drift of the base line. Only the subset of the Fv
and Ff records obtained between photocells crossing was
used for subsequent analysis. The vertical and forward velocities
(Vv and Vf, respectively) of the
center of mass were obtained as follows.
|
The average vertical force measured by the force platform,
v,plate, in a time
interval, nf
, corresponding to an integer number,
nf, of steps periods, (selected between peaks or
valleys of the force records), must equal the body weight measured with a
balance, v,scale.
v,plate was measured
after each run as the area below the Fv record in the time
interval nf divided by nf.
We analyzed records where
v,plate/v,scale=1.005±0.02
(N=124) for the group of old subjects and 1.002±0.01
(N=229) for the group of young subjects.
v,plate was then
subtracted from the Fv array and the result
(Fv–v,plate)/Mb
(where Mb is the mass of the body) was integrated to
obtain the record of vertical velocity changes for the time interval between
photocells crossing.
One or more regular steps were subsequently chosen for analysis between two
peaks or valleys of the record of Vv changes corresponding
to a time interval nv where nv is
an integer number of steps. The regularity of the steps was determined by the
difference between positive and negative increments in the
Vv and Vf changes divided by the sum
of the increments. In the old group this ratio was 3.83±3.73%
(vertical) and 10.95±9.2% (forward) (N=124), whereas in the
young group it was 3.55±3.29% (vertical) and 12.98±11.63%
(forward) (N=229). During running on the level, the upward and
downward vertical displacements of the centre of mass of the body are on
average equal over nv steps, i.e. the average
Vv must be nil. On this basis, the area below the
Vv changes (
Vv) record,
corresponding to the nv interval selected above, was
divided by nv and the result subtracted from the
whole Vv record between photocells crossing to
obtain the instantaneous positive (upward) and negative (downward) values of
Vv.
The Vf record was determined by integration of
the Ff/Mb array during the time
interval between photocells crossing, tphoto. The
area below this Vf record was then divided by
tphoto and the result subtracted from the same
record to locate the average running speed on the tracing. The average running
speed, measured as photocells distance/tphoto, was
then summed to the resulting array to obtain the instantaneous values of
Vf.
The instantaneous vertical velocity Vv(t) was
used to calculate the instantaneous kinetic energy of vertical motion
Ekv(t)=0.5MbVv(t)2
and, by integration, the vertical displacement of the centre of mass,
Sv(t), with the corresponding gravitational
potential energy
Ep(t)=MbgSv(t)
(where g is the acceleration of gravity). The kinetic energy
of forward motion was calculated as
Ekf(t)=0.5MbVf(t)2,
the total translational kinetic energy of the centre of mass in the sagittal
plane as
Ek(t)=Ekf(t)+Ekv(t),
and the translational mechanical energy of the centre of mass in the sagittal
plane as
Ecm(t)=Ekv(t)+Ekf(t)+Ep(t).
Since, as mentioned above, selection was initially made between peaks (or
valleys) of the Vv, the records were expanded to
include the previous valley (or peak) of Ep(t)
until a clear picture of the step(s) was obtained
(Fig. 1).
Algorithms were made to calculate the work done during the selected steps
between Ep valleys (or peaks): Wv,
Wkf and Wext were calculated from the
amplitudes of valleys and peaks, and the initial and final values in the
Ep(t), Ekf(t) and
Ecm(t) records. Positive values of the energy
changes gave positive work, negative values gave negative work. In a perfect
steady run on the level the ratio between the absolute values of positive and
negative work done in nv steps should be equal to one.
Experimental values were as follows: in the old subjects group
(N=124):
=0.99±0.08,
=1.01±0.13,
=0.99±0.07;
in the young subjects group (N=229):
=0.99±0.07,
=1.03±0.14,
=1.00±0.07.
These means refer to steps where
0.6<W+/W–<1.5.
