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First published online January 8, 2007
Journal of Experimental Biology 210, 366-372 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02632
Experimental study of coordination patterns during unsteady locomotion in mammals
FRE2696, CNRS, MNHN, Université P6, Col. de France, Muséum National d'Histoire Naturelle, Département Ecologie et Gestion de la Biodiversité, FRE 2696, Pavillon d'Anatomie Comparée, CP 55, 57 rue Cuvier, 75231 Paris cedex 05, France
* Author for correspondence (e-mail: abourach{at}mnhn.fr)
Accepted 7 November 2006
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Summary |
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Key words: gait, mammals, interlimb coordination, anteroposterior sequence
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), and
asymmetrical gaits (gallops and bounds), in which the two footfalls are
unevenly spaced in time in at least one pair. Hildebrand
(Hildebrand, 1965;
Hildebrand, 1977) proposed two
distinct sets of parameters to classify either symmetrical or asymmetrical
gaits. It was thus impossible to study the transition between the two kinds of
gait using its methods, as the quantification of the gaits used different
parameters. In Hildebrand's work, which became the framework for most studies
in quadrupedal locomotion, gait was classified by taking stride duration as
the time reference. Stride duration is the time lag between two successive
footfalls of the same limb during which the footfalls of the other three limbs
need to happen. The succession of the four limbs' footfalls was examined
within this time unit. Splitting a locomotor sequence into such strides was
effective in the study of steady locomotion. However, as soon as gait
transition or disturbed locomotion occurred, splitting a locomotor sequence
into strides was not appropriate because the reference limb changed often and
therefore the footfalls did not take place in the reference stride. Many
aspects of interlimb coordination during tetrapod locomotion were thus not
studied, such as the transition between symmetrical and asymmetrical gaits, or
unsteady locomotion, although such occurrences are frequent in the daily life
of animals.
Recently another framework to classify gait was proposed, based not on a
unit of time, but instead on a succession of definite actions in time and
space (Abourachid, 2003).
Abourachid's framework, called the anteroposterior sequence (APS), is defined
as the association of the consecutive cycles of the two forelimbs followed by
the consecutive cycles of the two hindlimbs. The APS is based on generally
well-accepted assumptions: (1) two morphologically similar limbs, associated
in the two pairs (fore and hind pairs), work together
(Cartmill et al., 2002;
Hildebrand, 1965) under the
control of central pattern generators (CPG)
(Grillner et al., 2000;
Orsal et al., 1990;
Pearson, 1976;
Viala and Vidal, 1978) and (2)
during forward locomotion, the forelimbs reach the obstacle first. CPG
activation is initiated by an activity of the brainstem locomotor system.
Thus, at least for locomotor initiation, there is a rostrocaudal activation of
the spinal network (Grillner et al.,
2000).
This framework suggests a common basic pattern of movement for all gaits: coordinated movements of forefeet, coordinated movements of hindfeet and a relationship between these two pairs. In contrast to stride-based analysis, the advantage of the APS approach is that one can characterize all limb coordination, irrespective of the steadiness of the locomotion, because the analysis is not constrained by stride duration. Three temporal parameters, which are slightly different from those Hildebrand proposed for symmetrical gaits, are now sufficient to identify all quadruped gaits, symmetrical as well as asymmetrical (Fig. 1). These parameters are: (1) the fore lag (FL), defined as the time lag between the two forefeet footfalls, which measures temporal coordination within the fore pair, (2) the hind lag (HL), defined as the time lag between the hindfeet footfalls, which measures temporal coordination within the hind pair, and (3) the pair lag (PL), defined as the time lag between two ipsilateral feet footfalls, which measures temporal coordination within the two pairs. The symmetrical gaits have both footfalls in each pair evenly spaced in time, and therefore FL=HL=50%. The distinctions between the symmetrical gaits (walks, trot and pace) arise from differences in coordination between the two limb pairs, which can be seen in different PL values. Asymmetrical gaits occur when FL and HL deviate from 50%, and each asymmetrical gait can be identified according to the nature and the magnitude of the deviation.
