Joint work and power associated with acceleration and deceleration in tammar wallabies (Macropus eugenii)
1 Concord Field Station, Department of Organismic and Evolutionary Biology,
Harvard University, Cambridge, MA 02138, USA
2 Department of Environmental Biology, University of Adelaide, Adelaide, SA
5003, Australia
* Author for correspondence (e-mail: cmcgowan{at}oeb.harvard.edu)
Accepted 22 September 2004
![]() |
Summary |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Key words: locomotion, hopping, joint power, inverse dynamics, tammar wallaby, Macropus eugenii.
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
The goal of this study was to determine, through inverse dynamics analysis, which hind limb joints in tammar wallabies are active in modulating the changes in energy associated with changing speed. While this approach is unable to provide the direct evaluation of muscle function achieved through in vivo studies, analysis of joint power and work provides a broader overview of how energy is modulated by the limb as a whole and thus provides further insight into how muscles and muscle groups are recruited to meet the demands of the environment.
During steady-state locomotion, an animal's muscles perform no net
mechanical work on the center of mass. Although individual muscles may do both
net positive (energy production) and negative work (energy absorption) during
steady speed movement, many muscles probably act as struts, generating force
under fairly isometric conditions. The tendons of these muscles provide
elastic energy savings by being stretched to absorb energy in the braking
phase of stance and recoiling to return their strain energy in the propulsive
phase (Biewener and Roberts,
2000; Dickinson et al.,
2000
; Ker et al.,
1986
; Roberts et al.,
1997
). When animals accelerate or decelerate, however, they must
produce or absorb net mechanical energy. Much of this is likely to occur in
the muscles of the limbs.
On a mass- or volume-specific basis, vertebrate skeletal muscles have
generally similar capacities to produce mechanical work. However,
muscle-tendon unit architecture can greatly influence the role they play in
locomotion (Biewener, 1998;
Biewener and Roberts, 2000
;
Roberts et al., 1997
;
Roberts, 2002
).
Muscles composed of short, pinnate fibers (and thus a relatively large
cross sectional area) coupled in series with long, thin tendons form
muscle-tendon units that are effective for storing elastic strain energy. This
is in contrast to muscles with long, generally parallel fibers that may be
better suited for changing length and doing mechanical work. However, longer
fibered muscles probably cost more energy per unit mass when they contract
because a larger volume of muscle must be recruited to generate a given amount
of force (Roberts et al.,
1998; Biewener,
1998
; Biewener and Roberts,
2000
). Hence, a trade-off may exist between a muscle's ability to
store elastic energy and its ability to generate power.
In wallabies, as in most cursorial animals, the majority of musculature is located proximally in the limb. Consequently, many of the muscles acting at the hip and knee are large and of a design that favors power production, while those that act at distal joints appear better suited for elastic energy savings. This suggests a possible regional specialization in the functional role of muscle groups acting at different joints within the wallaby's limb.
An important question is the extent to which the contractile behavior of an
individual muscle may change versus how muscle groups with differing
architecture may be recruited to modulate changes in mechanical function
during locomotion. Recent in vivo studies have begun to explore this
question, focusing on more distal limb muscles that favor elastic energy
savings. Work by Roberts et al.
(1997) compared turkeys
(Meleagris gallopavo) running on level and inclined surfaces, showing
that the turkey's lateral gastrocnemius muscle-tendon unit shifts from low
work and elastic savings on the level to net work production and elastic
savings during incline running. However, in a similar study of tammar
wallabies, Biewener et al.
(2004
) found that the lateral
gastrocnemius and plantaris muscles did not change their function. Both
muscle-tendon units stored elastic energy during level and inclined hopping
but contributed no net work to raising the animal's center of mass on a
10° incline. This suggests that the role of the ankle extensors in tammar
wallabies may be more limited by their design than in turkeys, and that
proximal limb muscles are recruited to provide the required work needed during
incline hopping or acceleration. As a result, a `division of labor' may exist
among hind limb muscle groups in wallabies, such that work for acceleration
would occur mainly at the knee and hip joints.
However, several hind limb muscles span multiple joints and studies
exploring the role of bi-articular muscles in locomotion have shown that
significant energy may be transferred between proximal and distal joints
(Bobbert et al., 1986;
Jacobs et al., 1996
;
Prilutsky and Zatsiorsky,
1994
; Prilutsky et al.,
1996
). In activities such as sprinting, jumping and landing, in
which substantial net mechanical work must be done on the center of mass (CoM)
of the body, energy passes from distal to proximal joints during the braking
phase of stance and from proximal to distal joints in the propulsive phase
(Jacobs et al., 1996
;
Prilutsky and Zatsiorsky,
1994
). This pattern is quite pronounced in jumping galagos
(Aerts, 1998
), in which 68% of
total external work is delivered at the ankle and as much as 65% of this
energy is transferred from the knee. Because of their similar musculoskeletal
arrangement, it seems probable that significant energy transfer may also occur
in wallabies. Thus, while proximal muscles are most likely to produce or
absorb energy, we expect that external measurements will show that the work
for accelerating or decelerating is delivered at the ankle joint, transferred
from the hip and knee via the relatively isometric contraction of ankle
extensors.
