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First published online December 14, 2007
Journal of Experimental Biology 211, 138-149 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.008243
Steady locomotion in dogs: temporal and associated spatial coordination patterns and the effect of speed
CNRS, MNHN, Université P6, Col. De France, Muséum National d'Histoire Naturelle, Département Ecologie et Gestion de la Biodiversité, UMR 7179, Pavillon d'Anatomie Comparée, CP 55, 57 rue Cuvier, 75231 Paris cedex 05, France
* Author for correspondence (e-mail: maes{at}mnhn.fr)
Accepted 31 October 2007
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Summary |
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 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Key words: gait, limb coordination, mammal, quadruped, speed, APS
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INTRODUCTION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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; Muybridge,
1899). Symmetrical and asymmetrical gaits were later distinguished
(Howell, 1944;
Hildebrand, 1965); in
symmetrical gaits, the footfalls of the two feet of the same pair (fore or
hind) are evenly spaced in time whereas in asymmetrical gaits this is not the
case for at least one of the two pairs of limbs. The fundamentals of gait
analysis were established over the next few decades by Hildebrand
(Hildebrand, 1965;
Hildebrand, 1966;
Hildebrand, 1977), Dagg
(Dagg, 1973), Gambaryan
(Gambaryan, 1974) and Sukhanov
(Sukhanov, 1974). However, the
methods used were not based on the same sets of parameters for studies of
interlimb coordination in symmetrical and asymmetrical gaits. The links
between gaits and the pattern of interlimb coordination over the entire range
of speeds used by an animal were not clarified. The first efforts to
investigate these links were based on the comparison of symmetrical and
asymmetrical gaits at a large range of speeds, based on kinematic parameters
(Herbin et al., 2004;
Herbin et al., 2006), or
through a linear discriminant analysis (LDA) for the automatic identification
of all gaits (Robilliard et al.,
2007). However, the changes occurring in limb coordination with
increasing speed remain unclear. The anteroposterior sequence (APS) approach,
first described in 2003 (Abourachid,
2003) and tested experimentally several years later
(Abourachid et al., 2007), aims
to quantify all kinds of interlimb coordination – symmetrical or
asymmetrical gaits and unsteady locomotion – to define the mechanisms
common to, and the differences between, the two types of gait. According to
Abourachid and colleagues, APS analysis considers quadrupedal locomotion to be
a succession of anteroposterior sequences of movement, where a sequence is the
association of consecutive cycles of the forelimbs followed by consecutive
cycles of the hindlimbs (Abourachid,
2003; Abourachid et al.,
2007). Thus, for all gaits, limb coordination involves coordinated
movements of the forelimbs, coordinated movements of the hindlimbs and a
relationship between these two pairs. Only three temporal parameters are thus
required to define all coordination patterns of the limbs, whatever the
steadiness of locomotion (Fig.
1A, Table 1). The
first aim in the present study was to investigate, within the framework of APS
analysis, changes in these three parameters with increasing speed, to
understand the way in which temporal limb coordinations support changes in
kinematics with changing speed.
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Limb movement is clearly characterised by both spatial and temporal
aspects, but spatial interlimb coordination has only recently been
investigated (Abourachid et al.,
2007). We define spatial interlimb coordination as the way in
which the four limbs are distributed in space at footfall. As the left and
right limbs of a pair are linked to the same rigid structure (thoracic belt
for the fore pair and pelvic belt for the hind pair), the distance travelled
would be simply equal to the product of speed and time. Due to this linear
relationship, we presupposed that the spatial coordination of the pairs of
limbs would reflect the temporal coordination of these pairs. However, because
the pairs of limbs are not linked to the same anatomical structure, but rather
are connected by a more or less flexible vertebral axis, it is less probable
to observe a linear relationship between temporal and spatial coordination of
the pairs of limbs. Thus, the second aim of this study was to verify these
assumptions by quantifying the relationship between temporal and spatial limb
coordination, to gauge the benefit of integrating spatial limb coordination
into studies on quadrupedal locomotion.
