Determination of peak vertical ground reaction force from duty factor in the horse (Equus caballus)
1 Structure and Motion Lab, The Royal Veterinary College, Hawkshead Lane,
Hatfield, Hertfordshire, AL9 7TA, UK
2 Structure and Motion Lab, University College London, Royal National
Orthopaedic Hospital, Brockley Hill, Stanmore, Middlesex, HA7 4LP,
UK
* Author for correspondence (e-mail: awilson{at}rvc.ac.uk)
Accepted 13 July 2004
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Summary |
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Key words: ground reaction force, field locomotion, accelerometer, duty factor, horse
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Introduction |
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Force is routinely measured with high precision and accuracy in the
laboratory environment using a force plate
(Elftman, 1938;
Cavagna et al., 1964
;
Pratt and O'Connor, 1976
).
Force plates, however, have a number of drawbacks. They are expensive, need to
be mounted in a purpose-built runway and rely on the subject hitting the plate
with exactly one leg. More recently, force platforms have been incorporated
into treadmills, offering advantages over standard installations, but studies
are still limited to the laboratory environment.
We are particularly interested in the horse (Equus caballus) as a model system for the study of locomotion. The horse has evolved a highly specialised musculoskeletal system and is capable of short bursts of high-speed locomotion as well as more sustained exercise at lower speeds.
Pressure-sensitive insoles are commonly used in human biomechanics;
however, their application in horses is limited as the technology is expensive
and fragile, and absolute calibration values are poor
(Hennig et al., 1982;
Cavanagh et al., 1983
). A
number of groups have developed instrumented horseshoes and have achieved
increasing levels of accuracy (Marey,
1882
; Björk,
1958
; Frederick and Henderson,
1970
; Hügelshofer,
1982
; Kai et al.,
2000
; Ratzlaff et al.,
1985
,
1990
;
Roepstorff and Drevemo, 1993
).
However, it is still difficult to record the entire force transmitted by the
foot while maintaining the requirements for grip, all in a thin construct of
minimal mass. Even small changes in digital mass may have significant effects
on kinematics due to the rapid accelerations experienced during the gait cycle
(Back et al., 1995
).
Limb force has been predicted from kinematic data, although this is
difficult. We have demonstrated that, in horses, there is a gait-independent
linear relationship (r2=0.950.99) between the peak
extension angle (the posterior angle subtended by the axis of the third
metacarpal bone and the axis of the phalanges) of the metacarpophalangeal
(MCP) joint and limb force (McGuigan and
Wilson, 2003). The joint angleforce relationship can be
calibrated at low speed using a force plate, and subsequently limb force can
be predicted from kinematics at higher speeds. The method is, however, limited
to the horse and requires the collection of kinematic data, which is difficult
outdoors.
Cine film has been used to estimate limb force in galloping buffalo
(Syncerus caffer) and ambling elephant (Loxodonta africana)
by applying the principle of conservation of momentum
(Alexander et al.,
1979). In steady-state locomotion, the total vertical impulse (the
integral of force with respect to time) applied to the centre of mass during a
stride must equal the product of body weight and the stride duration. There
is, therefore, an inverse relationship between stance time and peak vertical
force if a limb generates a certain impulse. That fraction of the stride time
for which the limb transmits force to the ground (i.e. the limb is in the
stance phase) is known as the duty factor. Alexander and co-workers used these
concepts, and the observation that the GRFtime curve in a spring-like
or running gait is approximately sinusoidal in shape, to generate the
following equation:
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The accuracy of this calculation relies on three assumptions and/or constants:
Application of the above technique for the prediction of peak GRFz requires
that stance time be accurately determined. Direct GRF measurement,
accelerometer data and kinematic methods have been compared for the objective
determination of the timing of foot on and foot off
(Schamhardt and Merkens,
1994). Force plate data are extremely accurate for both initial
ground contact time and the time of foot off. Kinematic analysis alone, on the
other hand, was reported to be insufficiently accurate for the determination
of either parameter. Analysis of digital acceleration offers an alternative
and has been used to develop a tool for the estimation of aerobic power during
walking and running in humans (Weyand et
al., 2001
). This method, however, also has potential
disadvantages. In the late stance phase, the foot pivots about the toe (an
event known as heel off) prior to the foot completely leaving the ground
(Fig. 1;
Schamhardt and Merkens, 1994
).