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White lines spaced 0.10 m apart were drawn perpendicular to the axis of a 10 m runway for dogs and an 8 m runway for cats. An obstacle was placed in the middle of the runway. Its height was adjusted in order to induce a break in interlimb coordination but not a powerful jump (30 cm high for dogs, 19 cm for cats). The dogs were led on a leash. They approached the obstacle using a slow gait, walking or trotting, did a small jump over the obstacle, breaking down the symmetrical coordination. Then they returned to a walk or a trot to leave. The cats moved freely and were encouraged with food to move on the runway. Each animal did 10 trials. The animals were filmed with a high-speed video recorder (Redlake® Motion scope1000sPCI, Tucson, AZ, USA) at 125 Hz during the whole progression. The camera was placed at obstacle level, 5 m perpendicular to the runway. Parallax deformations were corrected using the lines on the runway.
Data analysis
The records were analysed using Zoomplayer (Zoomplayer v4.03, 2000-2004
Inmatrix.com).
We did not use the same terminology as Hildebrand
(Hildebrand, 1965), in which
the trailing forelimb is the forelimb that touches the ground first, and the
leading forelimb is the one that touches the ground second but is the leader
in space. This terminology may cause confusion between trailing or leading
positions in space and time. Similarly, the right-left designation is not
appropriate because of the lateralisation of asymmetrical gaits. Instead, we
used a 1-2 designation for the sides of the animals. Thus, the 1-forelimb
(f1), which is the reference limb, is defined as the first to cross the
obstacle and the 2-forelimb (f2) is the other one. Hindlimb designation,
irrespective of footfall order, is dependent on forelimb designation.
Therefore, the 1-hindlimb (h1) is ipsilateral to the 1-forelimb (f1) and the
2-hindlimb (f2) is ipsilateral to the 2-forelimb (f2). In this study, the jump
is the only time in the trial when animals used an asymmetrical gait, so we
used the jump sequence to find the reference limb. The times of footfall and
of take-off of each limb were noted with a precision of 0.008 s. The distance
between each footprint and the obstacle were noted with a precision of 0.05 m,
with negative distances before the obstacle and positive distances after.
The data were shown graphically on classical gait diagrams
(Marey, 1873;
Vincent and Goiffon, 1779) and
track diagrams (Fig. 2), with
four superimposed lines representing the four limbs. In the APS framework, the
gait diagram was modified so that two upper lines represent the forelimbs, and
two bottom lines represent the hindlimbs. For both forelimbs and hindlimbs,
the upper line represents the 1-limb. This is not the usual order, which is,
from top to bottom, left hindlimb, left forelimb, right forelimb, and right
hindlimb (Hildebrand, 1966). On
the gait diagram, the x axis is time and the stance phase, when the
foot is on the ground, is marked. On the track diagram, the x axis is
distance and the place where the foot was put down is marked. Therefore, each
trial was analysed using both its gait diagram (temporal aspects of the
movement) and its track diagram (spatial aspects of the movement). After the
identification of anteroposterior sequences (APSs) from the diagrams, the APSs
were labelled. The APS just before the obstacle was labelled 0. The APSs were
labelled in decreasing order from the obstacle to the beginning of the trial
(from 0 to -4), whereas the APSs after the obstacle were labelled in
increasing order (from 1 to 5). In each APS, the following time and space
parameters were calculated. The time parameters, as previously defined, were:
(1) the fore lag (FL), (2) the hind lag (HL) and (3) the pair lag (PL). By
analogy with time parameters, the space parameters were: (1) the fore gap
(FG), defined as the gap between the placement of the two forefeet, which
measures spatial coordination within the fore pair (2) the hind gap (HG),
defined as the gap between the placement of the two hindfeet, which measures
spatial coordination within the hind pair, and (3) the pair gap (PG), defined
as the gap between the placement of the two trailing feet, which measures
spatial coordination between the two pairs. To normalise the measurements in
all trials, each parameter was expressed as a percentage of the 1-forelimb
cycle duration for the lags and stride length for the gaps. The mean values of
these parameters were calculated from all trials and plotted vs APS
number. All data were analysed with SAS software. The significant threshold of
tests was fixed at 0.05. Variance equality of data was estimated using the
F-test and if variance was equal, data were analysed using Student's
t-test.