Aerial time, brake-push durations and vertical displacement during contact
Since the mechanical energy of the centre of mass is constant when the body
is airborne (air resistance is neglected), the aerial time was calculated as
the time interval during which the derivative
dEcm(t)/dt=0. This time interval was
measured using two reference levels set by the user above and below the
section of the record where
dEcm(t)/dt
0
(Cavagna, 2006). The brake
duration, tbrake, i.e. the time during which external
negative work is done, was calculated as the time interval during which the
dEcm(t)/dt record was below the
reference level. The push duration, tpush, i.e. the time
during which external positive work is done, was calculated as the time
interval during which the dEcm(t)/dt
record was above the reference level. Due to the noise of the
dEcm(t)/dt record, the aerial time was
in some cases overestimated (7%), and tbrake and/or
tpush were in some cases underestimated (5–7%)
(Cavagna, 2006). Similarly, the
downward and upward displacements of the centre of mass during contact,
Sc,down and Sc,up
(Fig. 2), were measured from
the descending and ascending portions, respectively, of the
Ep(t) curve during the time interval where
dEcm(t)/dt was lower or greater,
respectively, than the two reference levels.
|
 | (1) |
|
Within the step Ep
Ek transduction
The time course of the transduction taking place within the step between
gravitational potential energy Ep and kinetic energy of
the centre of mass Ek was determined from the absolute
value of the changes, both positive and negative increments, of
Ep, Ek and Ecm in
short time intervals within the step cycle
(Cavagna et al., 2002):
 | (2) |
and β,
where Ek increases or decreases, respectively,
simultaneously with the gravitational potential energy Ep
(Cavagna et al., 2002). Note
that positive and negative external work is done both in the phases
and β of the step [r(t)=0] and in the phases of the
step where a transduction occurs between Ek and
Ep [0<r(t)<1].
The cumulative value of energy recovery,
Rint(t), resulting from the instantaneous
Ek–Ep transduction, was measured
from the area below the r(t) record divided by the step
period: Rint(t)=[
t0r(u)du]/. At the end
of the step Rint()=Rint
(Cavagna et al., 2002).
Statistics
The data collected as a function of running speed were grouped into classes
of 1 km h–1 intervals as follows: 3 to <4 km
h–1, 4 to <5 km h–1..., 20 to <21 km
h–1. The data points in Figs
2 and
4 represent the mean ±
s.d. in each of the above speed intervals and the figures near the symbols in
Fig. 2 give the number of items
in the mean. A paired samples t-test was used to determine when the
means, within a subject group with the same number of items at a given speed
interval, are significantly different
(Table 1). When comparing the
means of different variables between the two subject groups having different
numbers of items, an independent-samples t-test was used
(Table 2). The t-tests
were performed using SPSS for Windows version 11.0.1 (SPSS, Chicago, IL,
USA).
|
|
|
|
RESULTS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
When the aerial phase is nil, at the lowest running speeds (e.g.
Fig. 1A,B), the whole vertical
displacement takes place with the foot in contact with the ground and
Sc/Sv=1. With increasing speed, an
aerial phase of progressively greater extent takes place during the step. It
follows that the fraction of the vertical displacement in contact with the
ground decreases. The decrement is less during the lift than during the fall,
i.e. Sc,up/Sv,up is greater than
Sc,down/Sv,down
(Fig. 2). In other words, the
height of the centre of mass at the instant of take-off is greater than its
height at the instant of touchdown: i.e. the ballistic lift is smaller than
the ballistic fall (light-blue segments of Ep in
Fig. 3)
(Cavagna, 2006).
This landing–take-off asymmetry is present in both subject groups, but is larger in the old subjects than in the young subjects, mainly due to a smaller reduction with speed of Sc,up/Sv,up: a larger fraction of the lift of the centre of mass takes place in contact with the ground in the old subjects.
The effective landing–take-off asymmetry
The landing–take-off asymmetry described above bears no relation to
loading and unloading of the spring-mass system during the bounce of the
centre of mass at each running step
(Cavagna, 2006). Indeed, as
mentioned above, landing and take-off may not occur at all during low-speed
running. It is obvious that, in this extreme case, the time of contact gives
no information on the loading of the elastic system. Even in the presence of
an aerial phase, the time of contact exceeds the time during which the
spring-mass system is loaded beyond its equilibrium position, where the
vertical force equals body weight
(Blickhan, 1989).
