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Spatio-temporal gait characteristics during transitions from trot to canter in horses
Zoology 116 (2013) 197–204
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Spatio-temporal gait characteristics during transitions from trot to canter in horses Sandra Nauwelaerts a,b,∗ , Peter Aerts a,c , Hilary Clayton b a b c
Functional Morphology Laboratory, Department of Biology, Antwerp University, Universiteitsplein 1, B-2610 Wilrijk, Belgium McPhail Equine Performance Center, Michigan State University, 736 Wilson Road, East Lansing, MI 48824, USA Department of Movement and Sport Sciences, University of Ghent, Campus HILO, Watersportlaan, B-9000 Ghent, Belgium
a r t i c l e
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Article history: Received 10 October 2012 Received in revised form 6 March 2013 Accepted 20 March 2013 Available online 15 June 2013 Keywords: Gaits Gait transition Locomotion Limb kinematics Quadrupeds
a b s t r a c t Gaits can be defined based upon specific interlimb coordination patterns characteristic of a limited range of speeds, with one or more defining variables changing discontinuously at a transition. With changing speed, horses perform a repertoire of gaits (walk, trot, canter and gallop), with transitions between them. Knowledge of the series of kinematic events necessary to realize a gait is essential for understanding the proximate mechanisms as well as the control underlying gait transitions. We studied the kinematics of the actual transition from trot to canter in miniature horses. The kinematics were characterized at three different levels: the whole-body level, the spatio-temporal level of the foot falls and the level of basic limb kinematics. This concept represents a hierarchy: the horse’s center of mass (COM) moves forward by means of the coordinated action of the limbs and changes in the latter are the result of alterations in the basic limb kinematics. Early and short placement of the fore limb was observed before the dissociation of the footfalls of one of the diagonal limb pairs when entering the canter. Dissociation coincided with increased amplitude and wavelength of the oscillations of the trunk in the sagittal plane. The increased amplitude cannot be explained solely by the passive effects of acceleration or by neck and head movements which are inconsistent with the timing of the transition. We propose that the transition is initiated by the fore limb followed by subsequent changes in the hind limbs in a series of kinematic events that take about 2.5 strides to complete. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Gaits can be defined by having specific interlimb coordination patterns that are used within a limited range of speeds and show discontinuous changes in one or more defining variables at a transition (Hildebrand, 1965; Abourachid, 2003; Robilliard et al., 2007). Each species performs a repertoire of gaits with transitions between gaits usually being performed when increasing or decreasing locomotor speed. Horses have become a paradigm in the gait literature because they exemplify the use of three main gaits: horses walk at low speed, trot at moderate speed and burst into a gallop at higher speeds. A wealth of experimental studies analyzing the kinematics and dynamics of equine gait patterns exists (e.g., Buchner et al., 1994; Minetti et al., 1999; Clayton, 1994a,b, 1995; Dutto et al., 2004) but the understanding of the mechanical events involved
∗ Corresponding author at: Functional Morphology Laboratory, Department of Biology, Antwerp University, Universiteitsplein 1, B-2610 Wilrijk, Belgium. Tel.: +32 3 265 2119. E-mail address: [email protected] (S. Nauwelaerts). 0944-2006/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.zool.2013.03.003
in transitions between the gaits is limited (Argue and Clayton, 1993a,b; Tans et al., 2009). Transitions from one gait to another are said to occur abruptly at a critical speed (Alexander, 1989). Several hypotheses on the ultimate causes of gait transitions have been tested. The most recognized hypotheses are the minimization of the energetic costs of locomotion (Hoyt and Taylor, 1981) and the minimization of the loading of the musculoskeletal system (Farley and Taylor, 1991). In addition, suggestions about the proximate mechanisms that may trigger gait changes have been put forward (Biewener and Taylor, 1986; Farley and Taylor, 1991). However, a striking lack of knowledge on the series of kinematic events occurring during a gait transition has remained. This is likely a consequence of the fact that only a few studies were designed with an experimental protocol that allowed investigation of what actually happens throughout the transition itself (Segers et al., 2006, 2007; Diedrich and Warren, 1995; Vilensky et al., 1991). Insights from such studies are essential for a better understanding of the proximate mechanisms as well as the control underlying gait transitions. Spinal interneurons play a key role in determining the form of rhythmic limb movements within a gait that determine the temporal characteristics of the stride (Grillner, 2002). The four central