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Trials with the same pattern of locomotion were used for statistical analysis (27 trials for dogs, 16 trials for cats). Other trials showed atypical patterns, with additional or fewer footfalls. These trials were rare (four trials for dogs and two for cats) and were not used for APS statistical treatment, but could be analysed qualitatively. The shortest trials, with fewer than six APSs, were discarded.
Gait and track diagrams
In each species, four phases were identified: approach, impulse, landing
and leaving. During the approach, from APS -4 until -1, the animal moved
toward the obstacle. The impulse was APS 0, just before the obstacle, during
which the animals began the jump. The landing was APS1, just after the
obstacle. The leaving phase was APS2 and up, when the animal moved away. Cat
trials (6 APSs) were shorter than dog trials (10 APSs).
In three dog trials, the trailing hindfoot was not put down during the landing phase (APS1), but was put down early in the first leaving APS (APS2). The other footfalls were not affected. In one dog and in one cat trial, the impulse (APS0) was similar to an approach but the trailing hindfoot was put down one time more at the end of the stance of the leading hindfoot, close to the obstacle. The other footfalls and the other APSs were not affected. In one dog and two cat trials, the animal changed its trailing feet during the jump, while no other differences were observed during the trial. These trials were not used for statistical calculations.
Time parameters
Fore lag (FL) and hind lag (HL)
Fig. 3 shows that during the
approach phase, FL and HL for dogs and cats remained constant (FL=51±3%
and HL=49±6% for dogs, and FL=50±4% and HL=52±7% for
cats; means ± s.e.m., P>0.05). Thus, the movements of the
paired limbs alternated and the animals used a symmetrical gait.
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During the landing phase, FL was the same as during impulse, whereas HL increased, resulting in fore and hind limbs with the same coordination (FL=31±11% for dogs and 31±11% for cats; HL=35±12% for dogs and 33±14% for cats).
During the leaving phase, FL and HL returned to the values of symmetrical gaits (50%). For dogs, the APS was symmetrical from APS2 onward (FL=49±4% and HL=50±6%), whereas for cats in APS2, FL was less than 50% (44±5%) and HL was more than 50% (59±11%). For cats, the first symmetrical APS after the obstacle was APS3 (50±2% and 54±5%).
Pair lag (PL)
During the approach phase, PL remained constant in both dogs and cats
(PL=63±12% for dogs and PL=66±10% for cats). However, the large
variability (STD) reflected the diversity of the symmetrical gait (from
lateral walk to trot) used by the animals, depending on the initial gait.
There was no change from one gait to another during the approach phase.
During the impulse phase, PL decreased to 50±7% for dogs and 51±7% for cats (P<0.05), indicating that the movements of the two pairs became closer in time. The variability was less than during the approach phase.
During the landing phase, PL increased (64±9% for dogs and 62±10% for cats) and the variability made it impossible to distinguish it from the next sequence PL.
During the leaving phase, PL (60±10% for dogs and cats) was similar to that during the approach phase, indicating a return to a walk or a trot.
Space parameters
Fore gap (FG) and hind gap (HG)
Fig. 3 also shows that
during the approach phase, FG and HG remained constant and did not differ from
50%, meaning that within each pair, one foot was put down in the middle of the
other foot's stride (FG=51±5% and HG=50±8% for dogs;
FG=52±6% and HG=52±8% for cats; P>0.05).
During the impulse phase, FG and HG decreased, indicating that for each pair, the feet were put down closer to each other (FG=34±8% and HG=28±12% for dogs; FG=28±8% and HG=22±12% for cats). In dogs, FG was greater than HG, indicating that the hindfeet were closer to each other than the forefeet. The difference between the pairs was not significant in cats.
During the landing phase, in dogs FG did not increase significantly (37±8%) compared to the impulse, whereas in cats it increased (41±9%). HG increased significantly (41±12% for dogs and 47±10% for cats) so that for landing, both FG and HG were not different in each species.
