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First published online May 21, 2007
Journal of Experimental Biology 210, 1885-1896 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02774
Validation of vertical ground reaction forces on individual limbs calculated from kinematics of horse locomotion
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
3 Department of Equine Studies, Swedish University of Agricultural Sciences,
750 05 Uppsala, Sweden
4 Equine Hospital, Vetsuisse Faculty, University of Zurich,
Winterthurerstrasse 260, CH-8057 Zurich, Switzerland
* Author for correspondence (e-mail: M_F_Bobbert{at}fbw.vu.nl)
Accepted 7 March 2007
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Summary |
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 TOP Summary IntroductionMaterials and methodsResultsDiscussionReferences |
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Key words: Equus caballus, trot, walk, biomechanics, limb stiffness, model, duty factor
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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; Rossdale et al.,
1985). The impact on the equine industry is huge. For example, in
1998 economic losses due to musculoskeletal injury in the Thoroughbred
racehorse were estimated at US$ one billion in the United States alone
(Kobluk, 1998). Obviously,
early diagnosis and treatment of lameness is important, both from an animal
welfare perspective and from an economic perspective.
In the diagnosis of musculoskeletal injuries, the eye of the clinician is
an invaluable tool. However, objective measures may have added value.
Kinematic analysis has been used to provide quantitative data on locomotion
patterns of healthy and lame horses (e.g.
Buchner et al., 1996a;
Buchner et al., 1996b;
Buchner et al., 2001;
Clayton et al., 2000;
Galisteo et al., 1997;
Keegan et al., 1998;
Keegan et al., 2000;
Kramer et al., 2000;
Uhlir et al., 1997).
Information about the forces on the individual limbs is highly desirable for
diagnosis and evaluation of treatments, and also seems indispensable to
further our understanding of adaptations of the locomotion patterns following
injury. After all, the adaptations will be intended to reduce the load on the
injured structures. As holds for studying locomotion in general, it is highly
desirable to have both forces on the individual limbs and whole-body
kinematics, so that changes in the forces can be linked to changes in the
locomotion pattern.
Various methods of obtaining information on individual limb forces have
been developed, each of which has advantages and disadvantages. First of all,
force plates can be used (e.g. Clayton et
al., 2000; Merkens and
Schamhardt, 1988; Merkens et
al., 1986; Morris and
Seeherman, 1987; Schamhardt
and Merkens, 1987; Schamhardt
et al., 1986). A force plate provides full information on the
ground reaction force vector, but a disadvantage is that it can measure the
force of only one limb at a time. Moreover, capturing a clean hit of the force
platform with the limb of interest may require two to six attempts, depending
on the variability of the horse and the type of gait studied
(Merkens et al., 1986;
Merkens et al., 1993a;
Merkens et al., 1993b). A
second method to obtain individual limb forces is to use instrumented
horseshoes (Barrey, 1990;
Kai et al., 2000;
Roepstorff and Drevemo, 1993).
This solves the problem of getting the horse to hit a force plate with the
limb of interest and allows for the study of many consecutive strides. The
early instrumented horseshoes were fragile and did not provide full
information on the ground reaction force, but a recently developed
dynamometric horseshoe (Roland et al.,
2005) seems robust and accurately provides the six components of
the load. However, if measurements are to be made on a horse, this horse will
need to be shod with instrumented shoes, and because the mass of the
instrumented horseshoes is greater than that of normal horseshoes, the stride
variables to be studied could be affected
(Roland et al., 2005). A third
method of obtaining information on the ground reaction force has been
presented by Weishaupt and colleagues
(Weishaupt et al., 2002;
Weishaupt et al., 2004a;
Weishaupt et al., 2004b;
Weishaupt et al., 2006). They
devised a treadmill the support surface of which was mounted on 18 force
sensors, allowing for simultaneous measurement of the vertical ground reaction
forces on each of the four limbs over multiple strides. This method requires
minimal instrumentation of the horse, but a slight downside is that the horse
needs to be accustomed to treadmill locomotion, and unfortunately the system
does not provide the full reaction force vectors. Also, slight differences
have been reported in kinematic patterns during treadmill locomotion and
kinematics during overground locomotion
(Buchner et al., 1994), but it
cannot be excluded that these were due to differences in the properties of the
support surface.