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pattern generators (CPGs), one controlling each limb, coordinate the rhythmic patterns of the limb movements that characterize the different gaits. Transitions involve a change in coordination of these rhythmic movements. We studied the kinematics of the transition from trot to canter during accelerating locomotion in miniature horses. In the idealized trot, diagonal limb pairs move in phase (right fore together with left hind and left fore together with right hind), whilst both contralateral (left–right, within a girdle) and ipsilateral (fore–hind on the same side of the body) pairs move maximally out of phase. This means that time-symmetrical footfalls are present between the girdles and between the body sides. During the transition to canter one of the diagonal pairs de-synchronizes to produce the typical threebeat rhythm of canter. As a result, the phasing between both the contra-lateral and the ipsilateral limb pairs changes. Investigating the transitions thus combines a focus on maximized alterations in contra- and ipsilateral interlimb coordination with the pragmatic advantage of keeping a cyclic time reference – the synchronized footfalls of one diagonal pair throughout the transition – bearing in mind, though, the possibility that neither the neural control nor the mechanics of the system make use of this reference system. The kinematics were characterized at three different levels: (i) the whole-body level (center of mass, COM), (ii) the spatiotemporal level of the foot falls (interlimb coordination) and (iii) the level of basic limb kinematics (overall flexion–extension; oscillations with respect to the trunk). This concept represents a hierarchy: the horse’s COM moves forward by means of the coordinated action of the limbs quantified by their spatio-temporal events and changes in these events are the result of alterations in the basic limb kinematics. In the present study, we investigated which kinematic events occur in a specific and consistent order during a transition from trot to canter. We measured the limb movements, more specifically, how the horse changes footfall coordination pattern by altering limb kinematics. We tested how abrupt transitions occur at each of the hierarchical levels when changing from trot to canter using thresholds. Apart from the limbs, movements of the head–neck segment could potentially influence the COM mechanics. We therefore tested the involvement of neck and head movements in the transition. Because some trunk kinematic events could be caused by a passive acceleration effect, we also tested whether the boundary acceleration threshold (e.g., Aerts et al., 2003) is reached during transitions.
2. Materials and methods 2.1. Experiments Five miniature horses (mass: 116 ± 38 kg; mean ± SD) were used in this study. Thirty-four reflective markers of 6 mm were attached to the skin over anatomical landmarks on the body and limbs of each animal using adhesive tape while the horse was standing square (see Fig. 1). Eight Eagle infrared cameras (Motion Analysis Corp., Santa Rosa, CA, USA) operating at 120 Hz were used to cover a capture volume of 1 m × 1 m × 8 m. The capture volume was calibrated using a wand technique that yielded an error in linear measurement of 1 mm. We chose to work with the breed of miniature horses in order to obtain a larger number of strides within the restrictions of a capture volume using eight cameras. A runner led the horses in hand in a straight line through the capture volume using a loose lead rope while accelerating at trot with the intention of stimulating a transition from trot to canter. No direct cues to change gaits were given so the transitions were initiated by the horses. Data collection continued until a minimum of 15 trials that included a trot–canter transition had been recorded from each horse. In order to be retained for analysis, the
Fig. 1. Positions of markers: three markers on the head (forehead, distal end of left and right facial crests), four markers on the neck (wings of the atlas (C1) and caudal part of the left and right transverse processes of C6), six lateral markers on each forelimb (tuber spinae scapulae (scapula), greater tubercle of humerus (shoulder), lateral epicondyle of humerus (elbow), ulnar carpal bone (carpus), lateral condyle of third metacarpus (fore fetlock), and midlateral hoof wall), two markers on the back (withers (T6) and croup (S2)) and six markers on each hind limb (ventral part of tuber coxae (pelvis), greater trochanter of femur (hip), lateral condyle of the femur (stifle), talus (hock), lateral condyle of third metatarsus (hind fetlock) and midlateral hoof wall). Measured angles are indicated as shaded arcs. The trunk angle (˛) is the sagittal plane angle between the trunk segment and the horizontal; the value is positive when T6 is higher than S2 and negative when T6 is lower than S2. Neck angle (ˇ) was measured between the neck segment and the back segment (T6–S2) on the ventral aspect. Limb angles ( and ı) were calculated as the angle between the limb axis (from either scapula or hip to the lateral hoof marker) and an axis perpendicular to the trunk axis. In the left corner, the drawing is placed on a picture of one of the miniature horses used in the present study to demonstrate its similarity in proportions to averaged-sized horses.