During the leaving phase, FG and HG values indicated that the feet were regularly spaced within each pair (FG=49±5% and HG=51±8% for dogs, FG=52±7% and HG=52±6% for cats).
The lags and gaps within the pairs (FL-FG and HL-HG) were similar for all the APSs for dog data (P<0.01). For cats, the pattern of increases and decreases was the same, but the values were different during the landing phase, the gaps being larger than the lags.
Pair gap (PG)
During all trials, the mean PG remained stable near 0% (2.7±10.8%
for dogs and 1.9±5.9% for cats), meaning that the ipsilateral feet were
placed at almost the same place. However, for dogs, the variability was larger
during the approach and the leaving phases than for impulse and landing
phases, meaning that during the impulse and landing phases, the feet positions
were more precise. For cats, the variability was lower than for dogs.
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Methodological considerations
Normalisation of measurements
We needed to normalise the measurements to compare the motions of the four
feet and to compare the APSs. We chose to normalise our measurements to the
distance and time corresponding to the cycle of one foot. Another possibility
would have been to normalise using the cycle of one forelimb as the reference
for the forelimbs, and using the cycle of one hindlimb as the reference for
the hindlimbs. However, we then would have had the unsatisfactory situation of
having different references in time and space for two parts of one animal. The
choice of one limb cycle as a unit event, irrespective of the limb, has
repercussions for calculations, particularly during transition phases when the
cycle duration and cycle length of the four feet are not identical. If the
cycle duration (length) of the chosen limb is larger this will minimise the
time lags (gaps), and vice versa.
Unlike conventional analyses in which stride duration is the time reference, and the locomotor sequence is split into strides, the choice of one limb cycle as a unit event for the purposes of normalisation only does not mean that the movements of the other feet have to happen during this cycle.
Coherence of results obtained using the APS method
Symmetrical sequences
The approach phase and leaving phase presented the same coordination
patterns and can be discussed together. The three time parameters of FL, HL
and PL allowed us to identify the gaits
(Abourachid, 2003). When FL and
HL equalled 50%, this was a measure of strictly alternating movements of
paired limbs, typical of symmetrical gait
(Hildebrand, 1965). This is in
accordance with the strict alternation of the CPG that occurs during slow
locomotion (Grillner et al.,
2000). The pair lag quantifies the coordination between the two
pair movements and indicates the type of symmetrical gait
(Fig. 1). Dogs and cats used a
lateral walk, identified by a mean PL around 60%. PL variability is high
(10%), higher than the variability of FL and HL. No specific symmetrical gait
was imposed during the experiment, and dogs and cats used either a trot
(PL=50%) or a lateral walk (PL>55%), which explains the variability of PL.
In both species, FG and HG indicate that during symmetrical gaits the distance
between the positions of the two forefeet and the distance between the
positions of the two hindfeet are the same, and equal half the distance
between the two successive positions of one forefoot. In symmetrical gaits,
the FL, FG, HL and HG were the same, showing that these parameters reflected
the link between the temporal and spatial inter-limb coordination.
Dogs and cats put their hindfeet close to the place where their ipsilateral forefeet were placed (PG=5% for dogs, PG=0.5% for cats). Dogs put down their hindfeet in front of their forefeet, bypassing the forefeet. We also observed a concomitant slight lateral bending of the back. Cats put down their hindfeet and forefeet at almost the same place without observable lateral bending of the back. This result suggests that PG could be related to the back's role during locomotion.
Asymmetrical impulse sequence
During the impulse phase, FL, FG, HL and HG were less than 50%, showing
that the movements in the pair were no longer strictly alternating and were
more synchronised than during the approach phase. The footfalls of the hind
pair occurred closer, more in-phase than the footfalls of the forelimbs, and
the hindfeet were positioned closer than the forefeet. The same pattern was
reported in dogs (Alexander,
1974) and in horses (Leach et
al., 1984). The decrease in PL arose from an increase in the swing
phase during the `parabolic' jump, which increased the cycle duration (100%).
The PG remained constant because the stride length (100%) was measured on the
ground and did not take into account the parabolic trajectory of the animal.