Assuming that the ground reaction force passes through or near the animal's
CoM, which is located anterior to its hip, we also expect large extensor
moments to be generated at the hip and ankle joints during stance. Therefore,
these joints may play a role in producing the work needed to accelerate or
decelerate the animal. This pattern has recently been observed in jumping
horses (Dutto et al.,
2004).
Our goal in this study, therefore, was to explore how proximal
versus distal limb joints modulate the work necessary for tammar
wallabies to change speed during level hopping, using inverse dynamics
analysis. From this analysis, we sought to identify the roles of proximal
versus distal muscle groups of tammar wallabies in relation to their
fiber-tendon architecture and whether a division of labor exists within their
hind limb. Based on the results of our prior in vivo studies of their
distal ankle muscle-tendon units (Biewener
et al., 1998; Biewener et al.,
2004
), we expect that much of the work necessary for acceleration
and deceleration will be produced by proximal hind limb muscles, but will be
delivered largely at the ankle joint through energy transfer via
bi-articular muscles.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Runway and experimental protocol
A 22 mx0.75 m runway was constructed from light-gauge field fencing
strung from fence posts placed in the ground over a level stretch of the
grassy outdoor paddock. The runway was closed at both ends to completely
contain the animals. A 0.60 mx0.40 m force-plate was set flush with the
ground at approximately the midpoint of the runway. The force plate was
positioned on a 5 cm thick concrete slab buried in the ground and a wooden
frame the same depth as the force-plate was used to keep the surrounding soil
from contacting the plate. The wallabies were placed in the runway area and
encouraged to hop from end to end. Accelerations were elicited by startling
the animal from behind as it approached the plate at a steady speed.
Decelerations occurred often with little outside prompting from the
investigators. Approximately 15-20 trials were collected from each animal but
only a small subset could be analyzed for this study. For trials to be
included, the wallaby had to make at least one hop preceding the hop on the
plate, both feet had to strike the plate simultaneously, and all joint markers
had to be visible for video analysis. In addition, only those trials in which
the animal's acceleration was primarily in the horizontal direction were
analyzed, excluding trials in which the animals jumped more vertically from
the plate. Twenty-nine trials, ranging from four to seven trials from each
animal, fit these criteria for analysis. There was no significant effect of
individual on the variables measured as determined by an analysis of variance
(ANOVA).
In all five animals, segment lengths and muscle moment arms were palpated
and measured with digital calipers. These measurements were later confirmed by
dissection of four of the animals that were killed after being used in a
subsequent experiment. In the dissected animals, masses and moment arms were
recorded for all muscles in the limb. An additional cadaver was used to
determine segment masses and moments of inertia for the thigh, shank, foot and
toes (following the method of Blickhan and
Full, 1992) for use in the inverse dynamics calculations
(Table 1) (see below). These
values were corrected to individual values for each of the animals used in
this study assuming geometric scaling
(Table 2).
|
|
Ground reaction forces
Ground reaction forces (GRF) were recorded using a multi-component
piezoelectric force-plate (Kistler type 9286AA; Kistler Instruments Corp.,
Amherst, NY, USA) with an integrated charge amplifier (crosstalk between
channels <1.0%). Forces were recorded in the vertical, horizontal and
lateral directions. Lateral forces were always quite small and for the
purposes of this study were ignored. Force-plate recordings were sampled at
1000 Hz and transferred to computer and stored by means of a BioWareTM
type 2812A1-3 A/D system (DAS1602/16 A/D board) operated using BioWare v.3.0
software (Kistler Instruments Corp.).
Kinematics
Trials were filmed in the lateral view with a digital high-speed video
camera (Redlake Motionscope PCI-500, San Diego, CA, USA) recording at 125 Hz.
Video and force-plate data were synchronized via a trigger that
simultaneously stopped video recording and sent a voltage pulse to a separate
channel being recorded in conjunction with the force-plate outputs. The camera
was positioned approximately 7 m from the runway to reduce the effects of
parallax. The hind limbs of the animals were shaved using small animal
clippers and the joint centers of rotation were palpated and marked with white
paint. Points marked included the hip, knee, ankle, metatarsophalageal (MP)
joint and the tip of the longest phalange as well as a trunk point identified
by the anterior tip of the ilium (Fig.
1). Joint markers, as well as the location of the force-plate and
in-field scale bars were digitized using a customized MATLAB (v.6.5, The
MathWorks, Natick, MA, USA) routine. Because of the skin movement over the
knee during locomotion, the coordinates of the knee joint were calculated by
generating the equations for circles centered at the coordinates of hip and
ankle, with the length of the femur and tibia being their radii, respectively.