Many studies of limb coordination in quadrupeds have been carried out on
small mammals. Studies on dogs have focused on mechanics or kinematics
(Alexander, 1974;
Cavagna et al., 1977;
Jayes and Alexander, 1978;
Lee et al., 1999;
Walter and Carrier, 2007)
rather than on limb coordination. Furthermore, symmetrical and asymmetrical
gaits were not analysed simultaneously in the few studies dealing with limb
coordination (Hildebrand,
1966; Hildebrand,
1968; Hildebrand,
1977; Bertram et al.,
2000). However, it is quite easy to control dogs during overground
locomotion (on a steady flat ground), which most closely resembles locomotion
in the natural environment, whereas a treadmill is generally needed to induce
locomotion in studies of small mammals. Moreover, large amounts of data can be
obtained with a simple video recording method, and no rider is required, in
contrast to studies on horses. Finally, the dog is a medium-sized mammal with
generally well-defined gaits. This makes it potentially useful for the
definition of general trends in the locomotor behaviour of mammals.
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MATERIALS AND METHODS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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The dogs moved along a 12 m flat carpet. White lines perpendicular to the axis of the runway and at 0.10 m intervals were used for investigations of the spatial characteristics of locomotion and for correction for parallax deformation. Free space at the experimentation site made it possible for the animals to take a run-up for high-speed gaits. Animals were led on a leash sufficiently long to have no effect on locomotion. The dog handlers were asked to practice walking or running with their animals at five constant speeds (0.8 m s–1, 1.3 m s–1, 2.0 m s–1, 3.2 m s–1 and 5.3 m s–1), designed to incite dogs to use their entire locomotion repertoire. Dog handlers adjusted their speed using a stopwatch and the white marks on the runway. These speeds corresponded to walking, trotting and galloping speeds in the dogs, with slow and fast modulation in each gait. For rapid gallops, at speeds beyond the running speed of the handlers (speed >7 m s–1), the dogs ran alone towards a ball placed on the ground at the opposite end of the runway. Each dog performed three trials at each speed, giving a total of 90 trials.
Recording and film analysis
A high-speed video recorder (BASLER A504K; Highland, IL, USA), placed
perpendicular to the runway, 8 m from its centre, was used to film the dogs
throughout their progression along the carpet. We used different recording
frequencies, depending on the speed of the animals (50 Hz for slow walking, 75
Hz for fast walking, 100 Hz for trot and 200 Hz for gallops). The records were
analysed using Virtual Dub (version 1.6.12;
http://www.virtualdub.org/).
The timing of the footfalls (when the foot makes contact with the ground) and
take-off (when the last toe leaves the ground) of the limbs was noted, using
frame number, and the positions of the feet on each touchdown were determined
using the white lines marked on the carpet (precision 0.05 m). Timings were
recorded three times for one trial at each speed to establish a maximal error
of one frame. The data were visualised, using classical gait diagrams
(Vincent and Goiffon, 1779;
Marey, 1873) and track
diagrams (Dagg, 1974;
Abourachid et al., 2007),
making it possible to spot APSs (see below for terminology). Gaits were
manually identified, and kinematic and APS parameters were then
calculated.
Gait identification
For each trial, we used APS terminology to avoid confusion between trailing
and leading limbs in time and space: one side of the dog was numbered 1 and
the other 2 (Jayes and Alexander,
1978; Abourachid et al.,
2007). When the dog used a symmetrical gait, the assignment of the
number 1 to the left or right side was of no importance, because both sides
had similar locomotion characteristics and functions. For asymmetrical gaits,
the 1-forelimb (f1) corresponded to the first forefoot to touch the ground
during a gallop sequence. Other limbs were referred to as 2-forelimb (f2),
1-hindlimb (h1) and 2-hindlimb (h2).
Each gait was identified based on classical definitions
(Hildebrand, 1966;
Hildebrand, 1977;
Gambaryan, 1974) within the
APS framework (Abourachid,
2003; Abourachid et al.,
2007), resulting in three symmetrical gaits (lateral walk, pace
and trot) and two asymmetrical gaits (transverse gallop and rotary gallop)
(Fig. 1B).