Instead of directly measuring ground reaction forces on the individual
limbs of the horse, it can be attempted to estimate them from kinematics. A
method to do so has been proposed by McGuigan and Wilson
(McGuigan and Wilson, 2003).
The method builds on the observation that the distal forelimb of the horse
behaves like a spring, i.e. the force carried by the limb is directly related
to the distance between the elbow and the hoof, and also to the fetlock joint
angle (McGuigan and Wilson,
2003). This means that the latter two kinematic variables can be
used as a type of `strain gauge', provided that they have been calibrated,
i.e. that the relationship between limb force and elbow-hoof distance or
fetlock angle is known. For this calibration, McGuigan and Wilson
(McGuigan and Wilson, 2003)
used kinematic data collected simultaneously with force plate data at trot.
Then, using fetlock angles measured during gallop, they applied the
calibration results to estimate the peak vertical ground reaction forces on
the individual forelimbs.
The method developed by McGuigan and Wilson
(McGuigan and Wilson, 2003) is
elegant and involves no interference with the horse other than the application
of markers defining the kinematic variables to be used in force calculations.
Also, it can be applied to overground locomotion. However, the calibration
requires the use of a force platform, and therefore suffers from the
associated disadvantages. An indirect approach to calibration would be to use
limb forces estimated from duty factor, with the duty factor of a limb being
the proportion of the stride for which that limb is in contact with the ground
(Alexander et al., 1979;
Witte et al., 2004). It has
been shown that at trot, peak vertical ground reaction forces for individual
limbs could be predicted from duty factor with errors of only 3%
(Witte et al., 2004). The
predicted peak forces at trot could be used for calibration of the `strain
gauges', and the calibrated `strain gauges' could be used to determine forces
at other gaits. However, the calculation of forces from duty factors,
henceforth referred to as `duty factor method', relies on information about
the distribution of the total ground reaction force over the individual limbs,
which must have been acquired in previous research with the help of direct
force measurements. Furthermore, it involves assumptions about symmetry and
periodicity that will not hold in lame horses.
It would be ideal if calibration of the `strain gauges' could be achieved
using kinematic data collected for analysis of the locomotion pattern. In
principle, such data allow for calculation of individual limb forces for
phases during locomotion in which only two limbs are simultaneously in contact
with the ground. After all, kinematic data can be used to calculate the
acceleration of the centre of mass of the horse, and hence the magnitude and
direction of the total ground reaction force vector. As explained in
Fig. 1, this information can be
combined with the rate of change of angular momentum of the horse, also
calculated from the kinematic data, to determine the moment arms of the total
ground reaction force relative to the two supporting hoofs
(Bobbert and Santamaria, 2005).
The ratio of these moment arms then gives an indication of the relative
contribution of each of the supporting limbs to the total ground reaction
force, so the individual limb forces can be calculated. The forces obtained
using this ground reaction force distribution method, henceforth referred to
as `GRF distribution method', can then be combined with distal limb length or
fetlock angle for the calibration of these indicators of limb force. Finally,
given the results of the calibration, time histories of individual limb forces
can be estimated from time histories of distal limb length or fetlock angle.
From a mechanical point of view this approach is straightforward, but it seems
a long shot and the question may be raised whether it produces accurate
results when real-world kinematic data are used. One of the problems, for
example, is that markers placed on the skin may move considerably relative to
the underlying bony landmarks (van Weeren
and Barneveld, 1986; van
Weeren et al., 1988; van
Weeren et al., 1990a; van
Weeren et al., 1990b), causing errors in the force
calculations.
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). To
evaluate the accuracy of the calculated forces, we compared them with vertical
reaction forces of the individual limbs provided by the treadmill-integrated
force measuring system. We also compared the individual limb forces calculated
from kinematics with forces calculated from duty factors of the limbs.