The knee joint location was determined by the intersection point of these two
circles that most closely matched the digitized knee point. The other
intersection point was always clearly incorrect. The trigger pulse, in
conjunction with the digitized coordinates of the scale bar and force-plate
were used to scale and align the kinematic data with GRF data.
|
Calculation of joint moments, power and work
Inverse dynamics analysis was used to calculate the total net moment at
each joint. The analysis consisted of combining GRF, kinematics and
morphometric data to create a linked segment model consisting of a toe, foot,
shank and thigh (Fig. 1). The
following equations were solved for each segment, beginning with the most
distal, where the GRF was applied:
![]() | (1) |
![]() | (2) |
where Fx,y are the external forces in the horizontal
and vertical directions (including forces due to gravity), m is the
mass of the segment, ax,y are the linear
accelerations of the center of gravity (CG) in both directions,
Mj is the moment generated by Fx,y
about the CG, Ij is the moment of inertia about the CG,
and j is the angular acceleration. It was assumed that, at
each instant, the value derived for M was equal to the net moment
being exerted by the muscles acting at that given joint
(Aerts, 1998
;
Winter, 1990
). In this
experiment, positive values for M represent an extensor moment
(balanced by extensor musculature), and negative values a flexor moment
(balanced by flexor musculature). The center of pressure (CoP) of the GRF
acting on the toe was supplied by the force-plate. Errors in the alignment of
kinematic data with CoP can have a considerable effect on the calculation of
joint moment (up to 25% at the extremes in the case of a tammar wallaby).
Therefore, each trial was checked graphically to ensure that the CoP lined up
under the large fourth toe, which is the only portion of the foot in contact
with the ground throughout stance. The CoP occurred at the proximal portion of
the toe at initial contact and moved distally until it was centered under the
toe tip just before the foot left the ground. In this way, the alignment of
kinematics and CoP was as accurate as possible.
Instantaneous power at each joint was calculated by multiplying the joint
moment by the angular velocity at that joint. Total limb power was derived by
summing the instantaneous powers from each joint. The net work delivered by
each joint during stance was determined by integrating the power curve for
that joint over the stance time. Total limb work was the sum of work performed
at all of the joints. These values were compared with the net center of mass
work, calculated from GRF and the kinematics of the initial conditions
(Cavagna, 1975).
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Tammar wallabies controlled their acceleration by modulating the propulsive (+HGRF) and breaking (-HGRF) components of the horizontal ground reaction force, with little change in vertical force (VGRF). Representative data from a large acceleration trial, a steady hopping trial, and a large deceleration trial (Fig. 2) show the extremes of the ground reaction force patterns that we observed. An initial breaking force was followed by a propulsive force in all but the largest acceleration and deceleration trials that we recorded (not shown in Fig. 2). Mean GRFs averaged over stance and normalized to the animal's body weight (BW) versus acceleration are shown in Fig. 3. When accelerating, mean +HGRF increased linearly with increased acceleration magnitude (r2=0.93, P<0.0001) while -HGRF remained constant, averaging -0.14±0.06BW (±S.D.). The mean VGRF during accelerations also showed a small but non-significant increase with increased acceleration (r2=0.23, P=0.072). Conversely, when decelerating, mean -HGRF increased linearly with increased acceleration magnitude (r2=0.89, P<0.0001) whereas +HGRF changed very little, averaging 0.11±0.64BW. During decelerations, the mean VGRF was independent of acceleration (r2=0.08, P=0.320).
|
|
Kinematics
Limb protraction and retraction angles were measured as the angle of a line
joining the hip and toe, relative to vertical at first and last contact with
the ground, respectively, with excursion angle being defined as the sum of
these two angles. During accelerations, the retraction angle increased
significantly (Fig. 4B;
r2=0.63, P=0.0001). The protraction angle also
showed a trend towards increasing with increased acceleration, however with
the current sample size this was not significant
(Fig. 4A; r2=0.23, P=0.068). During decelerations, both
protraction and retraction angles increased significantly with increased
deceleration magnitude (Fig.
4A,B; r2=0.53, P=0.008;
r2=0.66, P=0.0001, respectively). Limb excursion
angle also increased significantly with both acceleration and deceleration
magnitude such that minimum limb excursions occurred during steady speed
trials (Fig. 4C;
r2=0.63, P=0.0002; r2=0.74,
P=0.0003, respectively).
|
Because recorded acceleration trials represent a continuum of the animals' acceleration performance during hopping, we selected four trials from each condition to characterize differing kinematic patterns for acceleration and deceleration versus steady speed (Fig. 5). The trials selected represented the extremes of acceleration and deceleration conditions. Mean accelerations for each of the resulting groups were -5.27±0.86 m s-2, -0.07±0.45 m s-2 and 5.88±0.80 m s-2 for deceleration, steady speed and acceleration conditions, respectively. Comparisons among these three sets of trials reveal that the largest differences, with respect to steady speed trials, during decelerations occurred at the knee and MP joints (Fig. 5B,D). The knee showed earlier and increased flexion in the first half of stance followed by decreased extension in the latter half. The MP joint underwent a greater initial extension, followed by flexion and then greater extension in the last third of stance. This resulted in the limb being more flexed at midstance and at toe off (Fig. 2C, inset).
|
Differences in kinematic patterns during acceleration trials relative to steady speed were observed at all four joints. The hip, knee and ankle joints were all more flexed at the onset of stance. The hip then extended throughout the stance phase with no initial flexion (Fig. 5A). Correspondingly, the knee flexed less early in stance and extended more later in stance compared to steady speed trials (Fig. 5B). Being more flexed at the start of stance, the ankle reached peak flexion at midstance but then re-extended to a similar angle seen at the end of stance in both steady and deceleration trials (Fig. 5C). The MP joint flexed to a greater extent later in stance compared with both steady speed and deceleration trials, and then re-extended rapidly at the end of stance (Fig. 5D). The overall result was that the limb was more flexed at the start of stance and underwent a greater amount of net extension throughout stance (Fig. 2A, inset) when the animals accelerated. Consistent with these patterns, net joint excursion angles recorded for all the trials showed a significant relationship with acceleration, with the hip, knee and ankle joints undergoing greater net extension and the MP increased net flexion with increased acceleration (Fig. 6).
|
Joint moments
External and internal (inertial plus gravitational) moments were summed to
give the total net moment at each joint. Internal moments were very small
relative to external moments at all joints except the hip
(Fig. 7). However, even at the
hip joint internal moments never exceeded 15% of the peak external moment.