Kinematic parameters
For all trials, and for each APS, the following parameters were calculated:
cycle duration (D; seconds), corresponding to the period between two
consecutive footfalls for the foot concerned; stance (St; s) and
swing (Sw; s) duration (the period of contact for a limb and the
period of limb flight, respectively); cycle frequency
(F=D–1; Hz); stride length (L; m),
corresponding to the distance between two successive footprints for the same
foot; and duty factor (DF=St/D; %), the fraction of
the cycle for which the foot is in contact with the ground
(Alexander et al., 1977). We
also calculated the forelimb–hindlimb difference in duty factor
(DFdiff = forelimb mean DF – hindlimb mean
DF) (Hutchinson et al.,
2006). We assessed temporal limb coordination by calculating the
fore lag (FL), hind lag (HL) and pair lag (PL)
(Fig. 1A): FL = time
between the f1 and f2 footfalls; HL = the time between the h1 and h2
footfalls; and PL = the time between the f1 and h1 footfalls, as a
percentage of f1 cycle duration
(Abourachid, 2003). Similarly,
we investigated spatial limb coordination by calculating fore gap
(FG), hind gap (HG) and pair gap (PG)
(Fig. 1A): FG = the
distance between the f1 and the f2 foot contact positions; HG = the distance
between the h1 and h2 foot contact positions; and PG = the distance between
the f1 and h1 foot contact positions in the same sequence, as a percentage of
f1 stride length (Abourachid et al.,
2007). When possible, we used the various parameters from previous
studies to calculate the FL, HL and PL that would have been obtained if these
studies had been carried out with the APS method. We also estimated these lags
from gait diagrams in several reference publications, making it possible to
compare our results for malinois dogs with those for other quadrupeds.
Speed (u=Lf1/Df1; m
s–1, where Df1 and
Lf1 are the cycle duration and stride length of the f1,
respectively) was used to calculate Froude number
[Fr=u2(gh)–1,
where g is free fall acceleration (g=9.81 m
s–2) and h is the mean withers height], for possible
future comparisons with other species
(Alexander and Jayes,
1983).
Statistical analysis
The mean values of APS parameters were compared. As not all the data were
normally distributed and homoscedasticity was not always observed,
Mann–Whitney non-parametric tests were performed. Values of
P<0.05 were considered statistically significant for differences
between time and space, between the different coordination types (fore-, hind-
or interpair coordination) or between gaits (GraphPad Prism, version 3.0;
GraphPad Software, Inc., San Diego, CA, USA).
For the relationship between each APS parameter and speed, a runs test was
used to determine whether the data deviated significantly from a straight line
(one-tailed ANOVA). If the data did not deviate significantly from a straight
line (P>0.01), an F-test was used to determine whether
the slope differed significantly from zero (P<0.05). This approach
was used to identify trends in the relationships between APS parameters and
speed, rather than to try to account entirely for the dispersion of the data.
We then used Zar's method (Zar,
1984), which is equivalent to an ANCOVA and compares straight
regression lines by testing whether their slopes and intercepts are
significantly different. Values of P<0.05 indicated a significant
difference in the slopes or intercepts of the regression lines (GraphPad
Prism, version 3.0).
The statistical significance of differences between PL and `PG+TR' (P<0.05) was assessed by an ANOVA, as the two sets of data followed a normal distribution for all gaits (Kolmogorov–Smirnov test).
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RESULTS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Cycle characteristics
We obtained a large overall range of speeds (from 0.4 to 10.0 m
s–1) and specific but overlapping ranges for each gait
(Fig. 2A). Trot was the only
symmetrical gait with a speed range overlapping those of asymmetrical
gaits.
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0.4 s and 0.1 s,
respectively. The contribution of swing to cycle duration increased with
speed. Within their own speed ranges, almost all gaits followed the general
pattern for cycle and stance duration (Fig.
