Contribution of the forelimbs and hindlimbs of the horse to mechanical energy changes in jumping
1 Institute for Fundamental and Clinical Human Movement Sciences, Vrije
Universiteit, van der Boechorstraat 9, NL-1081 BT Amsterdam, The
Netherlands
2 Department of Equine Sciences, Faculty of Veterinary Medicine, Utrecht
University, Yalelaan 12, NL-3584 CM Utrecht, The Netherlands
* Author for correspondence (e-mail: M_F_Bobbert{at}fbw.vu.nl)
Accepted 5 November 2004
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Summary |
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Key words: Equus caballus, locomotion, biomechanics, elastic strain energy, energy storage, muscle work
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Introduction |
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Given the availability of sophisticated measurement equipment and the accumulation of knowledge over the years, one would expect that little remained to be discovered about horse locomotion. However, we were unable to find in the literature a comprehensive analysis of the contribution of the forelimbs and hindlimbs to the energy changes in galloping and jumping horses.
This is perhaps not so surprising if one realizes that in these locomotor
tasks the forelimbs, and usually also the hindlimbs, are used asymmetrically.
Hence, an in-depth analysis of the role of the limbs would require
simultaneous measurement of the kinematics of the body segments and the ground
reaction force vector under each of the four legs, which is almost impossible.
However, several studies have contributed pieces of the puzzle. For example,
for galloping, Minetti et al.
(1999) have calculated
mechanical energy changes from kinematics, while McGuigan et al. (2003) have
estimated the amount of elastic energy stored and released by the forelimbs.
For the hindlimb push in jumping, van den Bogert et al.
(1994
) have calculated
mechanical energy changes from kinematics, while Dutto et al.
(2004
) have performed an
inverse dynamics analysis using kinematics and ground reaction forces measured
with a force plate. Unfortunately, however, the results of the latter two
studies cannot be combined because the jump heights were very different: 1.50
m in the study of van den Bogert et al.
(1994
) and 63 cm in the study
by Dutto et al. (2004
).
The purpose of the present study was to gain more insight into the contribution of the forelimbs and hindlimbs of the horse to energy changes during the push-off for a jump. For this purpose, we collected kinematic data from 5-year-old Warmbloods performing free jumps over a 1.15 m high fence. From these data, we first calculated the ground reaction force vector and the mechanical energy changes of the body. To support the validity of the approach it was shown that the calculated ground reaction forces were similar to ground reaction forces measured in other studies using force plates. The mechanical energy changes were then combined with the changes in length and joint angles of the limbs. We were especially interested in the amount of energy stored and released by the forelimbs, which was estimated from the distance between elbow and hoof.
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Materials and methods |
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Kinematic data were collected while the horses performed free jumps over a
vertical target fence in a jumping track. The height of this fence, 1.15 m,
was chosen such that all horses could clear it without too much difficulty (at
this stage in their career, the maximum height that some of the horses could
clear with a rider on their back was about 1.40 m; others could jump over 1.50
m). The approach to the target fence was standardized: the target fence was
preceded by two lower vertical fences placed at distances that restricted the
horses to one canter stride in between each pair of fences. The second fence
was 6.40 m from the first fence and the target fence 7.0 m from the second
fence. More details of the experimental setting have been provided elsewhere
(Santamaría et al.,
2005).
The horses were familiarized with the experimental setting by having them practice in the jumping track a few days before the day of the actual measurements. For the measurements, skin markers were fixed at anatomical locations on the body (Fig. 1). The markers were monitored in stance and during jumping by six infrared cameras operating at 240 Hz (ProReflex, Qualisys Medical AB, Göteborg, Sweden). The cameras were placed laterally to the target fence on a semicircle, such that the field of view included the last canter stride before the target fence, the jump, and the first canter stride after the fence. After warming up, the horses performed free jumps until we had collected four successful jumps in which the fence was approached with a left lead of canter, as well as four successful jumps in which the fence was approached with a right lead of canter (i.e. with the left forelimb as trailing limb). From these, we selected for further analysis one jump in which the left forelimb was the leading limb, and one in which it was the trailing limb.