Whereas the internal moment acts to increase the joint moment at the hip early
in stance during acceleration and steady speed trials, it reduces the
magnitude of the total moment during the middle third of stance when it is
highest. This was the case for all trials. In general, total joint moments
were similar in magnitude and differed between conditions mostly with respect
to timing. For all conditions, the largest peak moments were recorded at the
hip and ankle joints. During deceleration, total joint moments peaked earlier
and fell to nearly zero for the last 20% of stance at all joints but the knee.
Conversely, during acceleration joint moments generally peaked later in
stance.
|
In all trials, the hip moment peaked before those of the other three joints, occurring between 20-30% of stance. When decelerating, the hip moment fell to near zero for the last 30% of stance. In contrast, during accelerations the hip moment declined less rapidly and was maintained until foot off. The joint moment pattern at the knee generally reversed from an initial negative (flexor) moment during the first 20-30% of stance to a positive (extensor) moment for the remainder of stance, as the GRF vector moved posterior to the joint center of rotation. This switch tended to occur earlier in stance during breaking, with the ensuing peak positive moment also occurring earlier and being greater in magnitude. At the ankle joint, the total moment reached a peak at 40% of stance during breaking and steady speed trails, but occurred later during accelerations. Similar to the hip, the joint moment at the ankle declined more rapidly during the latter half of stance during breaking and remained higher during acceleration trials compared with when the animals hopped at a steady speed. The joint moment at the MP was positive in all trials and, like the ankle moment, peaked at 40-50% of stance.
Joint power and net work
Following representative patterns of joint moments
(Fig. 7),
Fig. 8 shows examples of joint
power versus stance duration for the extremes of each condition.
Consistent with the joint moment patterns observed, external and total power
(including that caused by segment inertia and weight) differed only at the hip
and was only detectable during the largest accelerations. Over all trials,
internal work accounted for less then 1% of the total net work done at each
joint. At all joints, except the knee, there was a significant relationship
between net joint work and acceleration
(Fig. 9).
|
|
In general, the hip joint absorbed a small amount of energy as the hip flexed in the first 20% of stance. This was followed by the production of positive power as the hip extended, resulting in positive net work in all trials. The amount of positive power and net positive work performed at the hip increased with increasing acceleration (Fig. 9A). Increased work at the hip was the product of both higher peak power and a longer duration of positive power production (Fig. 8C).
Joint power at the knee generally began with a brief positive peak early in stance, as the knee flexed during a flexor moment. This was followed by a negative peak as the knee continued to flex while the moment shifted to an extensor moment, and finally a second positive peak as the knee re-extended at the end of stance during an extensor moment. The timing of the polarity shifts in knee joint power was variable, and the magnitudes of the peaks tended to be low relative to the other limb joints in any given trial. The resulting net work performed by the knee was nearly always positive and was independent of acceleration (Fig. 9).
The ankle joint showed a very consistent pattern of negative power for the first 40-45% of stance followed by positive power during the remainder of stance. This resulted from the generally symmetrical flexion-extension pattern of the ankle joint, as it was subjected to an extensor moment throughout stance (Fig. 7). The magnitude and duration of the peaks in negative and positive power were strongly associated with each condition (Figs 8 and 9C). During steady speed hopping, negative joint work during the first half of stance was similar to the magnitude of positive work performed during the second half of stance, yielding little or no net joint work. During breaking, shifts in the magnitude and duration of the negative and positive power peaks at the ankle resulted in more negative and less positive work, so that the ankle absorbed energy (net negative work). During accelerations, the magnitude, but not the duration, of positive joint power generated during the latter half of stance changed most. Peak negative power and negative work performed by the ankle remained similar to that observed for steady speed trials. The large increase in the magnitude of positive power resulted in a substantial increase in the amount of net positive work performed at the ankle as acceleration increased (Fig. 9C).
Power at the MP joint was near zero or slightly positive early in stance, but reached a negative peak at midstance and returned to near zero by 80% of stance. In some of the larger accelerations, a second small positive peak at the end stance occurred (Fig. 8A). Surprisingly, the peak magnitude and duration of negative power production increased with increasing acceleration due to greater joint flexion during an extensor moment, resulting in a significant increase in negative work at the MP joint (Fig. 9D).
The net work done on the center of mass (CoM) determined from integration of the ground reaction forces was also strongly correlated with acceleration (r2=0.97, P<0.0001; Fig. 10). However, when compared with the total work done by the limb (summed joint work), CoM work exhibited a significantly steeper slope. Therefore, with increasing acceleration or deceleration, the work done by the limb was less than the overall work done on the animals' CoM. This suggests that a significant amount of power was produced via movements of the trunk and/or tail.
|
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Results from recent in vivo studies in tammar wallabies suggested
that a division of labor exists between the muscle groups of the hind limb,
with power being modulated at the proximal joints by the large muscles acting
at the hip and the knee. Biewener et al.