3). However, swing duration remained constant only during trot,
transverse gallop and slow rotary gallop (P>0.05). In particular,
once a plateau had been reached for the slow rotary gallop, the cycle and
swing durations suddenly decreased, tending to increase subsequently with
increasing speed (at speed exceeding 7.5 m s–1;
P>0.05).
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Moreover, the DF decreased with increasing speed (Fig. 4A). It fell below 50%, resulting in the duration of swing being higher than that of stance (Fig. 3), for speeds exceeding 2.0 m s–1 (approximately Fr=0.7). This threshold corresponded to slow trot and pace – the beginning of running gaits and the introduction of suspension phases, during which no foot of the animal was in contact with the ground. The DFdiff as a function of speed showed an irregular distribution centred on zero (Fig. 4B). The DF of the forelimbs was higher than that of the hindlimbs in 62.5% of sequences and similar to that of the hindlimbs in only 9.0% of sequences. A higher DF of the forelimb was observed for all gaits, except the fast rotary gallop, in which hindlimb DF was higher than forelimb DF in 78.9% of sequences. We observed a simultaneous gradual decrease in the variation of DFdiff about the mean value, from higher than ±0.2 to lower than ±0.05, with increasing speed (Fig. 4B).
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In almost all gaits, there were no suspension phases (no foot on the
ground) at low speed, whereas two possible suspension phases were observed at
high speed (Fig. 2B,C). There
was no suspension phase during lateral walk, by definition, but also at the
lowest speeds for symmetrical `running gaits' (pace and trot). In this last
case, one diagonal limb couplet (f1–h2 or f2–h1) during trotting
or one lateral limb couplet (f1–h1 or f2–h2) in pace touched the
ground just before the take-off of the foot of the other diagonal or lateral
couplet. As speed increased, one or two suspension phases per sequence were
observed for trot, pace and gallops. A first suspension phase (sp1) separated
the stance of the first diagonal limb couplet (f1–h2) from the second in
trot and the first lateral limb couplet (f1–h1) from the second in pace.
For asymmetrical gaits, sp1 occurred after the two forelimb stances and
corresponded to a flexed suspension phase
(Hildebrand, 1959;
Dagg and De Vos, 1968) or
crossed flight (Gambaryan,
1974). The second suspension phase, sp2, separated the stance of
the second diagonal limb couplet (f2–h1) from the first in trot and the
second lateral limb couplet (f2–h2) from the first in pace. For
asymmetrical gaits, sp2 occurred after the two hindlimb stances – sp2
therefore typically corresponded to the extended suspension phase
(Hildebrand, 1959;
Gambaryan, 1974). The
frequency of these suspension phases increased with speed, but there was never
an sp2 in the absence of an sp1 in the sequence. However, the sp2 pattern was
irregular in transverse gallop, and the rotary gallop was the only gait for
which no sequence was observed without at least one suspension phase,
regardless of speed.
Finally, stride length increased linearly from slow to high speeds (Fig. 5). Only the fast rotary gallop distinguished itself from the general tendency, with a slope significantly higher than those of other gaits.
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). We obtained slightly lower PL values
(96±3%), so this gait may actually be considered to be a paced walk.
However, as the corresponding PL value was significantly higher than
that for lateral walk (84±5%) (P<0.05), we nonetheless
considered this gait as pace. As the PL is around 100%, the footfall
of a given hindlimb occurs at the start of the next cycle of its ipsilateral
forelimb. The ipsilateral limbs are therefore synchronised.
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The HL value confirmed the distinction between the transverse gallop (HL>0%) and the rotary gallop (HL<0%). Dogs did not use the bound, half bound or pronk. The two sets of data obtained for the rotary gallop, resulting from the two experimental conditions (dogs running beside their handlers – slow rotary gallop; dogs running alone – fast rotary gallop), differed in having slightly different FL and HL values (slow rotary gallop, FL=21±3% and HL=–18±3%; fast rotary gallop, FL=18±1% and HL=–15±1%).