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The time histories of the marker coordinates were first smoothed at 8 Hz
using a 4th order zero-lag Butterworth filter. Next, we had to deal with the
problem that markers placed on the skin may move considerably relative to the
underlying skeletal landmarks (van Weeren et al.,
1990a,1990b
).
For walking and trotting, the errors have been analysed and correction
algorithms developed (van den Bogert et
al., 1990
), but for jumping no further information was available.
To remedy the problem for the limbs we assumed, as others have done previously
(Dutto et al., 2004
;
van den Bogert et al., 1994
),
that the limbs were chains of rigid segments interconnected in hinge joints,
with joint axes and lengths of the rigid segments defined by the markers
applied in square standing (Fig.
1). Assuming furthermore that the limbs moved only in the sagittal
plane and that no error occurred in the markers on the hoofs, we optimised on
each frame the configurations of the chains of the left forelimb and the left
hindlimb by minimizing the sum of squared distances between the locations of
the chain joints and the actual marker locations. The optimised coordinates of
the chains were used to calculate distances between selected skeletal
landmarks, segment angles and their derivatives, and joint angles. The
distance between elbow and hoof of the left forelimb was used to estimate the
force carried by the limb, assuming that it behaved like a linear spring with
a stiffness of 166 N m-1 kg-1
(McGuigan and Wilson,
2003
).
The segmental model of Buchner et al.
(1997) was used to determine
the locations of mass centres of the limb segments and the head and neck. To
determine the location of the centre of mass of the trunk, which accounts for
more than 65% of the total mass of the horse, a rigid template was defined
using selected markers in square standing (see
Fig. 1). Subsequently, for each
frame during the jumps, the position and orientation of this template was
found by minimizing the sum of squared differences between template marker
locations and actual marker locations. The movement of the centre of mass of
the trunk, and the trunk orientation, were extracted from the movement of the
template during the jump. The motion of all segmental mass centres, combined
with segment inertial parameters (Buchner
et al., 1997
), was used to calculate the position, velocity and
acceleration of the centre of mass (COM) of the horse. For this calculation we
had to assume that the right limbs moved symmetrically with the left limbs,
because we did not have markers on the right shoulder, elbow, hip and stifle
of the animals. The error incurred by this assumption is small, however,
because the right forelimb and right hindlimb each contribute only about 6% of
the total mass of the horse, and they do in fact move more or less in phase
with their counterparts during the canter and jump.
From the motion of the segments and the COM of the horse, we calculated the
following mechanical energy components: potential energy
(Epot), rotational energy (Erot),
kinetic energy due to the horizontal velocity of COM
(Ekin,COM,x), kinetic energy due to the vertical velocity
of COM (Ekin,COM,y), kinetic energy due to the velocity of
segmental mass centres relative to the mass centre of the body
(Erest), and total energy (Etot, sum
of the previous terms). We also calculated the effective energy, i.e. the sum
of Epot and Ekin,COM,y, which is the
energy ultimately contributing to jump height
(Bobbert, 2001). Taking the
derivative of Etot with respect to time yielded total
power output (
tot). The magnitude of the total
ground reaction force (FGR) was calculated from body weight
and acceleration of the centre of mass yCOM. Its line of
action was calculated using the fact that the moment of the ground reaction
force about the centre of mass equals the rate of change of angular momentum,
which also was calculated from the segmental motions.
The push off for the jump occurs during the last canter stride before the target fence. In a canter stride the sequence of limb placement is the following: trailing hindlimb - leading hindlimb - trailing forelimb - leading forelimb. Each limb is placed anterior relative to the previously placed limb. In the present study, the total push-off was divided into a forelimb push and a hindlimb push (Fig. 2). The forelimb push started with touchdown of the trailing forelimb and ended with take-off of the leading forelimb, as determined from hoof kinematics. The hindlimb push started with touchdown of the trailing hindlimb and ended with take-off of the leading hindlimb. Most horses placed the hindlimbs very close together for the final push, which sometimes caused the marker on the hoof of the right hindlimb to be temporarily lost from view. In those cases we used only the kinematics of the left hind hoof to define the hind limb push. During both the forelimb push and the hindlimb push, we also detected the instant that the total energy was minimal.