(2004) showed that when
hopping on level versus inclined surfaces, the ankle extensors
retained spring-like function and contributed negligible net work to move the
animal's center of mass. However, previous work in jumping and sprinting
studies (Aerts, 1998
;
Dutto et al., 2004
;
Jacobs, 1996
) showed that,
while proximal muscles may produce most of the power for the jump, the power
is delivered at the ankle via multi-joint muscles. The results of our study
clearly show this same pattern. Of the four hind limb joints examined, the
ankle displayed the strongest correlation of joint work relative to the
animal's acceleration (Fig. 9),
accounting for 89% of the change in whole limb work versus
acceleration (Fig. 10). The
hip and metatarsophalageal (MP) joints also showed significant correlations
between joint work and acceleration but contributed much less to changes in
whole limb work and power compared with the ankle. Whereas the hip accounted
for 28% of the change in whole limb work by contributing mainly to
acceleration, the MP joint unexpectedly absorbed an increasing amount of
energy with increased acceleration (negative slope). This energy absorption
resulted from increased flexion of the MP joint, which is probably related to
the wallabies increasing the retraction angle of their limb during
accelerations, and represented -24% of the change in energy for the limb as a
whole over the range of acceleration and deceleration observed. In contrast,
the knee joint did not contribute to changes in limb power output.
Mechanical power and work
A goal of our work was to determine whether having muscle-tendon units
specialized for elastic energy savings limits a wallaby's ability to produce
power for accelerations. The potential trade-off that exists between muscles
of differing architecture suggests that the spring-like properties of the
wallaby hind limb may constrain their ability to generate power
(Biewener, 1998;
Biewener and Roberts, 2000
).
However, we found that this was not the case. The largest accelerations
recorded in this study required that the animals generate
4.0 J
kg-1 body mass. Of this, the legs provided
2.6 J
kg-1, indicating that the additional work must be done by movements
of the trunk and tail (see below). This differs from turkeys, in which the
legs provide all of the work for acceleration
(Roberts and Scales, 2004
). On
average, the extensor muscles of the hind limb make up 12% of body mass, which
indicates that for the maximum accelerations observed in this study the hind
limbs produced
79 W kg-1 leg muscle. This is consistent with
values that have been reported for direct in vivo measurements of
muscle power in diverse high power activities, such as bird flight and scallop
jetting (Biewener et al.,
1998
; Marsh et al.,
1992
) and is well within the range estimated for skeletal muscle
(Weis-Fogh and Alexander,
1977
); suggesting no limitation to overall limb power production
as a result of specialized spring-like muscle tendon units. Roberts and Scales
(2002
) reached a similar
conclusion for accelerating turkeys, for which they reported center of mass
power in terms of stroke power, or mean power during stance normalized to
total limb muscle mass. Values reported for turkeys reached a maximum stroke
power of 150 W kg-1. The same calculation for the tammar wallabies
studied here yields a maximum stroke power of
210 W kg-1
extensor limb muscle. Roberts and Scales
(2002
) included flexor and
adductor muscles in their measurement of muscle mass, but it seems unlikely
that these muscles contribute similarly to major extensor muscle groups (on a
per mass basis) to accelerate the animal, and thus were not included in our
measurement of limb muscle mass. For the purpose of comparison, including the
masses of these muscles yields a value of
145 W kg-1 total
hind limb muscle mass in the tammar wallabies, quite similar to that found for
turkeys.
The amount of energy absorbed during the maximum decelerations observed in
this study was 3.6 J kg-1 body mass. As for our observed
maximum accelerations, the hind limbs again accounted for only 61% of the
energy change of the CoM (the remainder probably again resulting from energy
absorption within the trunk of the animal). This equates to approximately -67
W kg-1 limb muscle averaged over a full locomotor cycle, or a
stroke power of -177 W kg-1 extensor muscle over the period of
stance. We are not aware of any direct in vivo measurements of the
power absorption of vertebrate muscle, but isolated muscle experiments
(Abbott et al., 1951
;
Hill, 1960
) and studies of
human running performance (Margaria et
al., 1963
) demonstrate that it is easier for muscles to absorb
than to produce energy. In a demonstration before the Royal Society of an
experiment first conducted by Abbot et al. (1952), A. V. Hill showed that, on
two mechanically linked, opposing bicycles, a woman doing negative work could
easily pedal to resist the efforts of a larger healthy male doing positive
work. This likely relates to a muscle's ability to generate higher forces
while being actively stretched, so that less muscle must be recruited
(consuming ATP) to produce the same tension. Hence, it also seems unlikely
that the negative powers observed during the maximum decelerations recorded
here represent an upper limit to the wallabies' hind limb muscle ability.