Consequently, the jump APS is characterised by an increase in the impulse in
the vertical direction only.
Asymmetrical landing sequence
During the landing phase, HL increased compared to impulse phase HL, so
that the landing phase HL value became very slightly larger than the FL value.
FL remained constant between the impulse and landing phases. The same
variations were observed for HG and FG, indicating a coherent relationship
between time and space measurements. The same kind of timing pattern can be
seen in horses, where the hindlimbs are less in-phase than during the impulse
phase (Schamhardt et al.,
1993).
Transition phases are quantifiable only using the APS method
The transition between symmetrical and asymmetrical sequences was observed
when the animal changed from the symmetrical approach to the asymmetrical
impulse, and from the asymmetrical landing to the symmetrical leaving. The
symmetrical-asymmetrical transition (approach-impulse) was achieved by a
decrease in FL and HL, indicating a change from the strictly alternating
pattern of limb pairs characteristic of symmetrical gait to a more in-phase
coordination within each pair. This pattern has already been described in the
general control strategy for vertebrate locomotion
(Grillner et al., 2000).
Increasing stimulation of the brainstem locomotor centre induced a change in
the pattern of coordination between strict alternating within each pair, as in
symmetrical gaits, to an approximate in-phase coordination of the pairs, as in
asymmetrical gaits. The transition between asymmetrical and symmetrical
sequences (landing-leaving) was also achieved in one sequence (sometimes two
in cats) by an increase in FL and HL values to 50%, and by a return to an
alternating motor pattern. The change in FL and HL is coordinated with similar
changes in FG and HG. We found no relationship between the change in PL and
the PG, which did not exhibit any special patterns during the transition
between asymmetrical and symmetrical sequences. Conventional stride based
methods did not permit us to assess the problem of transition between
symmetrical and asymmetrical gait. From a methodological point of view, the
stride-based method cut the locomotor sequence into strides, defined by the
cycle of one reference limb. The four footfalls had to happen during one
stride of that limb. It was typically a hind limb
(Hildebrand, 1966;
Hildebrand, 1977), but
sometimes a forelimb (Herbin et al.,
2004; Renous et al.,
2002). However, in our experiments, with conventional stride-based
analysis, the same foot could not be used as a reference for all trials. If a
hindlimb (h1 or h2) cycle was chosen as the reference, one footfall was
missing when the animal changed from a walk to a trot. If the trailing
forelimb (f1) was chosen, there were two leading hind (h2) footfalls during
the stride before the obstacle. If the leading forelimb (f2) cycle was chosen,
it was more often possible to follow the four footfalls in all strides. The
main problems arose then from the interpretation: during the stride containing
the jump, the leading forefoot (f2) and the two hindfeet were placed before
the obstacle whereas the trailing forefoot (f1) was placed after the obstacle.
This meant that the movements grouped together in the stride provided the
impulse over the obstacle for three limbs whereas the movement of one limb was
in a landing phase. There is no coherent biomechanical interpretation for this
situation. Furthermore, the fore lag was about 75%, highlighting a fore pair
that is out of phase, which is not consistent with the motor pattern of
interlimb coordination (Grillner et al.,
2000).
Particular cases
In a few trials, different patterns occurred during the impulse or the
landing sequences, and these were always observed for the hind pair. Either
the 1-hindfoot was put down once more before the obstacle or the 1-hindfoot
was not put down during the landing sequence. These observations highlight the
importance of studying each pair separately.
Methodological terminology
If we take a forelimb cycle as the time reference, or forelimb stride
duration as the space reference, instead of the hindlimb reference used by
Hildebrand, this makes the definition of either lateral or diagonal walks less
intuitive. According to the APS method, a lateral-sequence walk occurs when a
forelimb footfall is followed by the contralateral hindlimb footfall, whereas
a diagonal walk occurs when the ipsilateral hindlimb follows the reference
forelimb. The definitions used for different walks are dependent on the
framework, either stride-based or APS. Walks can, however, be easily analysed
in the APS context.