The error in stance time determination was 14.6% in a study of humans, which
was attributed to the inability to differentiate foot rotation from actual
foot off (Weyand et al.,
2001
). We propose that, in the horse, toe off can be accurately
detected and differentiated from heel off using an appropriately mounted
accelerometer due to the changes in the direction of foot acceleration.
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The ability to accurately determine the vertical force experienced by all
four limbs of large cursorial animals during high-speed locomotion in the
field would contribute greatly to our understanding of the athletic ability of
these animals, since peak limb force has been identified as limiting to
running speed. In order to apply the technique described by Alexander et al.
(1979), we must first validate
a method for determining the stride timing variables used to calculate duty
factor. Subsequently, the assumptions that equation 1 relies on must be
validated. It would therefore be useful to compare the actual GRF curves to a
sine wave of the same base and area and to determine whether this method
provides a good estimate of GRF throughout the stride or only at the peak
value.
The goal of this study was first to evaluate the accuracy of a system of limb-mounted accelerometers for detecting foot on and foot off in the horse. Second, foot on and foot off data would be used to test the hypothesis that peak GRFz can be predicted from duty factor. Specifically, experiments were designed to answer the following questions: (1) can the timing of foot on and foot off be determined using data from foot-mounted accelerometers during locomotion on both hard and soft surfaces; (2) what is the ratio of fronthind impulses as a function of speed and gait and (3) can the approach of Alexander et al. (equation 1) be applied to walking and asymmetrical gaits?
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Materials and methods |
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Determination of foot on and foot off and peak limb force at walk, trot and canter on a hard surface
Six Warmblood-type riding horses (mass 573705 kg; mean 636 kg) were
used for the walk and trot experiment, and four fit Thoroughbred horses (mass
453512 kg; mean 488 kg) were used for the cantering. All subjects were
assessed as being free of lameness by veterinary examination prior to each
experiment. Foot acceleration was measured using solid-state capacitive
accelerometers with a dynamic range of ±50 g (ADXL150, Analog Devices,
Norwood, MA, USA; sensitivity 38 mV g1). These were
protected by enclosure in epoxy-impregnated Kevlar fibres (total mass 2 g) and
mounted on the dorsal midline of the hoof, with the sensitive axis orientated
in a proximo-distal direction, using hot melt glue from a hot glue gun (Bostik
Findley Inc., Stafford, UK). The optimum position and range of the
accelerometer was first determined by experimentation with both ±5 g
and ±50 g accelerometers and with mounting on the lateral aspect of the
third metacarpal/metatarsal bone (MC/MT), the lateral and dorsal aspects of
the proximal phalanx and various positions on the foot during locomotion on
both hard and soft surfaces. Output signals were telemetered via
programmable narrow-band analogue FM radio telemetry devices operating at 458
MHz (ST/SR500; Wood and Douglas Ltd, Tadley, Hampshire, UK) and logged
via a 12-bit A/D converter and PCMCIA card (DAQcard700; National
Instruments, Newbury, Berkshire, UK) into a laptop computer running custom
software in LabView (National Instruments). The telemetry transmitter,
wave whip antenna and NiCad battery were mounted in a custom-designed
exercise bandage on the lateral aspect of the MC/MT (mass of telemetry unit 73
g and battery 88 g; total mass of bandage with telemetry unit, 376 g). A
short, fatigue-resistant cable was constructed of multi-strand copper wire
coiled around a flexible 2 mm-diameter core of mountaineering cord and coated
in silicon rubber (Wilson and Goodship,
1994
). This highly flexible cable ran along the lateral aspect of
the digit and linked the telemetry unit to the accelerometer
(Fig. 2).
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Horses were led by an experienced handler along an 80-m dirt and concrete runway in which a force plate was embedded (Kistler 9287BA; Kistler Instruments Ltd, Alton, Hampshire, UK). Both force plate and runway were covered in commercial conveyor belt matting. Force data were amplified by integral charge amplifiers, filtered through a low-pass filter (6 dB octave1 from 50 Hz) and collected simultaneously with accelerometer data in LabView (National Instruments). All data were logged at 1000 Hz.