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Gaps and spatial coordination
FG, HG and PG were calculated to investigate spatial
coordination (Fig. 1A,
Table 3). In symmetrical gaits,
FG=HG=50±5% (P>0.05) – the foot of
a 2-limb therefore makes contact with the ground in the middle of the
contralateral 1-limb stride length (Fig.
1). In asymmetrical gaits, FG<50±5% and
HG<50±5% (P>0.05) – the feet of the two
limbs of a pair therefore touch the ground close together, at a distance less
than half the stride length of one of these limbs
(Fig. 1). HG, like
HL, also distinguished between transverse gallop
(HG<50±5%) and rotary gallop (HG<0%). Moreover,
absolute values of FG were always higher than those for HG
in asymmetrical gaits (5.1±3.8%, P<0.05). Thus, in both
symmetrical and asymmetrical gaits, the gaps for limb pairs (FG and
HG) were similar to the lags for these pairs (FL and
HL) (P>0.05), except for the lateral walk, for which
variability was higher in space than in time, and the transverse gallop, for
which FL and HL were slightly lower than FG and
HG, respectively (P<0.05).
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The pair gap differed considerably between different symmetrical or asymmetrical gaits (Table 3). These pair gap values were both highly variable and very different from the pair lag (P<0.05), in contrast to the similarity observed for FL–FG and HL–HG.
Finally, the widely accepted gait variability of 5% for time parameters
(Hildebrand, 1966) was
respected for most lags and gaps (Tables
2,
3). However, variability
exceeded 5% for PL in transverse gallop and the slow rotary gallop
and for PG in almost all gaits, with standard deviations between 6%
and 15%.
Interlimb coordination: relationship to speed
Straight regression lines were used to assess trends in possible
relationships between APS parameters and speed
(Appendix 1). In the results
presented below, a linear regression line could be fitted to the data unless
otherwise stated.
Lags and gaps within pairs (FL, HL, FG and HG)
In all symmetrical gaits, FL, HL, FG and HG were constant
(Fig. 6), with values of
50±5%, whatever the speed (P>0.05,
Appendix 1). By contrast, the
fast rotary gallop was the only asymmetrical gait in which the values of the
four parameters remained significantly constant with increasing speed
(P>0.05). Moreover, all four parameters for transverse gallop and
FG for slow rotary gallop decreased significantly with increasing
speed (P<0.05). Only HL and HG for slow rotary
gallop increased significantly with increasing speed (P<0.05), due
to the inversion of hindlimb coordination with respect to forelimb
coordination. In general, data dispersion decreased with increasing speed.
PL and PG
The relationship between PL and speed depended on gait
(Fig. 7A). PL
increased significantly with increasing speed for the lateral walk and
transverse gallop (P<0.05), whereas it decreased significantly
with speed for the trot and slow rotary gallop (P<0.05)
(Appendix 1). By contrast,
PL showed no specific relationship to speed in pace and fast rotary
gallop (P>0.05). However, several PL values for the slow
transverse gallop of one dog closely resemble PL values of trot,
making the corresponding slope higher.
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PG increased with increasing speed for all gaits (P<0.05), except the slow rotary gallop, which had a constant PG (P>0.05), (Fig. 7B). Moreover, the positive relationship between PG and speed decreased in magnitude with increasing speed, from the lateral walk to the rotary gallop (Appendix 1). However, because of the dispersion of the data, the straight regression lines calculated indicate trends only in the relationship between PG and speed, without explaining data dispersion entirely (Appendix 1).
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DISCUSSION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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How can speed be increased?
The decrease in cycle duration reached a plateau at a speed of about 4.0 m
s–1 (about Fr=2). Beyond this threshold, increasing
stride length rather than increasing cycle frequency is used to increase
speed. Most quadrupeds use this strategy to increase speed
(Pennycuick, 1975;
Heglund and Taylor, 1988;
Hutchinson et al., 2006). The
threshold of 4.0 m s–1 corresponds to the zone of overlap
between symmetrical and asymmetrical gaits in our data. Thus, to increase
speed, dogs increase both cycle frequency and stride length if they use
symmetrical gaits, whereas they almost exclusively increase stride length if
they use an asymmetrical gait. Similar observations have been reported in
mice, but with a different threshold (speed of 42.5 cm–1,
around Fr=1) (Herbin et al.,
2004; Herbin et al.,
2006). Thus, the difference in the contributions of cycle
frequency and stride length to increasing speed seems to be a key difference
between symmetrical and asymmetrical gaits and may be one of the main
mechanisms underlying transitions from symmetrical to asymmetrical gaits.