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Results |
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Considering the similarity of the left lead jumps and the right lead jumps, we decided to average the mechanical variables over all jumps for the sake of conciseness in presenting the results. Average time histories for force and power are shown in Fig. 4, and average time histories for energy are presented in Fig. 5. The amount of kinetic energy due to velocity of segmental mass centres relative to COM was negligible and is not presented. Because average time histories tend to smooth out peaks that occur asynchronously in different horses, we also extracted relevant values from the individual curves; their means and standard deviations are presented in Table 1 for the forelimb push and in Table 2 for the hindlimb push. During the forelimb push, the total energy first dropped by 3.2 J kg-1 and then increased again by 4.2 J kg-1. During the hindlimb push, the total energy first dropped only slightly by 1.6 J kg-1 and then increased again by 4.1 J kg-1. The changes in total energy during the forelimb push were primarily due to changes in Ekin,COM,x. At the end of the forelimb push, this energy term was 1.6 J kg-1 less than at the start of the forelimb push, corresponding to a reduction of the horizontal velocity of COM from 6.3 to 6.0 m s-1. The effective energy increased by 2.3 J kg-1 during the forelimb push. During the hindlimb push, the increase in total energy was due almost entirely to a change in effective energy by 4 J kg-1. The large inter-individual variation in total energy was primarily due to inter-individual differences in the overall speed during the push-off. This can be confirmed from Fig. 5, which presents not only the 95% confidence limits for the absolute energy changes but also the 95% confidence limits for the energy changes relative to the mean value during the push-off; the latter are much smaller than the former. The same was true for Ekin,COM,x and Epot, with differences in offset of Epot being primarily due to differences in size of the horses.
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To gain insight into the role of the limbs, it is important to look at the changes in their length and joint angles. Average time histories for relevant length measures of the left forelimb and hindlimb are shown in Fig. 6, and joint angle histories are shown in Fig. 7. At this point it is relevant to note that during the stance phase of the limbs, it made little difference for most of the variables whether we calculated them from the original marker coordinates or from the corrected coordinates, obtained by fitting chains of rigid segments to the limbs. However, there were a few important variables for which it did make a difference: the distance between elbow and coronet, the shoulder angle and the elbow angle. The mean time-histories of these variables without correction have been shown with dotted curves for the trailing forelimb in Figs 6 and 7. With correction, the distance from elbow to coronet in the trailing left forelimb went from 0.889±0.026 m to 0.836±0.042 mand back again to 0.888±0.029 m during the forelimb push. When the left forelimb was leading, these values were 0.897±0.025 m, 0.853±0.033 m, and 0.899±0.029 m, respectively. As explained in Materials and methods, the distance between elbow and coronet was used to estimate the force carried by the forelimb. The results are presented in Fig. 8. As expected, the left forelimb reached its peak force during the first part of the forelimb push when it was trailing, and during the second part when it was leading. The peak force carried by this limb was 13.6±2.5 N kg-1 when it was trailing and 10.4 ± 2.6 N kg-1 when it was leading (values are means ± S.D. of peak values extracted from individual curves). Fig. 8 also shows the total force obtained by adding the force in the left limb during the jumps in which it was trailing to the force in that limb for the jumps in which it was leading, just to give a rough estimate of the contribution of the forelimbs to the ground reaction force.
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Discussion |
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In the literature, we found one paper by Schamhardt et al.
(1993) reporting ground
reaction forces measured using a force plate while a horse was jumping a 1.10
m high fence. Time histories were presented in that paper for the ground
reaction forces under each of the individual limbs, but for obvious reasons
these time histories pertain to different jumps and, unfortunately, they were
not synchronized. The forces of the hindlimbs may safely be added, because the
hindlimbs operate almost symmetrically, but adding the forces of the forelimbs
will tend to overestimate the total force because the forelimbs operate
asymmetrically (Fig. 8). In any
case, for each of the forelimbs Schamhardt et al.