transition trials had to fulfill two selection criteria: (i) the hoof markers were visible for a minimum of two strides before and two strides after the transition, which was necessary for construction of the gait diagrams; (ii) all markers were visible for at least three successive strides including the transition stride (stride zero: defined in Section 2.2), which was necessary for the COM analysis. 40 trials met these criteria and were retained for further analysis. Even though data were more difficult to obtain overground, we decided it was important to retain the effects of overall body inertia during acceleration as opposed to performing experiments on a treadmill (Van Caekenberghe et al., 2010a,b). To compare some of the spatiotemporal changes with changes due to increases in speed, 5 trials for each horse were recorded with the horse accelerating in trot and canter without transitioning. 2.2. Gait diagrams and spatio-temporal gait parameters Temporal and spatial footfall diagrams were constructed from the timing and position of the four hoof markers. To visualize temporal changes during the transitions more clearly, quadrilaterals were drawn on the gait diagrams by connecting the touchdowns and lift-offs of each diagonal pair. Stance durations and hoof heights for each hoof were determined for each stride. Stride length and stride duration were calculated separately for each limb as the distance and time, respectively, between successive footfalls. Speed was determined as the stride average of the instantaneous velocity of the COM. The four limbs of the horse were named (i) according to the anatomical girdle they belong to (fore or hind limb), (ii) according to the timing of the diagonal limb pair during the canter: the dissociating limb pair is the diagonal pair that is dissociated during the canter, while the non-dissociating limb pair is the other diagonal
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pair and (iii) according to their spatial orientation during the canter (leading or trailing limb of a contralateral pair; the former being the limb always kept in front of the other during a canter). As illustrated in Fig. 2, the first stride for which one diagonal pair of footfalls clearly deviated from an in-phase pattern was the first transition stride and it was assigned the stride zero number. This was done by visual examination of the vertical coordinates of the lateral markers over time for each trial. After detecting a continuous dissociation (pattern does not return to an in-phase pattern, point 1 in Fig. 2), the start of stride zero was determined as the contact of the dissociating fore limb prior to this dissociation. The strides preceding and following stride zero were designated negative and positive, respectively, and were numbered from the transition outwards. 2.3. Center of mass (COM) Since miniature horses have roughly similar proportions to normal-sized horses (insert in Fig. 1) and no specific data on inertial properties for this breed are available, COM position was calculated using the mass distribution and position of segmental COMs based on anatomical data from Buchner et al. (1997) and Van den Bogert (1989). COM velocities and accelerations were obtained from numerical differentiation of the positional data in the vertical and forward directions by calculating the incremental difference between two successive positions divided by the time interval. Time was set to zero at the start of stride zero. Intercepts of two linear regressions of the COM velocity against time through the velocity profile (i) prior to time zero (trots) and (ii) after time zero were compared to test whether the change in forward velocity at the transition was significantly different from zero (cf. transitions in humans; see Segers et al., 2007; example in Fig. 3). 2.4. Kinematics The trunk is considered the reference segment with regard to which limbs move. Trunk angle was defined as the angle between the line drawn from the marker on the withers to the one on the croup and the horizontal such that the angle increases when the front of the horse pitches up and decreases when it pitches down (˛ in Fig. 1). For every stride, minimal and maximal angles of the trunk were determined. Neck angle (representing the position of the head–neck segment) was defined as the ventral angle between a line connecting the C1 and C6 markers with a line connecting the T6 and S2 markers (ˇ in Fig. 1). Instantaneous limb length was calculated for each limb as the 3D distance between the positions of the