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Materials and methods |
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), to
which they had been accustomed prior to the day of the measurements. For the
current study we selected from each horse one walking trial at a speed of 1.6
m s–1 and one trotting trial at a speed of 3.4 m
s–1.
The treadmill-integrated force measuring system provided the vertical
ground reaction force on each of the limbs (FRy,i) at 480
Hz. For the kinematic analysis, markers were applied to the skin overlying
bony landmarks on both sides of the body
(Fig. 1). The markers were
monitored during stance and locomotion by 12 infrared cameras operating at 240
Hz (Pro Reflex, Qualisys Medical AB, Göteborg, Sweden). Force data and
kinematic data were captured simultaneously for a period of 15 s, both at trot
and at walk. First, we needed to know the contact phases of each of the limbs.
These were determined from the horizontal velocities of the hoofs, obtained by
numerical differentiation of the trajectories of the hoof markers after
smoothing these at 8 Hz using a fourth-order zero-lag Butterworth filter.
Next, we intended to calculate the lengths of the distal limbs from the marker
position–time histories and the position and acceleration of the centre
of mass. Before performing these calculations, however, we took two
precautions that were expected to benefit the validity of the outcome (see
also Bobbert and Santamaria,
2005).
First, for the limbs, we attempted to remedy the problem of motion of skin
markers relative to the underlying bony landmarks. For this purpose, we
assumed that the limbs were chains of interconnected rigid segments
(van den Bogert et al., 1994).
To define the lengths of the rigid link segments for each of the limbs we used
the configuration just before landing in trot. Assuming, furthermore, that no
error occurred in measuring the locations of the markers on the hoofs, we
optimised, for each individual video frame, the configuration of the chain of
each of the limbs by minimizing the sum of squared distances between the
locations of the chain joints and the actual marker locations. This also
allowed us to solve the problem that occasionally a fetlock marker or a
shoulder marker was lost from view during a section of a stride.
The second precaution taken was to define a rigid template for the trunk, using the locations of markers on the trunk in square standing. We also determined the location of the centre of mass of the trunk and of the marker on vertebra C7 relative to the rigid trunk template in square standing. Subsequently, for each individual video frame, the position and orientation of the template were found by optimisation, using as criterion the sum of weighted squared differences between template marker locations and actual marker locations. The weighting was introduced because the fore–aft excursions of some markers seemed larger than those of the underlying bones (for instance, at trot, the distance between the markers at the level of vertebrae T6 and T10 varied sinusoidally at the step frequency with a peak-to-peak amplitude of up to 2 cm in some horses, which was surely more than the variation in the distance between the spinous processes of vertebrae T6 and T10). The motions of the markers on vertebrae T17, L1, L3 and L5 seemed quite representative of those of the underlying bony landmarks, and therefore the squared differences between the locations of these markers in the template and their actual locations were counted twice in the optimisation criterion. The movement of the centre of mass of the trunk, the trunk orientation, and the location of vertebra C7, were then derived from the movement of the template during locomotion.
The time histories of the marker coordinates, some of which had been
reconstructed by fitting of templates, were smoothed at 6 Hz using a
fourth-order zero-lag Butterworth filter. Angles of the segments with the
horizontal were calculated, and a segmental model
(Buchner et al., 1997) was used
to determine the locations of mass centres of the limb segments and the head
and neck. The combination of these segmental mass centres, weighted according
to their relative masses, provided the location of the centre of mass of the
whole body (CM). Cubic splines were fitted to position-time and angle-time
histories, and the coefficients of the piecewise polynomials were used to
obtain linear and angular velocities and accelerations of the individual body
segments. This information was then used to calculate the linear acceleration
of CM, as well as the rate of change of angular momentum. Furthermore, the
coordinates of the joints of the limb chains were used to calculate the
distances to be used as indicators of limb force: the distance from elbow to
coffin joint in the forelimb, and the distance from stifle joint to coffin
joint in the hindlimb.
Individual limb forces were calculated from kinematics as outlined in the
introduction for phases in which only two limbs were in contact with the
ground. The first step, explained in Fig.
