Moments and power generated by the horse (Equus caballus) hind limb during jumping
1 Department of Kinesiology and Health Promotion, California State
Polytechnic University, Pomona, CA 91768, USA
2 Department of Biological Sciences, California State Polytechnic
University, Pomona, CA 91768, USA
3 College of Veterinary Medicine, Michigan State University, East Lansing,
MI 48824, USA
4 Department of Animal and Veterinary Science, California State Polytechnic
University, Pomona, CA 91768, USA
* Author for correspondence (e-mail: ddutto{at}csupomona.edu)
Accepted 17 November 2003
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Summary |
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Key words: horse, jumping, hind limb, knee joint, work, power, moment, ground reaction force, sagittal plane kinematics
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Introduction |
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During a jump that requires both horizontal and vertical displacement of
the center of mass, it has been hypothesized that, for a quadruped, the
resulting ground reaction force (GRF) generated by the hind limb would be
anterior (or cranial) to the limb, implying that this force vector would be in
front of the knee, which is the most anterior joint of the limb
(van Ingen Schenau and Bobbert,
1993). A GRF vector cranial to the knee has been observed
experimentally in a horse jumping over a 0.75 m barrier
(Biewener et al., 1988
). If the
GRF vector is anterior to the knee, a net flexor moment is generated at the
knee, while extensor moments would be observed at the hip and ankle (the hip,
knee and ankle are joints with muscle able to produce significant work in the
hind limb; Biewener, 1998
).
It might be expected that the more proximal joints, with muscles able to
generate work, would contribute the most to total work. This would certainly
be true of the hip and ankle of the horse, since they should have net extensor
muscle moments as hypothesized by van Ingen Schenau and Bobbert
(1993) and as shown from the
observed force vector by Biewener et al.
(1988
). In order to produce a
GRF vector in front of the knee, a net flexor moment would be generated at the
knee such that negative work would be done (due to knee extension during the
take-off). The MP should contribute little to the total work as it is
primarily controlled by small muscles and connective tissue (ligaments and
long tendons). We test these ideas here by determining the work generated by
the total hind limb in relation to the joint moments and powers produced at
the hip, knee, ankle and MP joints for horses jumping over a barrier of
moderate height (0.63 m).
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Materials and methods |
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A jumping barrier of modest height (0.63 m) was placed next to a force-measuring platform located in a runway. For each jumping trial, an animal trainer led the horse at a speed that produced a trot during the approach to the barrier. The animal trainer used a combination of a long tether and forward motion to allow the horse freedom of movement during and after the jump so as to not alter the horse's jumping behavior. Both force and video records were made of each jumping trial. Data for each trial were considered viable if only the right hind limb was on the force plate during the jump.
Determination of coordinates for the knee and hip joints
A significant amount of soft tissue is located over both the knee and hip
joints of the hind limb and, while retroreflective markers can be used to
identify these joints, the soft tissue between the markers and the joint has
been shown to impair the ability to determine joint location during movement
(van Weeren et al., 1992;
Back et al., 1995
). In an
attempt to reduce the error in determination of joint center location, the
positions of these two joints were mathematically derived using additional
markers placed over relatively stable anatomical locations (stable locations
are defined as points where there is little intervening soft tissue between
the skin surface and underlying bony structure).
The assumption was made that the segments that articulate in these joints maintain a constant length during the jump. The Cartesian coordinates for the knee joint were determined by using the geometric relationship between the shaft of the tibia, ankle joint and knee joint. Markers along the shaft of the tibia (ankle joint and tibial midshaft) formed a straight line representing the tibia. A polar coordinate relationship was determined (angle and radius) relative to the tibial markers using the ankle joint as the vertex of the angle representing the tibia and an imaginary line from the ankle joint to the knee joint. Knowing the distance and angle of the knee point relative to the tibial markers allowed for the calculation of the Cartesian coordinates of a corrected knee joint location, regardless of the orientation of the tibia.
The hip joint was located by using the calculated Cartesian coordinates for the knee joint, the Cartesian coordinates for the pelvic marker and the lengths of the thigh and pelvic segments determined from the standing-square recordings. It was assumed that the length of each segment described a radius of a circle centered upon the segment end farthest from the hip joint (the knee and the tuber coxae; Fig. 1). The circumferences of the two circles intersect at two places, the rearmost of which was the location of the hip joint center. The Cartesian coordinates for the position where the two circles intersect were then calculated using the equations that described the two circles.
Experimental apparatus
A 0.6 mx0.9 m force plate (model 9287BA; Kistler Instruments,
Winterthur, Switzerland) was used for all data collection. The force plate was
situated lengthwise in the middle of a runway. The runway consisted of a
cement base covered with a 10 mm-thick, high-density, black rubberized mat.