Swing duration was found to be constant in dogs. However, swing has
recently been reported to decrease in alligators
(Reilly and Elias, 1998), mice
(Herbin et al., 2004;
Herbin et al., 2006), horses
(Robilliard et al., 2007) and
elephants (Hutchinson et al.,
2006). Differences in data treatment may account for these
differences in results. Our data were not averaged, in contrast to those of
other studies. Thus, interindividual variability may be responsible for our
not observing a real decrease in swing duration, because the runs test showed
that our data could not be reasonably linearised.
At very high speed – for the fast rotary gallop – cycle
duration fell abruptly by around 0.1 s and then increased with increasing
speed. Even if only three of the five dogs ran at these speeds, each of these
three dogs showed a similar pattern (P>0.05). This was due to the
increase in swing duration with only a slight further decrease in stance
duration (Fig. 3). To our
knowledge, this pattern has never before been reported, probably due to the
lack of studies with a wide range of speeds, including very fast locomotion.
This increase in swing duration is due to the increase in duration of the
suspension phases. Each of the two suspension phases increased in duration
from 0 to around 0.05 s (L.D.M., unpublished results), leading to an increase
in swing duration of about 0.1 s. However, morphological characteristics may
be responsible for the first decrease in swing duration; we observed sagittal
flexing of the spinal column, resembling the movement of a sprung leaf,
particularly in the lumbar region. This behaviour was observed beyond 8.0 m
s–1 and enabled the animal to cover longer distances during
suspension phases, thus having a longer stride length, with a shorter swing
duration than during the slow rotary gallop. This mechanism makes it possible
to increase both swing duration and stride length, allowing the animal to
reach very high speeds. At these speeds, the dogs ran without handlers and
aimed to retrieve the ball, which was placed at the opposite end of the
runway, as rapidly as possible. They therefore optimised their locomotion, as
predators do when chasing their prey. This interpretation is based on
behavioural observations and was not measured. However, it has already been
shown in other mammals that sagittal flexion of the spinal axis is largely
responsible for an increase in the distance travelled by the hindlimbs
(Hildebrand, 1959;
Grillner, 1975;
Rocha Barbosa et al., 1996;
Schilling and Hackert,
2006).
Relationship between suspension phases and speed
The increasing frequency of suspension phases
(Fig. 2) contributed to the
increase in speed. The presence of suspension phases classically distinguishes
running gaits from walking gaits
(Hildebrand, 1966). However,
at the lowest speeds, suspension phases were not observed in symmetrical
`running gaits' (pace and trot). We interpret this as indicating that dogs
adapted their limb coordination, using pace or trot, in case they needed to go
faster, but no suspension phase was required because the speed was too low. A
similar pattern has been observed in horses trotting at low speeds
(Hoyt et al., 2006). A single
suspension phase was sufficient at slightly higher speeds and a second
suspension phase occurred at the highest speeds, to increase the distance
covered during the flight phase. Horses generally use a maximum of one
suspension phase, in the flexed position
(Hildebrand, 1959), although a
second suspension phase has been reported in rare cases
(Howell, 1944). Hildebrand
suggested that there might be even a third suspension phase between the stance
phases of the two forelimbs, during rotary gallop in the cheetah
(Hildebrand, 1959). The number
of suspension phases in the sequence therefore seems to increase with
flexibility of the back, from elephant
(Hutchinson et al., 2006) to
cheetah. The rotary gallop is the only gait that required at least one
suspension phase, probably to make the forelimbs withdraw from the trajectory
of the hindlimbs, thereby avoiding interference between the forelimb and its
ipsilateral hindlimb.