1, was to determine the distribution of the calculated total
ground reaction force (FR,total) over the limbs, by
determining the point P where the line of action of the calculated total
ground reaction force passed between the hoofs. Once P had been found, the
calculated FR,total was distributed over the individual
ground reaction forces FR,i of the supporting forelimb and
the diagonal hindlimb using the inverse ratio of their moment arms. In doing
so, it was implicitly assumed that the relative contribution of the two
supporting limbs to the horizontal component of the calculated
FR,total (FRx,total) is the same as
their relative contribution to the vertical component
(FRy,total), or in other words, that the two individual
limb reaction forces run in parallel. We are aware that the contributions of
the forelimbs and hindlimbs FRx,total may actually be
different (Dutto et al.,
2004). However, at trot we were interested primarily in the
distribution in the middle of the stance phase, where
FRx,total is less than 10% of
FRy,total (Dutto et
al., 2004; Merkens et al.,
1993b; Wilson et al.,
2001), so that a violation of our assumption will have only a
small effect on the distribution. At walk, the horizontal force is also small
compared to the vertical force throughout the cycle
(Merkens et al., 1986); we
calculated the distribution of FRy,total for several
instants that will be specified in the Results section, after presentation of
the force–time histories of the individual limbs.
The reaction force on each individual limb calculated at the instant that
FRy,total attained its peak at trot, together with the
length of the distal limb at this instant, gave us one point on the
force–length relationship of the distal limb. For the second point, we
used zero force and the distal limb length just before touch-down. With these
two points, the linear force–length relationship of each of the distal
limbs was defined. This relationship was then used to calculate for each frame
FR,i from the length of the distal limb. In the forelimb,
FR,i was assumed to act along the line from the foot to
the attachment of serratus ventralis on the scapula
(Dutto et al., 2006;
McGuigan and Wilson, 2003),
and for comparison with the measured FRy,i we multiplied
the calculated FR,i by the sine of the angle of this line
with the horizontal. In the hindlimb, FR,i was assumed to
act along the line from the foot to the point mid-way between tuber coxae and
trochanter major (Dutto et al.,
2006), and for comparison with the measured
FRy,i we multiplied the calculated
FR,i by the sine of the angle of this line with the
horizontal.
To determine the accuracy of calculating peak values of
FRy,total(t) at trot, we used the following
procedure. First, from the data captured over 15 s we took, for each horse,
the first 15 complete stride cycles, starting with touch-down of the left
forelimb. For each of the corresponding 15 left-diagonal and 15 right-diagonal
stance phases, we determined the peak of the calculated
FRy,total(t) as well as the peak of the measured
FRy,total(t), i.e. the sum of the vertical
reaction forces of the individual limbs provided by the treadmill-integrated
force measuring system. Next, we averaged these peak values over the stance
phases to obtain what we will call a `mean peak value' for calculated
FRy,total and a `mean peak value' for measured
FRy,total, and we took the difference between the elements
of each pair. Finally, we took the standard deviation of the differences
obtained this way. This standard deviation will be referred to as the
between-diagonal standard error of estimate (SEE); it is the standard error
that one makes in estimating the peak measured FRy,total
for a given diagonal of a given horse in trot on the basis of kinematics. If
one is interested only in the variations in peak FRy,total
over time, for example in a study in which lameness is temporarily induced
(e.g. Buchner et al., 1996a;
Weishaupt et al., 2004a), the
between-diagonal SEE is not important; in that case the within-diagonal SEE is
the parameter of interest. Within-diagonal SEE values were calculated as
follows. We subtracted from the peak values of the calculated
FRy,total of the individual stance phases the mean peak
value, performed the analogous operation for the peak values of the measured
FRy,total, and then took the difference between the two
elements of each pair. The standard deviation of the differences so obtained
will be referred to as the within-diagonal SEE.
Using a procedure analogous to the one described above, we determined the between-limb and within-limb SEE for calculating peak values of FRy,i(t) according to the GRF distribution method, and for calculating peak values of FRy,i(t) from distal limb length. Furthermore, SEE values were not only calculated for trotting but also for walking, in which case we selected for each horse nine complete stride cycles from the 15 s of data, starting with touch-down of the left forelimb. Last but not least, for several variables we calculated `grand mean peak values' by averaging not only over stance phases but also over horses.