The rubberized mat was also placed on the surface of the force plate. Covering
the surface of the force plate with the rubberized mat created a continuous
visual field for the horse, avoiding any reluctance on the part of the animal
to approach and perform the jump. Force data were sampled at a rate of 1000 Hz
for all tests. Force data were synchronized with high-speed video recording
using LabView® (v5.1, National Instruments Inc., Austin, TX, USA), which
generated a pulse to initiate simultaneous recording of both the force and
video data. Center of pressure was calculated from the force data with a
correction for the addition of the rubber matting to the surface of the force
plate. To ensure the validity of calculated center of pressure coordinates,
manual tests were performed by applying point loads to the surface of the
force plate at a variety of angles and positions. Center of pressure was
determined within 0.5 cm regardless of the direction that the load was applied
to the surface of the force plate.
Video records of all jumping trials were obtained using a high-speed (250 Hz) digital camera (PCI 250; Redlake Imaging Corp., San Diego, CA, USA). The camera was situated orthogonal to the plane of movement, at a distance of 8 m, so that approximately 3.5 m of the runway were recorded, including the force platform and the jump barrier. Prior to experimental testing, a 48-point, two-dimensional calibration frame, located in the plane of movement over the force plate, was recorded. Video records of two-dimensional (sagittal plane) motion for kinematic analysis were recorded and stored directly to a computer. Limb segment markers were digitized using the automatic point-tracking module of the Peak Motus® software (Peak Performance Technologies, Inc., Denver, CO, USA). Digitized coordinates were scaled to represent real-world Cartesian values using a two-dimensional Direct Linear Transformation constructed with the recorded calibration parameters. Kinematic coordinate data were smoothed with a dual pass fourth order Butterworth digital filter using a cut-off frequency of 20 Hz.
Data calculations
Angular positions for each joint were determined from the Cartesian
coordinates of the hind limb joints. Linear position and velocity of the tuber
coxae were determined from kinematic data. Moments and powers for each joint
were determined using inverse dynamic analysis
(Winter, 1990). Inertial
properties of the hind limb segments were estimated using published equations
(Buchner et al., 1997
). The
equations presented by Buchner et al. represent data for Dutch Warmblood
horses. Using these equations, the assumption is made that the proportional
relationship between the mass of the animal and the mass of the segments is
similar between the Dutch Warmblood horses and the horses used in this study.
While this relationship may not necessarily hold true, the effect of inertial
properties of the limb segments relative to ground contact forces are
relatively small; thus, discrepancies due to breed of horse on inertial
properties of the hind limb segments should have a negligible influence on
measured results during the stance phase of the jump.
Fig. 2 displays both the total
joint moment and the inertial moment due to the mass and moment of inertia of
each segment for one jumping trial (which is representative of all trials). It
is readily apparent that the contribution of the inertial properties to the
total joint moment is rather small; thus, errors due to the estimation of
these properties will not greatly influence the results of this study. Total
power generated by the hind limb was determined by summing the power of the
four joints at each relative time point. Finally, work performed by the joint
was determined by integrating the power curves.
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Collected data are descriptive; therefore, results are presented as means ± S.D. Moment and power values are presented relative to body mass. Ensemble averaging was used to combine trial results across the five test animals for the purposes of presenting results (the number of jumps used in this analysis ranged from five to eight jumps per horse, all for the same barrier height, for a total of 29 jumping trials). Reported peak values represent an average of the peak values taken from each individual trial for the particular parameter.
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Results |
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All four joints had relatively large changes in angular position during
ground contact (Fig. 4). The
hip, knee and ankle joints all had a similar pattern of flexion followed by
extension of the joint, whereas the MP joint behaved oppositely
(hyperextension followed by flexion). For the MP joint, the effect of
hyperextension during the early portion of stance is similar to the flexion
that is occurring in the other joints, and this motion contributes to the
overall shortening of the hind limb during this portion of stance. Subsequent
flexion of the MP would then contribute to the lengthening of the limb during
the latter part of stance. The average range of motion (ROM) was largest for
the MP (41.3±9.1°), followed by the knee (33.8±11.9°),
ankle (29.4±7.2°) and hip (24.9±6.3°). Maximal flexion
was reached first in the hip and ankle joints, then by the MP joint (or
maximum hyper-extension) and finally the knee joint
(Table 1). These values appear
consistent with kinematic results presented by van den Bogert et al.
(1994).