Conclusion
The APS framework allowed us to quantify perturbed locomotion. The results
obtained with APS were consistent with actual motor patterns and biomechanical
interpretations. We showed that the parameters allowed us to link the timing
and the spacing of the footfalls, and to quantify the spatiotemporal
dimensions of gait in different mammals, such as dogs and cats, and that the
results were in accordance with what is known in horses. However, the small
differences we observed between dogs and cats can reflect morphological
differences. The APS could thus be used to understand the implication of the
morphology in interlimb coordination. We confirm that diagonality is not
needed for gait description (Abourachid,
2003). The tendency to synchronise diagonal feet during
symmetrical gaits is a secondary effect of the inter-pair coordination, i.e.
from the interference between two periodic oscillators. Even if diagonality
were important for animal stability
(Cartmill et al., 2002;
Sukhanov, 1966), diagonality
is not the basic coordination pattern of quadrupedal locomotion. The use of
diagonal supports during slow motion corresponded to an increase in animal
stability. APS seems to reflect the biological functioning of quadrupedal
interlimb coordination and it provides a new heuristic framework for the study
of tetrapod locomotion.
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Acknowledgments |
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References |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Abourachid, A. (2003). A new way of analysing symmetrical and asymmetrical gaits in quadrupeds. C. R. Acad. Sci. III Sci. Vie 326,625 -630.
Alexander, R. M. (1974). The mechanics of jumping by a dog (Canis familiaris). J. Zool. Lond. 173,549 -573.
Cartmill, M., Lemelin, P. and Schmitt, D. (2002). Support polygons and symmetrical gaits in mammals. Zool. J. Linn. Soc. 136,401 -420.[CrossRef]
Grillner, S., Cangiano, L., Hu, G.-Y., Thompson, R., Hill, R. and Wallén, P. (2000). The intrinsic function of a motor system-from ion channels to networks and behavior. Brain Res. 886,224 -236.[CrossRef][Medline]
Herbin, M., Gasc, P. J. and Renous, S. (2004). Symmetrical and asymmetrical gaits in the mouse: patterns to increase velocity. J. Comp. Physiol. A 190,895 -906.[Medline]
Hildebrand, M. (1965). Symmetrical gaits of horses. Science 5,701 -708.
Hildebrand, M. (1966). Analysis of symmetrical gaits of tetrapods. Folia Biotheor. 6, 9-22.
Hildebrand, M. (1977). Analysis of asymmetrical gaits. J. Mammal. 58,131 -156.[CrossRef]
Howell, A. B. (1944). Speed in Animals. Chicago: University of Chicago Press.
Leach, D. H., Ormrod, K. and Clayton, H. M. (1984). Stride characteristics of horses competing in Grand Prix jumping. Am. J. Vet. Res. 45,888 -892.[Medline]
Marey, E. J. (1873). La Machine Animale. Paris: Bibliothèque scientifique internationale.
Orsal, D., Cabelguen, J. M. and Perret, C. (1990). Interlimb coordination during fictive locomotion in the thalamic cat. Exp. Brain Res. 82,536 -546.[Medline]
Pearson, K. G. (1976). The control of walking. Sci. Am. 235,72 -86.[Medline]
Renous, S., Gasc, P. J., Bels, V. L. and Wicker, R. (2002). Asymmetrical gaits of juvenile Crocodylus johnstoni, galloping Australian crocodiles. J. Zool. Lond. 256,311 -325.
Schamhardt, H. C., Merkens, H. W., Vogel, V. and Willekens, C. (1993). External loads on the limbs of jumping horses at take-off and landing. Am. J. Vet. Res. 54,675 -680.[Medline]
Sukhanov, V. B. (1966). General System of Symmetrical Locomotion in Terrestrial Vertebrates (in Russian). Leningrad:Inst. Zool. Acad. Sci.
Viala, D. and Vidal, C. (1978). Evidence for distinct spinal locomotion generators supplying respectively fore- and hindlimbs in the rabbit. Brain Res. 155,182 -186.[CrossRef][Medline]
Vincent, G. C. and Goiffon, A. F. (1779).Mémoire artificielle des principes relatifs à la fidèle représentation des animaux, tant en peinture qu'en sculpture . Alfort.
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