It is generally assumed that the legs do the majority of the work of terrestrial locomotion. As bipeds, we therefore expected that nearly all of the power needed for changing speed would be provided by the wallabies' hind limbs. Surprisingly, this was not the case. The amount of work done on the animal's CoM increased more rapidly with acceleration than did the work being done by the hind limbs (Fig. 10). For the largest accelerations and decelerations, the limbs accounted for only 60-65% of the work done on the CoM. During large accelerations, we observed that the wallaby's trunk and tail underwent considerable extension, substantially raising the animal's center of mass. Given that the average force experienced during stance in a large accelerating hop is approximately 245 N, a displacement of 1 cm would provide 2.45 J or 0.36 J kg-1 body mass of CoM work. Therefore, only a small displacement of the center of mass (approximately 4 cm in this case) would be required to account for the difference in work provided solely by the limbs during accelerations and decelerations. While this calculation is only approximate, it demonstrates how movements of the body and tail could readily account for 35% or more of work done on the center of mass in more extreme cases of acceleration and deceleration. Accurate movements of the center of mass are difficult to track, and with our data we are unable to test the extent to which such movements of the trunk and tail contribute to CoM acceleration. Nevertheless, it seems that this is an important component by which wallabies change speed while hopping over level terrain and may also be important to their ability to generate power when jumping and absorbing energy when landing.
Do thin tendons limit acceleration?
The ability to generate power may not be the only constraint on having
muscle-tendon units that favor elastic energy storage. In order to store a
significant amount of strain energy, the tendons must be thin enough to
undergo relatively high strains during steady speed locomotion. In general,
many mammalian tendons are relatively thick and operate with an average safety
factor of about eight or higher (Ker et
al., 1988). However, the ankle extensor tendons of tammar
wallabies hopping at sub-maximal steady state speeds have safety factors
between three and four (Biewener et al., 1995). Because of this, it is
possible that increased forces required to accelerate the animal could
potentially damage or rupture their tendons. Indeed, recent studies of fatigue
rupture in wallaby tendons (Ker et al.,
2000
; Wang et al.,
1995
) indicate that significant fatigue damage may occur on a
regular basis, requiring ongoing tendon repair.
In the context of acceleration and deceleration, wallabies appear to
minimize this problem by maintaining relatively uniform peak joint moments at
the ankle (Fig. 7), resulting
in a relatively constant safety factor for their leg tendons. We estimated the
average peak ankle extensor tendon stresses here to be 24.16±5.48 MPa,
based on peak joint moment (mean 15.89±3.60 Nm), muscle moment arm
(25.30±1.70 mm) and tendon cross sectional area (0.26±0.02
cm2). Given a failure strength of 100 MPa for tendon
(Ker et al., 1988), the
wallabies in this experiment operated with an average safety factor of
4.32±0.88, which did not vary with acceleration
(r2=0.02, P=0.508). The wallabies maintained
uniform peak joint moments while changing speed by maintaining the alignment
between their limbs and the resultant GRF vector. When accelerating, wallabies
significantly increased the retraction angle of their limbs
(Fig. 4B) with little increase
in limb protraction angle (Fig.
4A). As a result, the limb was held in line with the anteriorly
directed GRF vector through most of stance
(Fig. 2A, inset). When
decelerating, limb protraction and retraction angles both increased
significantly (Fig. 4A,B). The
former aligns the limb with the GRF vector when the forces are highest, while
the latter may reduce the ankle joint moment in the last 20-30% of stance by
aligning the joint more closely with the GRF vector
(Fig. 2C, inset). Consequently,
although wallabies operate with relatively low tendon safety factors that
favor elastic energy savings, they are able to maintain fairly constant peak
tendon stresses by shifting their hind limb orientation to match changes in
the direction of the ground reaction force when accelerating to change
speed.
Do wallaby ankle extensors perform substantial work?
Prior in vivo studies of tammar wallabies hopping on an incline
showed that the ankle extensors do not contribute to the work of raising the
animals' center of mass (Biewener et al.,
2004), suggesting that the role of these muscle-tendon units in
locomotion is restricted to spring-like behavior. However, during
accelerations and decelerations, much of the work produced by the limb was
delivered at the ankle. This raises the question of whether the work produced
at the ankle is done by the ankle extensors or is transferred from more
proximal joints via bi-articular muscles. While we cannot measure muscle work
directly in this study, our results suggest that the ankle extensor muscles
contribute some fraction of the work that appears at the ankle joint during
acceleration and deceleration. Muscle-tendon length of the ankle extensors can
be estimated from their moment arms at the knee and ankle and the angle
changes at these joints. Net joint angle excursion increased significantly
with acceleration and was of comparable magnitude at both the ankle and the
knee (Fig. 6). Given the larger
moment arm of the ankle extensors at the ankle (mean: 23.80±1.03 mm)
versus the knee (mean: 9.50±2.13 mm), this indicates a
significant increase in calculated muscle-tendon unit length with increased
acceleration (r2=0.55, P<0.0001). For the
maximum accelerations recorded, we estimate that the muscle-tendon units
underwent an overall net shortening of
8% during stance. A similar
magnitude of net lengthening was observed in maximum decelerations. Because
net changes in muscle-tendon unit length can only be caused by net shortening
or lengthening of the muscles, this indicates that some work was done while
the muscles were generating tension. Although indirect and prone to error,
this analysis suggests that the ankle extensors contribute to changes in limb
work when wallabies change speed during acceleration and deceleration, in
contrast to there being no evidence of this during inclined hopping
(Biewener et al., 2004
).