(1993
) report a peak
horizontal braking force of about 4 N kg-1 in the first part of the
forelimb push, and a peak propulsive force of 1-2 N kg-1 in the
second part of the forelimb push, with the braking impulse being greater than
the forward impulse. Total forces calculated in the present study were of
similar magnitude (Fig. 4), and
also the braking impulse was greater than the forward impulse. Albeit
reassuring, this is not conclusive because considerable variation has been
reported in the extent to which horses slow down before jumping over an
obstacle (Merkens et al.,
1991
; Schamhardt et al.,
1993
). This was also true for the horses in the present study; the
reduction in horizontal velocity during the forelimb push ranged from 0.05 to
0.71 m s-1 [the horse jumping 1.10 m high in the study of
Schamhardt et al. (1993
)
produced a net braking impulse with both forelimbs of about 0.5 Ns
kg-1; if it were only for the forelimbs, this horse would have
slowed down by 0.5 m s-1]. The peak vertical force during the
forelimb push reported by Schamhardt et al.
(1993
) was about 17 N
kg-1 in the trailing forelimb and 13 N kg-1 in the
leading forelimb. These numbers add up to a total force value greater than the
one calculated in this study (Fig.
4), but this is not problematic because the force peaks of the
trailing and leading forelimb do not occur simultaneously
(Fig. 8). In contrast with the
forelimbs, the hindlimbs operate almost symmetrically during the push off. The
peak braking force and the subsequent peak propulsive force of both hindlimbs
together were about 6-8 N kg-1 in the study of Schamhardt et al.
(1993
). These peak values are
very similar to the values calculated from kinematics in this study
(Fig. 4). The same was true for
the peak vertical force, which was about 23 N kg-1 in the study by
Schamhardt et al. (1993
).
Support for the validity of the variables calculated from kinematics can
also be obtained from the fact that the results were in line with
biomechanical principles. For instance, as required, the vertical force
calculated in the airborne phase was close to zero
(Fig. 2; see also
Santamaría et al.,
2004b), the effective energy in this phase was almost constant
(Santamaría et al.,
2004b
), and the vertical displacement of COM in the airborne phase
calculated from the vertical velocity of COM at take-off was within 1 cm from
the displacement derived directly from the height of COM (Santamaría et
al.,
2004a
,b
).
In this study we could even go so far as to calculate the centre of pressure
of the ground reaction force. Because this brings together both the calculated
ground reaction force and the rate of change of angular momentum, it is most
vulnerable to errors. Nevertheless, during the major part of the forelimb push
and the hindlimb push, the centre of pressure was found to be at a plausible
location (Fig. 3), supporting
the validity of the force and energy calculations from kinematics. During the
last 20% of the forelimb push, the centre of pressure was found outside the
base of support (Fig. 3), which
is obviously impossible. Moreover, in this phase the horizontal component of
the ground reaction force was unrealistically high (it is a friction force, so
it cannot be larger than the vertical component of the ground reaction force).
In this phase of the push-off, the animals had started to flex their trunk and
the template did not fit as well as it did in the earlier phases of the
push-off, which probably caused the force calculations to run awry. In the
first 20% of the hindlimb push the centre of pressure was also found outside
the base of support (Fig. 3),
but thereafter it behaved realistically again until the last 20% of the
push-off. It should be stressed again that unrealistic centre of pressure and
force values do not necessarily mean that the energy values were erroneous,
because calculation of the latter involves lower derivatives than calculation
of the former.
Due to the relatively small mass of the limbs, errors in limb kinematics
would hardly show up in the energy and force calculations, and therefore the
validity of the calculated limb kinematics requires a separate treatise. The
key question is whether fitting chains of rigid segments to the limbs, as we
did, helps to correct for movement of skin markers relative to the bony
landmarks. The data collected by van Weeren et al.
(1990a,b
)
would be suitable to investigate this for walking and trotting, but to the
best of our knowledge such an investigation has not been conducted so far, so
independent support for the validity of the limb kinematics is lacking.