The question may be raised how the accuracy of calculating peak
FRy,i according to the GRF distribution method compares
with that of calculating peak FRy,i according to the duty
factor method proposed by others (e.g.
Alexander et al., 1979;
Witte et al., 2004). To be
able to answer this question, we also calculated peak
FRy,i using the following equation:
 | (1) |
): 0.285 for each of the forelimbs and 0.215 for each of the
hindlimbs at trot, and 0.295 for each of the forelimbs and 0.205 for each of
the hindlimbs at walk. Values for ß were extracted from the measured
FRy,i(t) using a threshold of 100 N. |
Results |
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; Merkens et al.,
1993b). For example, at trot, the grand mean minimum value of
FRx,total (i.e. the peak braking force) amounted to
–3.2±0.4 N kg–1 and occurred at 26±2% of
the stance phase, and the grand mean maximum value of
FRx,total (i.e. the peak propulsive force) amounted to
2.9±0.5 N kg–1 and occurred at 60±2% of the
stance phase.
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) and duty
factors ß extracted from measured FRy,i(t).
Fig. 8 shows the resulting mean
peak FRy,i values together with the mean peak measured
FRy,i values. At trot, the grand mean peak
FRy,i calculated using
Eqn 1 was 11.2±0.5 N
kg–1 in the forelimb, with the inter-limb SEE being 0.7 N
kg–1 and the intra-limb SEE amounting to 0.16 N
kg–1, and 9.6±0.4 N kg–1 in the
hindlimb, with the inter-limb SEE being 0.4 N kg–1 and the
intra-limb SEE amounting to 0.2 N kg–1. Suffice it to say
here that even with error-free ß-values [they were error-free because
they had been extracted from measured FRy,i(t)],
the duty factor method when used to calculate peak values of
FRy,i did not clearly outperform the GRF distribution
method.
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As explained in the Materials and methods section, the peak calculated FR,i values, obtained according to the GRF distribution method, were used to determine the force–length relationships of the distal limbs, under the assumption that these relationships were linear. The stiffness of the distal forelimb obtained this way was 130±16 N kg–1 m–1 (range: 101–156 N kg–1 m–1) and that of the distal hindlimb was 73± 4 N kg–1 m–1 (range: 64–78 N kg–1 m–1). These force–length relationships were subsequently used to calculate FR,i(t) from distal limb length–time histories, and combined with limb angle–time histories to obtain FRy,i(t) as a function of time. For trotting, the calculated FRy,i(t) of three horses are shown together with the measured FRy,i(t) in Fig. 2. The match between the calculated and measured curves was quite good (it needs no argument that the small impact peaks in the measured FRy,i(t) of the forelimbs could not be reproduced from the distal limb length–time histories). Fig. 9 shows mean peak measured FRy,i values together with mean peak FRy,i values calculated from distal limb length. At trot, the overall correspondence between calculated and measured FRy,i(t) was satisfactory, as was to be expected given that peak FRy,total could be accurately calculated from kinematics (Fig. 4), that the distribution over the fore- and hindlimbs could be calculated reasonably well (Fig. 6), and that peak FRy,i occurred almost at the same time in the forelimb and diagonal hindlimb in contact with the ground (Fig. 2).
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At walk, the calculation of FRy,total was successful
(Figs 3,
4), but the calculation of time
histories and peak values of individual limb forces using the GRF distribution
method turned out to be quite a challenge. There are two phases in each
half-cycle in which the body is supported by only two limbs (insets in
Fig. 3 and bars below time
axes), one in which the body is supported by a forelimb and the ipsilateral
hindlimb (phase I, grey bars in Fig.