The time of foot placement (foot on) was taken as the first frame in which
the vertical force rose above 50 N, and foot off was defined as being the
first frame in which the vertical force (GRFz) fell below 50 N
(Clayton et al., 1999). In the
horse, the well-defined increase and decrease in GRFz, which occur at foot on
and foot off, respectively, mean that a 50 N threshold accurately identified
the timing of these events. These times were used to visually assess the
accelerometer data and define the acceleration features that corresponded to
foot on and foot off. The operator was then blinded to the force data for the
remainder of the analysis. The times of foot on and foot off were manually
extracted from the accelerometer traces using transcription freeware
(http://www.etca.fr/CTA/gip/Projets/Transcriber).
For each stride, the times of foot on and foot off, as determined using the
force plate, were subtracted from those determined using the accelerometer
such that an error value was obtained that was negative if the accelerometer
time was early and positive if it was late. From the accelerometer data, total
stride period was defined as the difference between two sequential foot on
events, and stance period as the time between foot on and the subsequent foot
off. Duty factor was then calculated as the ratio of stance period to stride
period and was used to calculate Fzmax using equation 1.
Force plate data were used to calculate ratios of front to hind peak vertical
force and front to hind vertical impulse, although for canter data this was
only possible for non-lead limbs. Peak vertical force was determined for each
limb strike and compared with the predicted force.
Measurement of MCP joint angle during high-speed treadmill locomotion
Flat, circular retro-reflective markers (Scotchlite 8850; 3M, Bracknell,
Berkshire, UK), 20 mm in diameter, were placed at the following skeletal
landmarks on the lateral aspect of the left forelimbs and the medial aspect of
the right forelimbs of the same four Thoroughbred horses used in experiment 1:
(1) proximal end of the fourth metacarpal; (2) proximal attachment of the
lateral/medial collateral ligament of the MCP joint to the distal third
metacarpal bone (centre of rotation of the MCP joint) and (3) lateral/medial
hoof wall approximately over the centre of rotation of the distal
inter-phalangeal (DIP) joint.
The horses had been habituated to locomotion on a high-speed treadmill
(Satö, Knivsta, Sweden; Buchner et
al., 1994). During the experiment, they wore neoprene brushing
boots and over-reach boots to avoid interference injuries while galloping.
After a warm-up period, the horses were exercised at increments of speed
between 1.6 m s1 and 12 m s1. During
canter locomotion it was recorded whether the left forelimb or the right
forelimb was the lead leg. Marker location in the sagittal plane was recorded
from the horses' left side (ProReflex; Qualisys AB, Gothenburg, Sweden). At
each speed increment, the horse was allowed 20 s to settle into a steady gait
pattern prior to the collection of 10 s of data.
MCP joint extension angle was calculated as the posterior angle subtended by the axes of the third metacarpal bone and proximal phalanx. The peak angle was determined for each stride of each file, and the mean peak MCP angle was determined for both front legs at each speed increment.
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Results |
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The features were most obvious and distinctive when the accelerometer was positioned on the dorsal hoof wall, orientated with the sensitive axis along the midline of the limb (Fig. 4). Initial experiments with the accelerometer mounted on the lateral aspect of the proximal phalanx resulted in satisfactory acceleration features corresponding to the foot on event; however, foot off became difficult to detect reliably, especially on a soft surface.
In the first experiment, a total of 147 stance phases were collected (46 at walk, 75 at trot and 26 at canter). Mean absolute error for foot on time was 2.4 ms at walk (median error 2 ms, inter-quartile range 2 to 1 ms), 1.8 ms at trot (median 1 ms, IQR 2 to +1 ms), 2.0 ms (median 1.5 ms, IQR +1 to +2 ms) for the non-lead limb and 3.0 ms (median 2.5 ms, IQR +1.5 to +3 ms) for the lead limb at canter. Mean absolute error for foot off time was 3.6 ms at walk (median 2 ms, IQR 5 to +1 ms), 2.4 ms at trot (median 1 ms, IQR 4 to 0 ms), 5.0 ms for the non-lead limb (median 4 ms, IQR 10 to +9 ms) and 2.8 ms for the lead limb (median 2 ms, IQR 7 to 1 ms) at canter.