However, some confidence can be gained from the following. One of the most
important variables in the present study was the distance between elbow joint
and coronet, because it was used to estimate the force and energy storage in
the forelimbs. As is appropriate for a passive spring, we found that the
maximum distance at touch-down of the left forelimb was the same as that at
lift-off, albeit that its largest value was about 1 cm greater in the jumps in
which it was leading than in those in which it was trailing. Also, the peak
forces calculated for the trailing and leading left forelimb were 13.6 and
10.4 N kg-1, respectively, not far from the peak vertical forces of
17 N kg-1 and 13 N kg-1 measured using a force platform
by Schamhardt et al. (1993
).
Moreover, the sum of the force curves of the trailing and leading left
forelimb (Fig. 8) approximates
the magnitude of the calculated total ground reaction force
(Fig. 4). These findings, we
feel, lend indirect support for the validity of the calculated limb
kinematics. Below, we shall assume that the calculations of energy changes and
limb kinematics are correct.
Contribution of the forelimb push to energy changes
The total energy first decreased by 3.2 J kg-1 until about the
middle of the forelimb push, and then increased by 4.2 J kg-1
(Fig. 5, Table 1). At the end of the
forelimb push, however, Ekin,COM,x was 1.6 J
kg-1 less than at the start while the effective energy was 2.3 J
kg-1 greater than at the start. It is tempting to speculate that
the forelimbs operate as the pole in pole vaulting
(Leach and Ormrod, 1984) or as
a pogo-stick (Wilson et al.,
2001
), the idea being that kinetic energy is first stored in the
forelimb tendons, and subsequently released to regenerate kinetic energy and
potential energy. For this `pogo-stick mechanism' to fully explain the
mechanical energy changes during the forelimb push, the two forelimbs together
should be able to store all the energy lost, about 3.2 J kg-1 or
1900 J. It has been claimed: "In a 500 kg horse, about 1000 J of
elastic energy are stored in the digital flexor tendons and suspensory
ligament (interosseus muscle) of each leg in each stride"
(Wilson et al., 2001
). In a
later study, McGuigan and Wilson
(2003
) conceptually divided
the forelimb into two springs: a proximal spring from the proximal end of the
spina scapulae to the elbow, and a distal spring from the elbow to the foot.
The latter was shown to behave as a linear spring with a stiffness of 166 N
m-1 kg-1, or 100 kN m-1 (these values follow
unmistakably from their Fig. 2,
but McGuigan and Wilson themselves arrive at a stiffness of 60 kN
m-1). In the present study, at the instant that the minimum was
reached in total energy, the length of the distal spring was reduced on
average by 5.3 cm in the left forelimb when it was trailing and by 4.4 cm when
it was leading (see also Fig.
6), and the amount of energy stored was estimated to be on average
246 J and 140 J, respectively (note that the stored energy increases with the
square of the compression; because the latter varied among horses, the average
stored energy cannot be derived from the average compression). This means that
the total energy stored in both distal springs together was only about 400 J
on average. The leg as a whole, of course, shortens more than the distal
spring (Fig. 6), which was
partly due to shortening of the proximal spring [only partly, because the
concept developed by McGuigan and Wilson
(2003
) does not take into
account the important changes in elbow angle
(Fig. 7)]. However, the
proximal spring is not really a spring: although biceps has a fibrous
component, the leg above the elbow is primarily made up of muscle. Although
some energy might surely be stored in series elastic elements of these
muscles, most of the compression involves energy dissipation by muscle fibres
acting eccentrically, transforming energy into heat. The left forelimb reached
a peak compression of only 7.1 cm when it was leading, but a peak compression
of no less than 15.6 cm when it was trailing. Obviously, in the trailing
forelimb there is room for considerable dissipation of energy by the elbow
extensors, such as the large triceps brachii, and muscles spanning the
shoulder, such as supraspinatus. Perhaps lengthening of the muscle fibres of
the digital flexors also dissipates some energy. Additionally, the muscles
connecting the scapula to the trunk and neck may dissipate energy while
actively resisting rotation of the shoulder blade relative to the trunk.