3), and the other in which it is supported by this forelimb and
the contralateral hindlimb (phase C, open bars in
Fig. 3). Unfortunately, in
these phases the GRF distribution method produced calculated force–time
curves that fluctuated considerably for some of the horses (extreme
fluctuations occurring in horse 2 are indicated by thin dotted lines in
Fig. 3); obviously, extracting
peak values from these curves would produce inaccurate results. What could be
done was to extract calculated FRy,i values at fixed
points in phases I and C (extracting values at 50% of phase I and phase C for
the forelimb, at 20% of phase C for the hindlimb and at 80% of phase I for the
hindlimb produced the dots in Fig.
3). When we took the largest of these two values for a given limb
during its contact phase and averaged them over contact phases, we still did
not get a very reliable estimate of the measured mean peak
FRy,i of this limb
(Fig. 7); the between-limb SEE
was 0.6 N kg–1 for the forelimb but no less than 1.0 N
kg–1 for the hindlimb. Alternatively,
FRy,i(t) could be calculated from time histories
of distal limb length, using the force–length relationships determined
on the basis of the results obtained at trot. In the forelimbs,
FRy,i(t) calculated from distal limb length
corresponded quite well with the measured
FRy,i(t), but in the hindlimbs the peak in the
second half of the stance phase was typically missing
(Fig. 3). Nevertheless, both
for the forelimbs and for the hindlimbs, the mean peak
FRy,i calculated from distal limb length corresponded
satisfactorily with the mean peak measured FRy,i
(Fig. 9). The grand mean peak
FRy,i in the forelimb was calculated to be 6.9±0.5
N kg–1 and measured to be 7.1±0.3 N
kg–1, with the inter-limb SEE being 0.4 N
kg–1 and the intra-limb SEE amounting to less than 0.2 N
kg–1. In the hindlimb, the grand mean peak
FRy,i was calculated to be 4.8±0.5 N
kg–1 and measured to be 4.7±0.3 N
kg–1, with the inter-limb SEE being 0.5 N
kg–1 and the intra-limb SEE amounting to less than 0.2 N
kg–1. When it comes to estimating the absolute value of peak
FRy,i, these results compare favourably with the results
obtained using the duty factor method; at walk, the grand mean peak
FRy,i, calculated using
Eqn 1 was 7.6±0.3 N
kg–1 in the forelimb, with the inter-limb SEE being 0.5 N
kg–1, and 5.2±0.3 N kg–1 in the
hindlimb, with the inter-limb SEE being 0.6 N kg–1. As
already pointed out by Witte et al. (Witte
et al., 2004), the overestimation of peak
FRy,i by the duty factor method was due to
FRy,i(t) departing from the positive half of a
sinusoid (Fig. 3).
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Discussion |
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The GRF distribution method that we proposed is straightforward from a mechanical point of view, and with the precautions taken in this study to reduce errors in the location of bony landmarks due to skin movement, we were able to reliably calculate FRy,total(t) both at trot (Fig. 2) and at walk (Fig. 3), and we could calculate peak forces of FRy,total(t) with a between-diagonal SEE of 0.5 N kg–1 or less (Fig. 4). This is of course required for the GRF distribution method to work, but far from sufficient. From Fig. 1, which gives a representative example of the situation at the instant that FRy,total reached its peak at trot, it will be obvious that the GRF distribution method also relies critically on the horizontal component of FR,total, on the exact location of CM, and on the rate of change of angular momentum, which pushes FR,total away from CM parallel to its line of action. The fact that we were able to accurately calculate the average relative load on the forelimb at the instant that FRy,total reached its peak at trot (calculated: 54.1%, measured: 54.3%), suggests that at this instant the horizontal component of FR,total and the exact location of CM could reliably be obtained from the kinematic data (despite our somewhat bold assumption that the reaction forces on the two limbs in contact were in parallel). The angular momentum was found to be relatively small and unimportant.