It is therefore more appropriate to consider `effective landing' as the
instant where the vertical force increases above body weight (rather than the
instant where the foot contacts the ground) and `effective take-off' as the
instant where the vertical force drops below body weight (rather than the
instant where the foot leaves the ground). Loading of the elastic system with
a force greater than body weight (downward deceleration and upward
acceleration) takes place during the lower part (Sce) of
the vertical oscillation of the centre of mass, and unloading (upward
deceleration and downward acceleration) during its upper part
(Sae) (Cavagna et al.,
1988).
The changes in gravitational potential energy, Ep,
translational kinetic energy,
Ek=Ekf+Ekv, and
their transduction Rint(t) are therefore depicted
in Fig. 3 during loading (red)
and unloading (blue) of the system relative to its equilibrium position,
regardless of the contact time and the aerial phase. These records have been
analyzed in detail (Cavagna,
2006) and are only briefly described here to assess the different
landing–take-off asymmetry in old and young subjects.
During the downward acceleration (Sae,down, Fig. 3, blue), the support of the body on the ground is low with the consequence that a large transduction of Ep into Ek occurs both in the presence and the absence of an aerial phase. The amount of this transduction is given by the increment Rint,down of the Rint(t) curve. As a consequence of this transduction, the kinetic energy Ek attains its highest peak in the running step, just prior to the effective landing (start of downward deceleration).
During the downward deceleration (Sce,down, Fig. 3, red), negative external work is done to decrease Ep and Ek simultaneously, as indicated by the horizontal tract of the Rint(t) curve showing that no transduction occurs between Ep and Ek: this is the β fraction of the step.
During the upward acceleration (Sce,up,
Fig. 3, red), positive external
work is done to increase Ep and Ek
simultaneously, as indicated by the lower horizontal tract of the
Rint(t) curve showing that no transduction occurs
between Ep and Ek: this is the
fraction of the step. At the end of the fraction the kinetic energy
Ek attains its maximum during the lift, which is lower
than that attained during the fall. The difference between the two
Ek peaks is on average greater in the old subject. Note
that whereas β is almost totally contained within
Sce,down, continues after the end of
Sce,up, within the upward deceleration of the centre of
mass (Sae,up, Fig.
3, blue). In other words, the muscular push is still lifting and
accelerating the body forwards even though the vertical force has dropped
below body weight. The intrusion of into Sae,up is
larger in the old subject.
During the upward deceleration (Sae,up, Fig. 3, blue), the transduction of Ek into Ep given by the increment Rint,up of the Rint(t) curve is confined to the last part of the lift because, as described above, Ep and Ek increase simultaneously for an appreciable part of Sae,up. Indeed, the transduction of Ek into Ep is almost nil in the oldest subject of Fig. 3. In particular, the ratio Rint,down/Rint,up is much larger in the old subject.
The different features of the rebound of the body described above translate
into different durations of positive and negative work (red/blue bars in
Fig. 1). These are plotted in
Fig. 4 as a function of speed.
It can be seen that, in both old and young subjects, the duration of positive
work tpush is greater than the duration of negative work
tbrake up to 
13 km h–1. At higher
speeds, both durations fall below 0.1 s and become similar. In the common
speed range, the ratio tpush/tbrake is
greater in the old subjects than in the young subjects
(Table 2).
The records in Figs 1, 3 and 4 show that the landing–take-off asymmetry is greater in the old than in the young subjects. The results supporting this conclusion are summarized in Table 2 where a comparison is made between old subjects, young subjects and the symmetric rebound of an elastic system.
|
DISCUSSION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
).