scapula (or hip) marker and the lateral hoof marker (i.e., the limb longitudinal axis), while limb angles (fore limb: ␥; hind limb: ␦ in Fig. 1) were calculated as the angle between the limb longitudinal axis and an axis perpendicular to the trunk axis in the sagittal plane. This definition ensures that an increase in angle corresponds with protraction of the limb with respect to the trunk segment while a decrease in angle implies retraction (zero is always perpendicular to the trunk). Overall limb kinematics were assessed by measuring maximal and minimal limb lengths, maximal limb protraction angle and its timing with respect to touchdown, and maximal limb retraction angle and its timing with respect to lift-off. 2.5. Boundary acceleration threshold Aerts et al. (2003) described a method of estimating the accelerative conditions that would have to occur in order for the forces on the fore limbs to become zero. This rough estimate of the minimal acceleration (a) necessary to lift the trunk is based on the ratio of the averaged craniocaudal position of the hind limbs when in contact with the ground with respect to the COM (x) against the absolute
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height of the COM (y) taking the gravitational acceleration (g) into account: a = x/y g. This ‘critical acceleration’ was then compared to the actual forward acceleration in order to test the hypothesis that the increase in trunk elevation could potentially be a passive effect of the acceleration of the COM.
2.6. Statistics A paired t-test was used to test for differences between the intercepts of the regression lines of velocity against time. Since the Shapiro–Wilk test did not detect violations of normality (n = 147) for any of the variables tested, repeatedmeasures multivariate analyses of variance (MANOVA) were used to determine differences in spatio-temporal gait characteristics and kinematic variables between successive stride numbers and between limbs. Tukey-B post hoc comparisons were used to detect grouping between the stride numbers and limbs (P < 0.05). Chi square tests were used to test the acceleration threshold hypothesis.
3. Results 3.1. Velocity profile of the COM No sharp change in forward velocity of the COM was observed during trot to canter transitions. The intercepts of the velocities during trot did not significantly differ from those in canter and they did pass the equivalence test (alpha = 0.05, power > 0.8). There is considerable variation in transition speeds, here defined as the horizontal velocity averaged over stride zero, both within subjects and between subjects: animal 1 (3.14 ± 0.38 m/s, N = 11), animal 2 (2.88 ± 0.09, N = 11), animal 3 (3.97 ± 0.22 m/s, N = 7), animal 4 (4.10 ± 0.13 m/s, N = 4) and animal 5 (3.76 ± 0.28 m/s, N = 5).
3.2. Discontinuous changes in stride duration and stride length In the temporal gait diagram (Fig. 4A), the quadrilateral shape seen in the dissociating limb pair in the transition stride was an intermediate between the rectangle during trot and the parallelogram during canter. Since no significant differences were found for all variables between strides +3 and +2 or between strides −4, −3 and −2 and the differences passed the equivalence test (alpha = 0.05, power > 0.8), the data were pooled into 5 groups (−2, −1, 0, 1, 2). The change from a gait in which both diagonal pairs are synchronized to a gait in which only one diagonal remains synchronized while the other is dissociated takes two strides to perform (stride 0 and +1). Trot to canter transitions (Fig. 4A and B) can be described by comparing mean stride duration (Fig. 5) and mean stride length (Fig. 6) between successive strides plotted against mean velocity. Comparing the change in stride duration to the expected changes due to the increase in velocity within a trot, the non-dissociating diagonal limb pair seems to follow the expected pattern. This is in sharp contrast to the dissociating limb pair; the fore limb decreases its stride duration while the hind limb stride duration increases in stride 0. This effect is only negated in stride +2. A similar pattern was found for the stride lengths: the dissociating hind limb shows an increase while the dissociating fore limb shows a decrease in stride length in the transition, only to be negated in stride +2. Interestingly, the stride duration of the dissociating fore limb in the stride prior to the transition stride was on average 59 ms shorter and its stride length 20 cm shorter compared to the mean of the three other limbs together.