Finally, some energy storage may occur in the vertebral column
(Minetti et al., 1999
).
The energy stored in elastic components will be released again and contribute to the gain of total energy during the second half of the forelimb push, but the energy dissipated needs to be regenerated in concentric contractions, primarily of the muscles just mentioned. Note that the length of the leading left forelimb was about 4 cm greater at take-off than at touch-down (Figs 6, 7) due to elbow extension (Fig. 7). This implies that the elbow extensors in the leading forelimb generate more energy than they dissipate.
Contribution of the hindlimb push to energy changes
The contribution of the hindlimb push to total energy changes during
jumping was previously studied by van den Bogert et al.
(1994) and Dutto et al.
(2004
). van den Bogert et al.
(1994
) studied the kinematics
of the hindlimb push in elite show-jumping horses clearing a 1.5 m high fence.
From their kinematic data they calculated that the horses produced no less
than 13 000 J, most of which was attributed to a change in
Ekin,COM,x (the horizontal velocity was initially 4.5 m
s-1, dropped to 3.5 m s-1, and then increased to 6.5 m
s-1). Assuming that the horses had a mass of 600 kg they produced
almost 22 J kg-1, thereby outperforming the lesser galago, leopard
and antelope, which are able to produce only 20 J kg-1 (for
references, see Bennet-Clark,
1977
). Dutto et al.
(2004
) conducted an inverse
dynamics analysis of the hindlimb push in horses jumping a 0.63 m high fence,
which was approached at a trotting speed of 3.25 m s-1. The sum of
the work performed about the hip, stifle, tarsus and MTP-joint was only 1.4 J
kg-1 for both limbs together. These values are very different from
the ones that we observed in the present study, in which the total energy
increased by about 2.5 J kg-1 during the hindlimb push. It seems
that the height of the fence and the speed at which it is approached (which
was controlled by the riders in the study of
van den Bogert et al., 1994
)
is of decisive importance for the energy changes during the jump.
In the present study, the positive work contribution by the hindlimb is
reflected by an increase in the total length of the legs from touch-down to
take-off. At touch-down, the length of the legs was not maximal, primarily
because the hip was flexed. The length of the hindlimbs first decreased by
11.8 cm and then increased by 23.1 cm (Fig.
6). Interestingly, the initial decrease in length of the leg was
smaller than the decrease in the distance between stifle and coronet
(Fig. 6), which amounted to
17.9 cm on average. The reason was that the hip joint extended
(Fig. 7), which implies that
part of the energy produced by the hip extensor muscles was stored in the
distal tendons. During the second half of the push off, in which all joints of
the hindlimb were extending, the calculated ground reaction force vector
passed in between the joints of the left hindlimb
(Fig. 3), suggesting that all
joints of the limb were contributing to work and power output. This conclusion
is different from that reached by Dutto et al.
(2004), who decided that the
stifle joint only produced positive work during the first part of the hindlimb
push. In the present study, peak power output during the hindlimb push was
found to be 75 W kg-1, much more than the 30 W kg-1
observed in the study of Dutto et al.
(2004
) and much less than the
59 000 W (or about 100 W kg-1) found in the study by van den Bogert
et al. (1994
). Again, height
of the jump and approach speed seems to be of decisive importance.
Concluding remarks
It was argued that during the forelimb push in jumping the amount of energy
stored in the distal tendons was on the order of 400 J, and that a
considerable amount of energy was first dissipated and subsequently
regenerated. Clearly, during the push-off in jumping the forelimbs are not
used as mere passive springs. Although suggestions were given as to which
muscles were involved in the dissipation and regeneration of energy,
disclosure of the precise role of the different muscles requires further
studies in which kinematic data are combined with force plate measurements and
electromyography. During the hindlimb push, the muscles of the leg were
primarily producing energy. The total increase in energy, about 2.5 J
kg-1, was different from values reported in other studies,
presumably because of differences in the height of the fence and the speed at
which it was approached. A future study will be concerned with how the energy
changes during the forelimb and hindlimb push depend on the height of the
fence.
List of symbols
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Acknowledgments |
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