In running, the kinetic energy of forward motion Ekf
increases and decreases essentially in phase with the potential energy
Ep (Cavagna et al.,
1964), with the consequence that the
Ekf–Ep transduction is
negligible. It follows that in running the
Ek–Ep transduction takes place
essentially between gravitational potential energy Ep and
kinetic energy of vertical motion Ekv. This transduction
is obviously complete during the aerial phase when the support of the body on
the ground is nil [r(t)=1], but it also occurs during
contact when the body is only partially supported by the foot on the ground in
the upper part of the trajectory of the centre of mass
[0<r(t)<1] [see the increment of the
Rint(t) curve in
Fig. 3A,B where the aerial
phase is nil]. During running, therefore, Rint gives a quantitative measure of the `lack of support' of the body on the ground over the whole step cycle, including both the aerial phase and the ground contact phase. Rint would attain unity in a hypothetical `step' made up completely of an aerial phase.
In the elderly, Rint,old=0.28±0.05, which is
about 70% of the value attained by the young subjects:
Rint,young=0.38±0.06
(P=3.66x10–44). This gives a measure of the
greater support on the ground during the step in the old subjects relative to
the young subjects. A lower flight time in the elderly has already been
reported during running at 10 km h–1
(Karamanidis and Arampatzis,
2005).
The Ek–Ep transduction has a different meaning during the descent Rint,down and during the lift Rint,up of the centre of mass (Fig. 3).
Rint,down, i.e. the Ep into
Ek transduction during the fall, can be viewed as a
mechanism exploiting gravity to passively increase the vertical downward
velocity and, as a consequence, the kinetic energy.
Rint,down precedes the negative work phase of the step.
This has two physiological effects. (i) It provides mechanical energy to be
stored within the muscle-tendon units during the subsequent brake, but (ii) it
requires a force to decelerate the body downwards which, in the old subjects,
may be insufficient and/or may decrease the safety of their
muscular–skeletal system
(Karamanidis and Arampatzis,
2005). A large value of Rint,down relies on an
adequate muscular force to be exerted during subsequent stretching. In the
elderly, Rint,down,old=0.18±0.02, which is about
85% of the value attained by the young subjects:
Rint,down,young=0.21±0.03
(P=3.97x10–25).
Rint,up, i.e. the Ek into Ep transduction during the lift, follows the positive work phase of the step and is greater the greater the push-average power developed before take-off. In fact, the greater the push, the greater the increment in kinetic energy of vertical motion and therefore its subsequent decrement when the centre of mass is lifted during the phase of partial support and the aerial phase. The push-average power depends in turn on the capability to (i) recover elastically the mechanical energy stored during the preceding negative work phase, and (ii) add work done during shortening by the contractile component. A large Rint,up therefore relies on an adequate muscular force to be exerted during shortening by the muscle-tendon units. In the elderly, Rint,up,old=0.10±0.04, which is about 60% of the value attained by the young subjects: Rint,up,young=0.17±0.04 (P=1.34x10–45).
Since Rint,down is 15% less in the elderly than in the
young subjects whereas Rint,up is 40% less, the ratio
Rint,down/Rint,up is appreciably
greater in the old subjects than in the young subjects
(Table 2). As mentioned above,
a large Rint,down requires a large force to be exerted
during the following negative work phase (stretching), whereas a large
Rint,up requires a large force to be exerted during the
preceding positive work phase (shortening). The finding that
Rint,down is less affected by age than
Rint,up suggests that the deficit in force during
stretching is less than the deficit in force during shortening, which is a
characteristics of aged muscle
(Vandervoort et al., 1990;
Porter et al., 1997;
Pousson et al., 2001;
Klass et al., 2005). The
relatively greater Rint,down and lower
Rint,up in the elderly translate into a larger difference
between peaks in kinetic energy attained during the fall
Ek,mx,down and during the lift
Ek,mx,up (Table
2).
The physiological meaning of tpush/tbrake being greater in the elderly
Fig. 4 and
Table 1 show that the positive
work duration tpush is greater than the negative work
duration tbrake up to 13 km h–1.
This is true in both subject groups, but the ratio
tpush/tbrake is on average greater in
the old subjects than in the young subjects
(Table 2).
During running on the level at a constant step-average speed, the momentum
lost during negative work,
braketbrake,
equals the momentum gained during positive work,
pushtpush.
When tpush>tbrake
(Fig. 4) then
push<brake,
i.e. the average force during positive work is less than the average force
during negative work, as expected from the force–velocity relation of
muscle (Cavagna, 2006).