Duty factor and fore-hind kinematic homogeneity
In malinois dogs, the mean fore–hind difference in duty factor was
mainly positive (in more than 60% of the sequences)
(Fig. 4B). This result is
consistent with data from studies on other mammals
(Biewener, 1983;
Hutchinson et al., 2006) and
reptiles (Renous et al.,
2002). Moreover, 60% of the body weight is supported by the
forelimbs in most quadrupedal mammals
(Björk, 1958;
Jayes and Alexander, 1978;
Rollinson and Martin, 1981),
especially dogs (Lee et al.,
1999), probably accounting for the higher duty factor or stance
duration of the forelimbs than of the hindlimbs. However, at very high speeds,
the duty factor of the hindlimbs exceeded that of the forelimbs in these
malinois dogs. As dogs power locomotion by torque about the hips
(Lee et al., 1999;
Usherwood and Wilson, 2005),
the duty factor of the hindlimbs probably takes over that of the forelimbs to
optimise the exchanges of forces between the ground and the hindlimbs. This is
consistent with the notion that very high speed makes the difference between
the weight-supporting role of the forelimbs and the propellant role of
hindlimbs more marked (Usherwood and
Wilson, 2005).
The variability of DFdiff decreased with increasing
speed, possibly due to increasingly precise stance and swing durations, due to
an increasing role of cognition in locomotion at increasing speed. As
stability increases strongly at high speeds if the swing duration becomes more
precise (Seyfarth et al.,
2003), a decrease in DFdiff should reflect an
increase in dynamic stability.
Relationship between temporal and spatial coordination and the effect of speed
Coordination within pairs
Experimental FL and HL values were consistent with
theoretical values (Table 1),
making it possible to distinguish between symmetrical and asymmetrical gaits,
as also evidenced by data from other mammals
(Table 4). However, variability
in FL or HL values was frequently found to result from
treadmill locomotion, especially in small mammals. Limb coordination may be
influenced by a permanent adjustment of the speed of the animal to treadmill
speed, as shown for various kinematic parameters in many studies
(Wetzel et al., 1975;
Eliot and Blanksby, 1976;
Alton et al., 1993;
Barrey et al., 1993;
Wank et al., 1998;
Dunbar, 2004;
Herbin et al., 2007).
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FG and HG values reflected those for FL and
HL (Table 3,
Fig. 1). These findings are
consistent with the results obtained with track diagrams of pacing camels
[FG=51% and HG=48%, calculated from Dagg
(Dagg, 1974)]. Thus, in
symmetrical gaits, the footfalls of the limbs of a given pair are evenly
spaced not only in time but also in space. In asymmetrical gaits, there is a
similar tendency to synchronise the two limbs of a pair not only in time but
also in space. This result confirmed our assumption: the spatial coordination
of the pairs of limbs reflects the temporal coordination of these pairs.
For asymmetrical gaits, HL and HG were lower than
FL and FG, respectively, indicating that hindlimbs have a
more marked tendency to become synchronised than forelimbs. This may
facilitate the propulsion exerted by hindlimbs, if we consider the animal as a
combination of a pendulum for the forelimbs and a spring for the hindlimbs
(Cavagna et al., 1977).
Certain lags and gaps maintained by the forelimbs during their stance may make
the `pole-vaulter movement' (Cavagna et
al., 1977) more efficient, making it possible to lift the centre
of mass without slowing down the forward progress of the whole body. This is
particularly evident at very high speeds, such as those reached by running
cheetahs, with HL=–9.5% and FL=15%
(Table 4). The highest relative
running speeds are reached by animals of the Rodentia, Marsupialia and
Lagomorpha (Iriarte-Diaz,
2002), which move mostly by bounding or half-bounding. Thus,
hindlimb synchronisation, which is almost achieved by running cheetahs, seems
to be one of the most useful strategies for reaching maximum speed, taking
bone, muscle and tendon strains into account
(Biewener and Taylor, 1986;
Iriarte-Diaz, 2002).