Unfortunately, at walk, the GRF distribution method did not work as well as it did at trot. It was not possible to detect a peak in the forces calculated according this method (Fig. 3, diagrams of horse 2), and we had to rely on force values extracted at fixed points in the contact phase of each of the limbs (floating dots in Fig. 3). Although the maximum of these force values did in fact approximate the peak values in the measured forces (Fig. 7), the approach seems quite unreliable if we consider at which point some of the force values were extracted from their corresponding curves (Fig. 3, diagrams of horse 2). Considering that FRy,total was approached quite accurately (top panels in Fig. 3), and that also at walk the angular momentum was found to be small and unimportant, it must be concluded that the calculation of the horizontal component of FR,total, and therewith the point where FR,total passes between the hoofs, was not very accurate at walk. This then brings us to the question how well the individual limb forces calculated from distal limb length compare with measured forces.
The calculation of individual limb forces from distal limb length is based on the notion that the distal limb operates as a linear spring. At trot, a good correspondence was obtained between FRy,i(t) calculated from distal limb length and measured FRy,i(t) (Fig. 2) and between their mean peak values during the stance phase (Fig. 4), for both the forelimbs and the hindlimbs. However, this is not really surprising. After all, the force–length relationships of the distal limbs were derived using force values and length values calculated at two instants at trot [the instant just before touch-down of the limb and the instant that the calculated FRy,total(t) attained its peak]; the crucial information was peak FR,i calculated according to the GRF distribution method, and we had already established that this method worked well at trot. In any case, the notion that the distal limb operates as a linear spring seems to hold for trotting, for both the forelimbs and the hindlimbs. It is important to note that the stiffness calculated for the `spring' between elbow and coffin joint varied considerably among the horses participating in this study, from 101 to 156 N kg–1 m–1 (mean, 130 N kg–1 m–1), which implies that skipping the calibration step and assuming a fixed value of stiffness for all horses will lead to considerable errors in estimation of FRy,i(t). The stiffness values calculated for the `spring' between stifle and coffin joint varied less among the horses, from 64 to 78 N kg–1 m–1 (mean, 73 N kg–1 m–1).
The problems that we encountered with the GRF distribution method at walk could potentially be solved using the force–length relationships of the distal limbs established on the basis of the results at trot. In the case of the forelimbs, FRy,i(t) calculated from distal limb length followed the measured FRy,i(t) quite well (Fig. 3). In the case of the hindlimbs, however, the situation was less favourable; the second peak in FRy,i(t), which occurred during the second half of the hindlimb stance phase, was not well reproduced (Fig. 3). It cannot be decided at this point whether this is an artefact due to the specific limb configuration in this phase, causing the fitting of a chain of rigid segments and therewith the determination of limb length to run awry, whether the limb perhaps does not operate like a perfect linear spring with no hysteresis, or whether it is caused by a change in stiffness of the distal hindlimb due to increased muscle activation, which obviously would violate altogether the notion of the distal limb acting as a simple linear spring. Suffice it to say, however, that despite these imperfections the mean peak FRy,i during the stance phase calculated from distal limb length corresponded satisfactorily with the mean peak measured FRy,i, both for the forelimb and the hindlimb (Fig. 9), with the inter-limb SEE being 0.6 N kg–1 and the intra-limb SEE amounting to less than 0.2 N kg–1.
Obviously, calculating individual limb forces using the GRF distribution
method is highly involved compared to calculating them using the duty factor
method. Why go through all the trouble of collecting and processing the
kinematic data, if according to Figs
7 and
8 the duty factor method
produces estimates of FRy,i that are just as good at trot
and perhaps even better at walk? After all, for the duty factor method one
only needs touch-down and take-off times of individual hoofs, and these can be
determined accurately from hoof-mounted accelerometers
(Parsons and Wilson, 2006). If
one is interested merely in the ground reaction forces on the individual limbs
in healthy animals, the duty factor method is indeed an attractive
alternative. Especially at trot, the shape of the individual force curves is
virtually identical to the positive half of a sinusoid
(Fig. 2) (see also
Witte et al., 2004), the
motion pattern is left-right symmetrical (the greatest difference that we
found in our horses between the mean measured force carried by the left and
right side was 2.5% of body weight for the forelimbs and 1.8% of body weight
for the hindlimbs), and the assumption of a fixed contribution of the
forelimbs and hindlimbs to the average FRy,total seems
acceptable (the mean contribution of a single forelimb ranged from 0.273 to
0.308 and that from a single hindlimb ranged from 0.20 to 0.227 across the
horses used in this study). However, in contrast to the GRF distribution
method, the duty factor method crucially relies on information that must have
been acquired beforehand with direct force measurements, namely the average
contribution of the forelimbs and hindlimbs to the average
FRy,total at trot and walk. When it comes to studying lame
animals, assumptions about left-right symmetry and the contribution of the
forelimbs and hindlimbs to the average FRy,total will no
longer hold (e.g. Weishaupt et al.,
2004a; Weishaupt et al.,
2006). In that case, the distribution of the average load over the
individual limbs is unknown, and its estimation becomes the very challenge.