In order to test the validity of the assumption that GRFz follows a sinusoidal curve as required by equation 1, wesuperimposed sine waves of the same base and area on each GRFz curve generated in experiment one. The amplitude of the sine wave generated was subtracted from the peak GRFz measured in each case. This produced an error value, which was positive if the peak GRFz was overestimated and negative if it was underestimated. Fig. 5 shows mean (± S.D.) GRFz curves across all strides recorded for front and hind limbs at walk and trot and lead and non-lead forelimbs at canter. The superimposed sine waves lie within 1 S.D. of the mean force for between 40% and 70% of the stride for both front and hind limbs at trot and canter. The mean value of the amplitude error was 0.3 N kg1 (4% of peak GRFz; N=72; range 1.1 to +1.3 N kg1) at walk, 0.8 N kg1 (7% of peak GRFz; N=109; range 2.1 to 0.7 N kg1) at trot, 0.6 N kg1 (5% of peak GRFz; N=36; range 1.1 to 0.3 N kg1) for the non-lead limb at canter and 0.4 N kg1 (3% of peak GRFz; N=7; range 0.6 to 0.2 N kg1) for the lead limb at canter (Fig. 6).
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The ratios of front to hind peak vertical force and front to hind vertical impulse were calculated and are expressed as percentages and plotted against peak GRFz for all strides in Fig. 7. Linear regression of front:hind force ratio against absolute forelimb force showed that the force ratio was gait dependent (y=1.61980.0358x, r2=0.272, P<0.0001). The mean front:hind force ratio (± S.D.) was 1.44±0.12 (N=140) at walk, 1.32±0.49 (N=218) at trot and 1.18±0.17 (N=23) for the non-lead limbs at canter. The ratio of vertical impulse, however, was minimally affected by speed and gait (y=1.37240.0064x, r2=0.018, P=0.0081). The average front:hind vertical impulse ratio was 1.33±0.11 (mean ± S.D.). This equates to a percentage vertical impulse distribution (front:hind) of 57%:43%. This impulse distribution was used in the subsequent calculations of predicted peak GRFz from duty factor.
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A scatter plot of predicted peak GRFz versus actual peak GRFz for all strides is shown in Fig. 8. This shows that the prediction is a slight overestimate for all walk strides, good for all trot strides but underestimates the non-lead leg peak force and overestimates the lead leg peak force at canter. Error was negative if the prediction underestimated the actual value. The mean error was 0.8 N kg1 (13% of peak GRFz; range 0.31.5 N kg1) at walk, 0.3 N kg1 (3% of peak GRFz; range 1.7 to 1.2 N kg1) at trot, 2.3 N kg1 (17% of peak GRFz; range 5.2 to 0.3 N kg1) for the non-lead limb at canter and 2.1 N kg1 (19% of peak GRFz; range 1.53.7 N kg1) for the lead limb at canter. When the means of the lead and non-lead limbs are plotted on the same graph, the point is very close to the line of normality.
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Fig. 9 shows the difference in peak MCP joint angle between the forelimbs plotted against speed for four horses. Because absolute angle values could differ due to differences in marker placement between the left and right limbs, the data have been normalised to ensure symmetry at a trot speed of 3 m s1. At canter, the mean difference in peak MCP angle between the two limbs decreased by a factor of three from 7.0° at the lowest speed (7 m s1) to 2.4° at the highest speed examined (12 m s1).
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Discussion |
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The mass of the equine metacarpus and digit is 3420
g(Buchner et al., 1997). Horses
commonly wear brushing boots (mass 200400 g) to prevent injury from
interference between limbs during training and racing. The combined mass of
the accelerometer, telemetry unit, battery and exercise bandage (376 g) is
within the mass range of commercial brushing boots and is therefore unlikely
to interfere with normal kinematics. In one study, attaching 88 g weights to
the toes of Standardbred trotters had minimal effect on stride length, stride
duration and the relative duration of stance and swing phases as a percentage
of the stride (Willemen et al.,
1994
). Our equipment is mounted further proximal on the limb,
where the effect on kinematics will be even less. In addition, the equipment
could be made lighter by reducing the battery size (currently 88 g) or by
using a smaller, and lower power, telemetry transmitter.