The present findings show that
tpush/tbrake is on average greater in
the old subjects (Table 2),
i.e. that
push/brake
is less in the old subjects than in the young subjects. This indicates a lower
force during shortening relative to stretching in old age, which is
qualitatively consistent with the more asymmetric force–velocity
relation of aged muscle (Vandervoort et
al., 1990; Porter et al.,
1997; Pousson et al.,
2001; Klass et al.,
2005).
At running speeds greater than about 14 km h–1, negative
and positive work durations fall below 0.1 s and approach each other, seen
more clearly in the young than in the old subjects. An explanation for this
finding has previously been proposed
(Cavagna, 2006) and is briefly
given below.
At each running step the muscle-tendon units are subjected to a
stretch–shorten cycle as the body bounces off the ground. Muscle-tendon
units are composed of two structures in series having a very different
response to stretch and recoil. While tendons have a similar
stretch–shorten relation due to their small hysteresis
(Ker, 1981;
Alexander, 2002), muscle exerts
a larger force during stretching then during shortening, depending on its
force–velocity relation. This fact results in a different response of
the muscle-tendon units to a stretch–shortening cycle depending on the
relative length change of muscle and tendon during the cycle
(Cavagna, 2006).
The lengthening of muscle relative to the lengthening of tendon depends on
the stiffness of muscle relative to that of tendon; the stiffness of muscle,
in turn, depends on its activation, i.e. on the force exerted by its
contractile component. If the muscle is relaxed, i.e. the force is nil, the
whole of the lengthening will be taken up by muscle. If the force is low, as
at low speeds of locomotion [e.g. fig.
3 of Biewener (Biewener,
1998)], an appreciable fraction of the length change will be taken
up by muscle. In this case, the average force developed during stretching is
expected to exceed that developed during shortening according to the
force–velocity relation of muscle, and the characteristics of the bounce
would deviate from those of an elastic body. If, on the other hand, the force
is high, as at high speeds of locomotion [e.g.
fig. 3 of Biewener
(Biewener, 1998)] and the
muscle is kept isometric, as some studies suggest for running
(Kram and Taylor, 1990;
Roberts et al., 1997;
Biewener et al., 1998), most of
the length change will be taken up by tendons and the characteristics of the
bounce will approach that of an elastic body.
These observations are in agreement with the finding that at low and
intermediate running speeds the positive work duration is greater than
negative work duration (Fig.
4), indicating that the average force during positive work is less
than the average force during negative work as expected from the
force–velocity relation of muscle. At speeds greater than 14 km
h–1, tpushtbrake,
indicating that
pushbrake,
as expected from an elastic system. This suggests that when the duration of
the rebound, tpush+tbrake, falls below
0.2 s (Fig. 4) the length
change of the muscle-tendon units is taken up almost completely by tendons and
other undamped elastic elements, with muscle in a quasi-isometric contraction.
Fig. 4 shows that this apparent
elastic behavior at high speeds is more evident in the young subjects than in
the elderly.
In conclusion, a muscular force greater during stretching than during shortening with a large energy loss during the stretch–shorten cycle, which are both consequences of the force–velocity relation of muscle, may explain, at least qualitatively, the ensemble of the deviations from the elastic model during the bounce of the body (Table 2). Assuming that the old subjects we tested exhibit the modification of the force–velocity relation characteristic of their age, the larger deviation from the elastic model found in the old subjects may be due to: (i) the greater difference in force between stretching and shortening described in the aged muscle, and (ii) the lower force developed by their muscles, implying a relatively larger length change of muscle relative to tendons within the muscle–tendon units.
LIST OF SYMBOLS AND ABBREVIATIONS
brake
push
is the sum of
the positive increments of Ecm during the period
is the sum of the
positive increments of Ekf during the period
is the sum of the positive
increments of Ep during the period
, β) or decrease (β)
simultaneously
tphoto
|
References |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Alexander, R. McN. (2002). Tendon elasticity and muscle function. Comp. Biochem. Physiol. 133A,1001 -1011.