Furthermore, if one wants to study how a horse manages to redistribute the
load, information about the forces on the individual limbs is no longer
sufficient and kinematic data are needed anyhow. In that case, it is highly
desirable to have ground reaction forces on individual limbs that are
consistent with the kinematic data, and the GRF distribution method seems to
be a suitable way of obtaining these. We are not claiming, of course, that the
forces calculated from kinematics could be used for an inverse dynamics
analysis; such an analysis requires also the true horizontal component and
centre of pressure of the ground reaction forces on each individual limb,
which can only be provided by direct measurement with a force plate. At the
same time it should not be forgotten, however, that an inverse dynamic
analysis can only be conducted reliably if one has a consistent set of
kinematic and kinetic data (Bobbert et al.,
1991; Bobbert et al.,
1992).
The final question is whether the calculation of individual limb forces
from kinematics, as proposed in this study, is sufficiently accurate to be
used in studying the adaptation of locomotion patterns following injury.
Obviously, forces estimated from kinematics will never be as accurate as
forces measured directly with a treadmill-integrated system like the one
developed by Weishaupt et al. (Weishaupt
et al., 2002), but if no direct force measurements are possible
the calculation of individual limb forces from kinematics seems to provide a
good alternative. In a study of induced weight-bearing lameness of the
forelimb at trot (Weishaupt et al.,
2006), it has been shown that horses manage to reduce peak
FRy,i on the affected limb by 4%, 9% and 24% for subtle,
mild and moderate lameness, respectively, with the relative contribution of
the forelimb to peak FRy,total during the lame diagonal
stance phase going down from 53 to 46%. Corresponding values for induced
weight-bearing lameness of the hindlimb at trot
(Weishaupt et al., 2004a) were
2%, 7% and 15%, respectively, with the relative contribution of the forelimb
to peak FRy,total during the lame diagonal stance phase
going up from 53 to 57%. In these types of studies, changes occur over time
and each horse can serve as its own comparison. This means that in calculating
the changes in peak FRy,i from kinematics as proposed in
the current paper, the relevant parameter is the intra-limb SEE, which
amounted to less than 0.2 N kg–1, i.e. less than 2% of the
peak FRy,i. It seems, therefore, that the method of
calculating peak FRy,i from kinematics is sufficiently
accurate to study the effects of induced lameness at trot, even if the
lameness is only mild to moderate. The method will also be useful for other
studies in which each horse can serve as its own comparison, such as studies
into the effect of treatment of lameness on the locomotion pattern. The most
urgent and perhaps most challenging studies, however, will be those of load
distribution in chronically lame horses. For those studies, the method
proposed in the present study has the advantage that it does not require the
lame horses to walk and trot on an instrumented treadmill, which they might
not be able to do, but it remains to be established whether the method is
sufficiently accurate to reveal asymmetries in loading of the individual
limbs.
In conclusion, the calculation of individual limb reaction forces from kinematics as proposed in the present study is quite accurate: the inter-limb SEE for estimating mean peak forces is of the order of 0.6 N kg–1, and the intra-limb SEE is even less than 0.2 N kg–1. Apart from that, the approach has an important advantage over other methods, such as the duty factor method: since ground reaction force patterns are calculated from kinematics, one has all the information required for a full biomechanical analysis of the origin of the force patterns, and therefore in the locomotion adaptations responsible for changes in these patterns.
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