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The hip and ankle joints exhibited early power absorption followed by power generation (Fig. 5). Both of these joints became power generators for take-off, beginning around 45% of ground contact. For both the hip and ankle joints, average power absorption peaked at approximately 7 W kg-1 (Table 1), at 22% (ankle) and 28% (hip) of ground contact. The MP joint also had slight power absorption for the initial 65% of ground contact and then became a power generator during the last 35% of ground contact. The amount of power absorption by the MP was relatively small compared with that of the ankle and hip joints. Mean peak power generation of 7.4 W kg-1 and 5.7 W kg-1 (Table 1) by the ankle and hip joints, respectively, occurred at 69% of ground contact for both joints. Peak power generation of 5.6 W kg-1 (Table 1) by the MP joint occurred later (at 82% of ground contact) than that of the hip and ankle joints. The knee joint generated power during initial contact until 57% of ground contact and then absorbed energy. Power generation across the knee peaked at 8.2 W kg-1 (Table 1) at 27% of ground contact time. During the latter portion of ground contact, the amount of power absorbed by the knee remained relatively small. During some trials, the knee joint behaved as a power generator during the latter portion of ground contact, as evidenced by the S.D. of the presented curve (Fig. 5).
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On average, there was net negative power (or absorption of power) by the hind limb during the first 40% of ground contact, and net positive power (or power generation) for the remainder of ground contact (Fig. 6). Mean peak power generation of the hind limb was 13.2 W kg-1 at 74% of ground contact. On average, one hind limb generated 0.71 J kg-1 of work during ground contact. Over the entire ground contact, all four joints had a net contribution of positive work, with most of the work produced by the knee joint (0.60 W kg-1). When averaged across all trials, the knee was responsible for 85% of the observed work of the hind limb, followed in order by the MP, ankle and the hip joints, with the hip joint producing an average of 2% of the work of the hind limb.
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During the first 40% of ground contact, the horizontal velocity of the
tuber coxae first decreased and then increased to a value 0.15 m
s-1 faster than at contact, and the vertical velocity went from a
negative (downward) velocity to zero (Fig.
7). During this portion of ground contact, the knee produced a
mean of 0.60 J kg-1 of positive work, while the other three joints
all produced negative work, with the net result being negative work
(Table 1). During the last 60%
of contact, the vertical velocity increased dramatically, while the horizontal
velocity increased slightly at the beginning and end of this time period. The
knee produced essentially no work (on average) while the other three joints
produced positive work during this time period.
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Discussion |
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For jumping horses in the present study, one hind limb generated an average
of 0.71 J kg-1 of work (work was normalized to body mass). This is
approximately 4.5 times the work of walking in horses (0.16 J kg-1
of work; Clayton et al., 2001).
Peak extensor moments at the hip were five times higher during jumping (2.64
Nm kg-1) than during walking
(Clayton et al., 2001
).
Unexpectedly, positive work associated with the jump was done by the
musculature of the knee rather than the hip or ankle joints. By contrast,
during walking most of the work was performed by the hip (0.23 J
kg-1), which is greater than the total work done by the hind limb
during walking, as the knee absorbs energy (produces negative work) during
walking (Clayton et al.,
2001
).
The observed behavior of the knee joint was consistent with our hypothesis
that the muscles acting at the knee would generate a flexor moment during
jumping. This results in the GRF vector passing anterior to the knee during
ground contact, similar to the observations of jumping horses made by Biewener
et al. (1988). More
interestingly, the knee generated positive work during the jump (rather than
producing negative work, which we had hypothesized) and was the major (85%)
contributor to the total work produced by the hind limb. Most of the power
generation (positive work) at the knee occurred early (first 40%) in the
contact period (Fig. 6), since
this is when the knee was flexing and generating a flexor moment. How might
the work generated by the knee contribute to the jump?
During the first 40% of stance, the knee musculature performed a majority
of the positive work done during the entire contact period. Muscles of the
other three joints were absorbing energy (performing negative work) during
this same time period. From initial hoof contact to 40% of stance, the mean
change in the resultant velocity of the tuber coxae was 0.04 m s-1
(Fig. 7), requiring 0.13 J
kg-1 of work. During this time period, the work performed by the
hind limb was -0.40 J kg-1. The animals did increase the horizontal
velocity of the tuber coxae by 0.15 m s-1 over the first 40%
of stance (Fig. 7) despite
producing a braking force for the first 28% of stance
(Fig. 8). The observed increase
in horizontal velocity of the tuber coxae therefore is probably due to the
positive work performed by the knee joint muscles during this time, because
the muscles of the knee were the only muscles producing positive work.
Furthermore, it is clear that during jumping a positive (propulsive)
horizontal impulse is required, resulting in half as much braking impulse as
is generated during trotting [0.06 Ns kg-1 (trotting) vs
0.03 Ns kg-1 (jumping); Fig.
8]. As the braking period is very short during jumping, the force
vector must be in front of the leg due to the joint moments generated during
stance. The remaining joints were responsible for slowing the downward motion
of the hips, resulting in the observed negative work performed by these
joints. Without knowing the movement of the center of mass or the fore limbs,
it is unclear exactly how the net negative work (-0.40 J kg-1)
performed by the hind limbs relates to the motion of the horse.