The four-limb telemetry system presented some technical difficulties during design. The effect of four transmitters in close proximity to one another and the reradiating and/or shielding effect of the horse was expected to significantly reduce the range from the manufacturers' claimed line of sight ranges of up to 2 km. However, during the series of experiments described here, undertaken at ranges of up to 300 m, signal reception and strength was never a problem. Analogue telemetry links use automatic gain control to ensure that the dynamic range of the system is used. The output voltage is therefore proportional to acceleration through the stride, but actual acceleration values cannot be obtained. This is seen in Figs 3, 4, where input amplitude will vary but the output amplitude remains the same.
Equation 1 relies on the sinusoidal nature of the GRFztime curve. This assumption holds true for the running gaits, where the limb compresses and extends during the stance phase to store and return elastic energy. In comparison, walking gaits are traditionally modelled as an inverted pendulum with the trunk vaulting over a relatively incompressible limb, resulting in a bimodal GRFtime curve. It is interesting, therefore, that the technique presented still provides a reasonable estimate of limb force at walk. Indeed, the predictions for walking are more accurate than those for slow cantering (Fig. 8). In the horse, walking still has spring-like properties although with less leg compression and reduced trunk lift at mid-stance.
During trot locomotion, the prediction of force from duty factor was shown to be accurate. However, during canter locomotion, equation 1 provided an underestimate for the non-lead limb and an overestimate for the lead limb. A considerable asymmetry therefore exists in the impulse applied by the two forelimbs since sine wave assumption was similar (Figs 5, 6).
Equation 1 requires knowledge of the distribution of the mass of the animal between the front and hind limbs. This should consider the ratio of the vertical impulses rather than simply the peak force since the equation is based upon momentum. This study shows that although the front:hind impulse distribution and the front:hind force distribution are both similar at 57:43, the front:hind peak force ratio did decrease with gait from walk to trot and canter. The reason for this change is unknown. The impulse distribution was shown not to change within the speed range studied and it is therefore appropriate to use the same ratio for all gaits in the calculation of peak force.
During this study, horses were examined on a treadmill at a range of canter
speeds. As speed increased, the difference in MCP joint extension angle
(linearly related to vertical limb force) between the lead and non-lead legs
decreased. Using the previously published population regression of limb force
against MCP joint angle of McGuigan and Wilson
(2003), this equates to a
reduction in leadnon-lead force difference from 1.8 N
kg1 to 0.5 N kg1. This indicates that as
speed increases, limb function becomes more symmetrical. At maximum racehorse
running speed (18 m s1), therefore, the error in peak GRFz
prediction may be greatly reduced. On the scatter plot of predicted
versus actual force, the mean of lead and non-lead limbs lies very
close to the line of normality (Fig.
8). This confirms that the GRFz trace is inherently sinusoidal in
nature and that the non-lead leg simply generates a larger impulse. It also
suggests that the distinct tail of the canter GRFz trace
(Fig. 5) does not contribute to
prediction inaccuracy. It may be possible to generate a speed-dependent
correction factor to increase the accuracy of the force prediction during
asymmetrical gaits; however, the leadnon-lead difference in absolute
peak limb force is variable between individuals
(Fig. 9). The reduction in peak
angle asymmetry seen at higher speeds suggests that such a correction may be
unnecessary for studies of maximum speed locomotion. The peak angle asymmetry
seen here at high speed is generally less than we found previously (7.7°),
where only one leg per horse was analysed
(McGuigan and Wilson,
2003
).
The superimposed sine wave of the same base and area did have a similar shape to the GRFz curve at both trot and canter. This demonstrated that the method can also be used to estimate GRFz with reasonable accuracy throughout stance at these gaits and not just at mid stance.
The system of limb-mounted accelerometers described in this paper proved to be practical for use in field conditions, making it possible to estimate the mechanical environment of the skeleton in individual horses and consider the factors that limit gallop speed in horses under different environmental conditions. In the future, it may be possible to automate the detection of the features in the accelerometer output in order to reduce the time required for data analysis.
Conclusions
It is possible to accurately predict peak GRFz from duty factor in the
horse. For asymmetrical gaits, a correction factor is required to compensate
for the difference between the lead and non-lead limbs of a pair. Mean peak
limb force can, however, be accurately determined for asymmetrical gaits. The
system described offers the potential for studying peak forces and bone and
tendon loading during field exercise.
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Acknowledgments |
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