Even so, it seems probable that a large fraction of the work and power
delivered at the ankle joint is produced by more proximal muscles of the limb.
Previous studies of jumping, landing and sprinting have shown that a
substantial amount of power is transferred between joints via bi-articular
muscles during these activities, with most of the power appearing at the ankle
joint (Aerts, 1998;
Jacobs et al., 1996
;
Prilutsky and Zatsiorsky,
1994
). Consistent with these studies, we also observed that most
of the power produced by the limb is delivered at the ankle joint when
wallabies change speed. If this power were produced by the wallaby's ankle
extensors alone, it would suggest a value as high as 325 W kg-1
muscle, which seems unlikely (Weis-Fogh
and Alexander, 1977
; Peplowski
and Marsh, 1997
). Instead, much of the power at the ankle is
likely to be transferred from hip and the knee extensors via the
ankle extensors, which could do so by contracting with little net length
change. The knee extensors, which constitute a larger percentage (29%) of the
total hind limb muscle mass than the ankle extensors (20%), appear well suited
for contributing this power. Effective power transfer also requires that the
knee and ankle joints extend simultaneously, consistent with the pattern that
we observed (Fig. 5). Based on
these considerations, we conclude that power transfer between proximal muscles
and distal joints likely plays an important role in power generation and
absorption when wallabies change speed, similar to the patterns described for
jumping galagos, humans and horses (Aerts,
1998
; Jacobs et al.,
1996
; Dutto, 2004). Interestingly, however, these results differ
from those recently found in accelerating turkeys
(Roberts and Scales, 2004
), in
which power transfer is considered to be minimal. Such differences may be due
to differences in the timing of limb extension patterns as well as relative
proportions of knee and ankle extensor muscles. In turkeys, the mass of the
ankle extensors is more then three times that of the knee extensors
(Roberts and Scales,
2004
).
Conclusions
Over the range of performance that we observed, our results show that the
energy change required for accelerating and decelerating is predominately
modulated at the ankle joint and to a lesser degree at the hip and
metatarsophalageal joint. Based on earlier work showing a limited contribution
of ankle extensors in useful mechanical work during incline hopping
(Biewener et al., 2004),
combined with analyses of joint dynamics reported here, we interpret the power
that emerges at the ankle joint as being largely produced by more proximal
muscles acting at the hip and knee. This power is transferred via the
bi-articular ankle extensor muscles, which themselves need not change length
appreciably. Our preliminary analysis suggests that the ankle extensors do
contribute some additional work to change the wallaby's speed, but it is
difficult to quantify how work is partitioned between the ankle extensors and
more proximal limb extensors. Further in vivo studies and more
extensive muscle modeling will be required to evaluate the role of power
transfer as we envision it here. While the changes in speed we were able to
record probably do not represent maximal performance, our estimates of
mass-specific power for the wallabies' hind limb muscles are well within the
range for mammalian skeletal muscle and are consistent with values reported
for other high power output activities. Although we estimate tendon strains in
the ankle extensors to be relatively high, an increased risk of tendon failure
does not appear to pose a limit to a tammar wallaby's acceleration performance
because peak ankle moments (and resulting tendon strains) do not increase
significantly with acceleration. Therefore, we conclude that having
muscle-tendon units specialized for elastic energy storage need not limit a
tammar wallaby's ability to accelerate or decelerate.
![]() |
Acknowledgments |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Abbott, B. C., Aubert, X. M. and Hill, A. V. (1951). The absorption of work by a muscle stretched during a single twitch or a short tetanus. Proc. R. Soc. Lond. B 139,86 -104.[Medline]
Abbott, B. C., Bigland, B. and Ritchie, J. M. (1952). The physiological cost of negative work. J. Physiol. 117,380 -390.
Aerts, P. (1998). Vertical jumping in Galago senegalensis: the quest for an obligate mechanical power amplifier. Phil. Trans. R. Soc. Lond. B 353,1607 -1620.[CrossRef]
Alexander, R. McN. (1988). Elastic Mechanisms in Animal Movement. Cambridge Cambridge, UK: University Press.
Alexander, R. McN. and Vernon, A. (1975). Mechanics of hopping by kangaroos (Macropodidae). J. Zool. 177,265 -303.
Alexander, R. McN., Maloiy, G. M. O., Ker, R. F., Jayes, A. S. and Warui, C. N. (1982). The role of tendon elasticity in the locomotion of the camel (Camelus dromedaries). J. Zool. 198,293 -313.
Biewener, A. A. (1998). Muscle function in-vivo: A comparison of muscles used for elastic energy savings versus muscles used to generate mechanical power. Amer. Zool. 38,703 -717.
Biewener, A. A. and Baudinette, R. V. (1995). In vivo muscle force and elastic energy storage during steady-speed hopping of tammar wallabies (Macropus eugenii) J. Exp. Biol. 198,1829 -1841.
Biewener, A. A. and Roberts, T. J. (2000). Muscle and tendon contributions to force, work and elastic energy savings: a comparative perspective. Exercise Sports Sci. Rev. 28, 99-107.[Medline]
Biewener, A. A., Corning, W. R. and Tobalske, B. W.
(1998). In vivo pectoralis muscle force-length behavior
during level flight in pigeons (Columbia livia). J. Exp.