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Another explanation for the relatively short braking period during the jump and the excess amount of work that appears at the knee during the first 40% of contact relates to the position of the torso of the horse (forelimbs off the ground) during the take-off. Since the tuber coxae is located on the pelvis, the horizontal velocity of this marker should provide a fairly good estimate of the horizontal velocity of the animal. There was a small discrepancy between the relationship of the early and large horizontal GRF and horizontal velocity. It is plausible that the extension moment of the hip acts primarily to provide propulsion for the jump and secondarily to assist in resisting the rotational inertia of the torso. During approximately 55-75% of contact, the hip was extending (Fig. 4) and the angular velocity was increasing, while the horizontal velocity of the tuber coxae was not increasing and there was a large, propulsive horizontal force. It appears that a small portion of the hip extension moment generated was required to resist the influence of gravity on the torso that would tend to flex the hip.
During the last 60% of contact, vertical velocity increased almost
continually. The hip, ankle and MP joint all generated positive work during
this time period that most likely acted to increase vertical velocity, while
the knee musculature did not directly contribute to accelerating the animal.
The positive work performed by the musculature of hip, ankle and MP joints was
slightly greater than the amount of work absorbed during the initial portion
of contact, an indication that the observed work was due to a combination of
stored elastic energy recovery and active muscle contraction, as observed by
Seyfarth et al. (2000) in human
long jumping.
It seems possible that power produced by knee extensors was transferred to
the hip and ankle by the action of the biarticular knee flexor muscles (e.g.
hamstrings and gastrocnemius) that also act to extend the hip and ankle.
Support for this idea is found in the similarity between the last 40% of the
stance in equine jumping and part of the downstroke in human cycling, where,
in both cases, a net flexor moment was generated at the knee while the hip,
knee and ankle were all extending. When these conditions occur during human
cycling there is co-activation of knee extensors and flexors and this has been
interpreted as resulting in the transfer of work performed by the knee
extensors to the hip and ankle (van Ingen
Schenau, 1990; van Ingen Schenau et al.,
1992
,
1995
). The fact that the knee
extended during the later part of jumping suggests that knee extensors were
active, and the very low power output of the knee during this phase of the
jump, with concomitant increased power production at the hip and ankle
(Fig. 5), is consistent with
the idea that power produced by knee extensors is transported to the hip and
ankle. However, further investigation of the activity of the knee musculature
(biarticular knee flexors and monoarticular knee extensors) during the jump is
required to test this idea.
Towards the end of the take-off, positive work by the hind limb was
maintained due to an increase in power generated by the MP joint. Positive
work was not performed until 65% of contact in the MP joint, which acted to
maintain the total positive power created by the hind limb. The MP joint does
not have a large muscle mass acting across it but is primarily controlled by
tendons attached to highly pinnate muscles with short fibers and by ligaments
in the limb, similar to that described for the forelimb metacarpalphalangeal
joint (McGuigan and Wilson,
2003). Perhaps it is the late release of stored elastic energy
that is responsible for some of the work observed in the MP joint during the
final third of the take-off.
Late release of the energy in the MP joint may also be part of the
proximal-to-distal flow of energy during take-off. During maximal vertical
jumps, the extensor muscles of the hind limb in cats were found to activate in
a proximal-to-distal order, and the kinematics of the hind limb joints
followed the same proximal-to-distal pattern
(Zajac et al., 1981). Also,
the peak moments about these joints occurred earliest in the proximal joints
during the jump. A similar pattern was observed in the peak moments generated
by the hind limb joints of the horse during the jump, particularly when
observing the relationship of the hip, ankle and MP joints. Additionally, the
power generated by these joints tended to follow a similar pattern, with the
peak power generation of the MP joint occurring later in stance than the hip
and ankle joints. This proximal-to-distal sequencing of peak power would be
indicative of energy transfer between the proximal joints (relatively large
muscle mass) and the more distal joints. The tendinous nature of the MP joint
is ideally designed for a late release of energy. As the force upon the joint
decreases, this could allow tendon recoil and recovery of stored elastic
energy. This is apparent in the late positive power burst observed at the MP
joint.
Because the work done by the hind limb produced a large propulsive force during take-off, it can be argued that the hind limb performs a majority of the work required for the jump. The total proportion of work performed by the hind limb will not be known until the work performed by the forelimb and movement of the center of mass are determined. Most of the work was performed early during the stance phase by the musculature of the knee, as determined through inverse dynamic analysis. The hip, ankle and MP joint did a large amount of positive work later in stance but this was balanced by negative work early in stance. Further investigation is required to determine how the positive work of the knee musculature contributes to the overall movement of the jumping animal and the proportion of the work produced by the hind limb relative to the total work required.
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Acknowledgments |
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References |
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