Biewener, A. A. (1998). Muscle-tendon stresses and elastic energy storage during locomotion in the horse. Comp. Biochem. Physiol. 120B,73 -87.[CrossRef][Medline]
Biewener, A. A., Konieczynski, D. D. and Baudinette, R. V. (1998). In vivo muscle force–length behavior during steady-speed hopping in tammar wallabies. J. Exp. Biol. 201,1681 -1694.[Abstract]
Blickhan, R. (1989). The spring-mass model for running and hopping. J. Biomech. 22,1217 -1227.[CrossRef][Medline]
Cavagna, G. A. (1975). Force platforms as
ergometers. J. Appl. Physiol.
39,174
-179.
Cavagna, G. A. (2006). The
landing–take-off asymmetry in human running. J. Exp.
Biol. 209,4051
-4060.
Cavagna, G. A., Saibene, F. P. and Margaria, R.
(1964). Mechanical work in running. J. Appl.
Physiol. 19,249
-256.
Cavagna, G. A., Franzetti, P., Heglund, N. C. and Willems,
P. (1988). The determinants of the step frequency in running,
trotting and hopping in man and other vertebrates. J.
Physiol. 399,81
-92.
Cavagna, G. A., Willems, P., Legramandi, M. A. and Heglund, N.
C. (2002). Pendular energy transduction within the step in
human walking. J. Exp. Biol.
205,3413
-3422.
Karamanidis, K. and Arampatzis, A. (2005).
Mechanical and morphological properties of different muscle-tendon units in
the lower extremity and running mechanics: effect of aging and physical
activity. J. Exp. Biol.
208,3907
-3923.
Ker, R. F. (1981). Dynamic tensile properties
of the plantaris tendon of sheep (Ovis aries). J. Exp.
Biol. 93,283
-302.
Klass, M., Baudry, S. and Duchateau, J. (2005).
Aging does not affect voluntary activation of the ankle dorsiflexors during
isometric, concentric and eccentric contractions. J. Appl.
Physiol. 99,31
-38.
Kram, R. and Taylor, C. R. (1990). Energetics of running: a new perspective. Nature 346,265 -267.[CrossRef][Medline]
Ochala, J., Dorer, D. J., Frontera, W. R. and Krivickas, L. S. (2006). Single skeletal muscle fiber behavior after a quick stretch in young and older men: a possible explanation of the relative preservation of eccentric force in old age. Pflugers Arch. 452,464 -470.[CrossRef][Medline]
Phillips, S. K., Bruce, S. A. and Woledge, R. C.
(1991). In mice, the muscle weakness due to age is absent during
stretching. J. Physiol.
437, 63-70.
Porter, M. M., Vandervoort, A. A. and Kramer, J. F. (1997). Eccentric peak torque of the plantar and dorsiflexors is maintained in older women. J. Gerontol. A Biol. Sci. Med. Sci. 52,B125 -B131.[Medline]
Pousson, M., Lepers, R. and Van Hoecke, J. (2001). Changes in isokinetic torque and muscular activity of elbow flexors muscles with age. Exp. Gerontol. 36,1687 -1698.[CrossRef][Medline]
Roberts, T. J., Marsh, R. L., Weyand, P. G. and Taylor, C.
R. (1997). Muscular force in running turkeys: the economy of
minimizing work. Science
275,1113
-1115.
Vandervoort, A. A., Kramer, J. F. and Wharram, E. R. (1990). Eccentric knee strength of elderly females. J. Gerontol. 45,B125 -B128.[Abstract]
CiteULike 
Complore 
Connotea 
Del.icio.us 
Digg 
Reddit 
Technorati 
Twitter What's this?
Related articles in JEB:
This article has been cited by other articles:
|
|
 |
|
  G. A. Cavagna and M. A. Legramandi The bounce of the body in hopping, running and trotting: different machines with the same motor Proc R Soc B, December 22, 2009; 276(1677): 4279 - 4285. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 K. Phillips MUSCLES MAKE ENERGY TRANSFER ASYMMETRIC J. Exp. Biol., May 15, 2008; 211(10): iii - iii. [Full Text] [PDF]
|
|
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