Coordination between pairs of limbs
PL values were previously thought to depend on speed, and no
detail was provided about the range of values
(Table 1). In this study,
although speed clearly had some effect, because variability did exceed the
widely accepted level of 5% in some cases, PL was found to be
specific for each gait and could be used to distinguish between symmetrical
gaits, whereas no such distinction was possible with FL and
HL alone. This proved to be the case in several other mammals
(Table 4). Thus, PL
values are more dependent on gait than on speed.
In terms of spatial coordination between pairs of limbs, when PG
is 50%, the hindlimb foot contacts the ground midway between two successive
footprints of the ipsilateral forelimb
(Fig. 1). However, this
situation is unlikely to occur without at least one flexed suspension phase.
It is therefore necessary to move with a running gait and at high speed (fast
pace and rotary gallop). This is particularly true for PG values
exceeding 50%. PG is mostly lower than 50%, indicating that the
hindlimb contacts the ground before the midpoint in the stride length of the
ipsilateral forelimb (e.g. high speed in lateral walk and trot and low speed
in pace or transverse gallop). Similar findings have been obtained for camel
pacing [PG=36%, from track diagram in Dagg
(Dagg, 1974)]. When the animal
trots or walks at very low speed (u<1.3 m s–1 for
walk and u<3 m s–1 for trot), PG reaches 0%. This
indicates that the hindfoot contacts the ground at the same place as the
ipsilateral forefoot. Generally, the hindfoot contacts the ground slightly
ahead of the ipsilateral forefoot in the same sequence. This makes the back of
the animal deviate from the line of travel, most often during several
consecutive sequences, to avoid interference between the hindlimb and its
ipsilateral forelimb (Hildebrand,
1968), especially at high speeds.
Moreover, unlike coordination within pairs of limbs, PG and
PL are very different for each gait (Tables
2 and
3). Indeed, the pairs of limbs
are not in the same position on the anteroposterior axis, translating the
spatial movement of the hind pair back a trunk length of the animal with
respect to the spatial movement of the fore pair. By trunk length, we mean the
distance between the shoulder and the hip – this was measured in a
static posture, using marks made on the skin of the dogs from the caudal angle
of the scapula to the hip (estimated by palpation). Thus, the distance
travelled by the centre of mass of the animal, during a period equal to the
pair lag in a real time unit (pl; s), is equal to the sum of the pair
gap in real space unit (pg; m) plus the trunk length (tr;
m). Hence, speed can be expressed as follows:
 | (1) |
 | (2) |
;
Schilling and Hackert, 2006),
allows the hindlimbs to travel over a greater distance during swing phase
(Hildebrand, 1959;
Grillner, 1975;
Rocha Barbosa et al., 1996;
Schilling and Hackert, 2006),
touching the ground further forward than theoretically predicted
(Fig. 8C). Finally,
Eqn 2 not being observed may be
used to quantify the involvement of trunk flexibility (laterally for trot and
sagittally for rotary gallop) in locomotion.
|
Conclusions
If we observed a great continuity in kinematic parameters from slow walking
to fast running in malinois dogs, the respective contributions of cycle
frequency and stride length to the increase in speed nevertheless showed a
strong difference between symmetrical and asymmetrical gaits. Setting up
suspension phases then sagittal flexing of the trunk, which induced an
increase of the swing duration at very high speed, also supported the increase
in speed. This came with changes in spatiotemporal limb coordination. As
initially supposed, spatial coordination within pairs of limbs reflected the
temporal coordination within pairs of limbs, while temporal and spatial
coordination between the pairs of limbs was strongly linked through trunk
length. Variations in this last relationship seemed to reflect the involvement
of trunk movement in locomotion, which would require a rigorous
three-dimensional kinematic analysis to be clearly characterised. These
parallels between temporal and spatial coordination with increasing speed
should increase our understanding of particular cases of limb coordination and
probably facilitate the interpretation of fossilised tracks left by ancient
quadrupeds.
LIST OF SYMBOLS AND ABBREVIATIONS
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Acknowledgments |
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References |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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