Biol. 201,3293
-3307.
Biewener, A. A., McGowan, C. P., Card, G. M. and Baudinette, R.
V. (2004). Dynamics of leg muscle function in tammar
wallabies (M. eugenii) during level versus incline hopping.
J. Exp. Biol. 207,211
-223.
Blickhan, R. and Full, R. J. (1992). Mechanical work in terrestrial locomotion. In Biomechanics: A Practical Approach (ed. A.A. Biewener) New York: Oxford University Press.
Bobbert, M. F., Huying, P. A. and van Ingan Schenau, G. J. (1986). A model of the human triceps surae muscle-tendon complex applied to jumping. J. Biomech. 19,887 -898.[CrossRef][Medline]
Cavagna, G. A. (1975). Force plates as
ergometers. J. Applied Physiol.
39,174
-179.
Cavagna, G. A., Heglund, N. C. and Taylor, C. R. (1977). Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure. Am. J. Physiol. 233,R243 -R261.[Medline]
Daley, M. A. and Biewener, A. A. (2003). Muscle
force-length dynamics during level versus incline locomotion: a
comparison of in vivo performance of two guinea fowl ankle extensors.
J. Exp. Biol. 206,2941
-2958.
Dickinson, M. H., Farley, C. T., Full, R. J., Koehl, M. A. R.,
Kram, R. and Lehman, S. (2000). How animals move: an
integrative view. Science
288,100
-106.
Dimery, N. J., Alexander, R. McN. and Ker, R. F. (1986). Elastic extension of the leg tendons in the locomotion of horses (Equus caballus). J. Zool. 210,415 -425.
Dutto, D. J., Hoyt, D. F., Clayton, H. M., Cogger, E. A. and
Wickler, S. J. (2004). Moments and power generated by the
horse (Equus caballus) hind limb during jumping. J. Exp.
Biol. 207,667
-674.
Hill, A. V. (1960). Production and absorption of work by muscle. Science 131,897 -903.[Medline]
Jacobs, R., Bobbert, M. F. and van Ingan Schenau, G. J. (1996). Mechanical output from individual muscles during explosive leg extensions: the role of biarticular muscles. J. Biomech. 29,513 -523.[CrossRef][Medline]
Ker, R. F., Dimery, N. J. and Alexander, R. McN. (1986). The role of tendon elasticity in hopping in a wallaby (Macropus rufogriseus). J. Zool. Lond. A 208,417 -428.
Ker, R. F., Alexander, R. McN. and Bennett, M. B. (1988). Why are mammalian tendons so thick? J. Zool. 216,309 -324.
Ker, R. F., Wang, X. T. and Pike, A. V. L.
(2000). Fatigue quality of mammalian tendons. J. Exp.
Biol. 203,1317
-1327.
Margaria, R., Cerretelli, P., Aghemo, P. and Sassi, G. (1963). Energy cost of running. J. Appl. Physiol. 18,367 -370.
Marsh, R. L., Olson, J. M. and Guzik, S. K. (1992). Mechanical performance of scallop adductor muscle during swimming. Nature 357,411 -413.[CrossRef][Medline]
Peplowski, M. M. and Marsh, R. L. (1997). Work
and power output in the hindlimb muscles of Cuban tree frogs Osteopilus
septentrionalis during jumping. J. Exp. Biol.
200,2861
-2870.
Prilutsky, B. I. and Zatsiorsky, V. M. (1994). Tendon action of two-joint muscles: Transfer of mechanical energy between joints during jumping, landing and running. J. Biomech. 27,25 -34.[CrossRef][Medline]
Prilutsky, B. I., Herzog, W. and Leonard, T. (1996). Transfer of mechanical energy between ankle and knee joints by gastrocnemius and plantaris muscles during cat locomotion. J. Biomech. 29,391 -403.[CrossRef][Medline]
Roberts, T. J. (2002). The integrated function of muscles and tendons during locomotion. Comp. Biochem. Physiol. Mol. Integr. Physiol. 133,1087 -1099.[CrossRef]
Roberts, T. J. and Scales, J. A. (2002).
Mechanical power output during accelerations in wild turkeys. J.
Exp. Biol. 205,1485
-1494.
Roberts, T. J. and Scales, J. A. (2004).
Adjusting muscle function to demand: joint work during acceleration in wild
turkeys. J. Exp. Biol.
207,4165
-4174.
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.
Roberts, T. J., Chen, M. S. and Taylor, C. R.
(1998). Energetics in bipedal running. II. Limb design in running
mechanics. J. Exp. Biol.
201,2753
-2762.
Taylor, C. R. (1994). Relating mechanics and energetics during exercise. Adv. Vet. Sci. Comp. Med. 38A,181 -215.[Medline]
Wang, X. T., Ker, R. F. and Alexander, R. McN. (1995). Fatigue rupture of wallaby tail tendons. J. Exp. Biol. 198,847 -852.[Medline]
Weis-Fogh, T. and Alexander, R. McN. (1977). The sustained power output from striated muscle. In Scale Effects in Animal Locomotion (ed. T. J. Pedley), chapter 30. London: Academic Press.
Winter, D. A. (1990). Biomechanics and Motor Control of Human Movement. Second edition. New York: John Wiley and Son, Inc.