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Fig. 2. Example trial of how stride zero was defined in the individual trials. Dissociation (1) of the diagonal pair was detected based on the profile of the vertical coordinates of the hoof markers through time. Stride zero started with the start of the stance phase (2) of the forelimb of the diagonal pair that dissociated.
3.3. Non-limb kinematics Maximal trunk angle (pitch up) increased in stride 0 and stride 1, while minimal trunk angle peaks decreased slightly in stride 0, and more obviously in strides 1 and 2 (Fig. 7). No significant changes in maximal and minimal neck–trunk joint angles were found between strides (Fig. 8). No clear patterns were detected between the timing of trunk oscillation and the footfalls. 3.4. Limb pro- and retraction kinematics In the non-dissociating hind and dissociating fore limbs, maximal protraction angles gradually increased by 10◦ over the five strides we examined. While the maximal protraction of the nondissociating fore limb initially also increased, maximal protraction decreased in the transition, causing the two fore limbs to differ in maximal protraction angle by almost 14◦ in the first full canter stride, stride +2 (Fig. 9). Protraction in the dissociating hind limb did not show a consistent trend and seemed to oscillate around the same average value. Minimal limb angle (retraction) of the entire limb remained constant for the non-dissociating fore limb (alpha = 0.05, power = 0.43), and increased (less retraction) after the transition in the
dissociating fore limb. Minimal retraction increased after the transition for the dissociating hind limb. There are small effects of a couple of degrees with the pattern of change being similar for the three limbs (see Fig. 9). Caution is needed in the interpretation of these results because the minimal limb angles were correlated to each other, which might cause issues of multicollinearity with the MANOVA test. Pearson correlations were all higher than 0.9 between the four minimal angles. Retraction increased more dramatically (decreased retraction angles) in the dissociating hind limb prior to the transition, making it the limb with the most pronounced retraction in the canter. Timing of the maximal protraction angle with respect to touchdown was variable and was significantly different between strides only for the dissociating hind limb, with maximal protraction occurring near touchdown in trot and occurring 350 ms prior in the canter. Timing of minimal retraction with respect to lift-off was close to lift-off for all limbs in the canter, while occurring 200 ms earlier for the non-dissociating limb pair in the trot. Maximal limb lengths did not significantly change between strides. Minimal limb lengths changed in the hind limbs with both limbs having smaller minimal lengths in strides −2, −1 and 0 by 2–3 cm, representing about 5% of total limb length.
Fig. 3. Velocity profile of the COM for an example trial of a transition from trot to canter. Time was set to zero at the start of stride zero (see Fig. 2). Linear fits were drawn through the horizontal velocity against time profiles and the intercepts of the two lines were compared to test for a jump in velocity, defined as an abrupt change in the velocity progression in the transition region. Even though there was high variability in the velocities and the acceleration (slope) between the trials, intercepts of the trot and canter regressions were found to be equivalent.
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Fig. 4. (A) Timings of hoof touchdowns and hoof lift-offs based on the average footfalls of all trials. Time in seconds on the x-axis. Horizontal lines indicate the stance phase of each leg; diagonal limbs are connected by vertical lines creating quadrilaterals. When the diagonal pair hits and lifts off the ground simultaneously, this quadrilateral will be rectangular for both diagonals. During a canter, it will be rectangular for the non-dissociating diagonal and a parallelogram for the dissociating diagonal. Limbs are color-coded: black for dissociating fore, red for non-dissociating fore, green for dissociating hind and blue for non-dissociating hind. (B) Example trial of the positions of hoof prints of a horse that is trotting (from left to right) and transitions to canter. The x-axis shows the position in the direction of movement in meters, while the y-axis shows the mediolateral position. Distance between two ticks is 1 m on both axes. Limbs are color-coded: black for dissociating fore, red for non-dissociating fore, green for dissociating hind and blue for non-dissociating hind. Diagonal pairs that hit the ground simultaneously are connected with a black line. When the pair is dissociated, an arrow is drawn from the hoof that makes contact with the ground first to the hoof that hits second. The hoof that hits second is indicated by a slash through its symbol.
Fig. 5. Stride duration in seconds for each limb in each stride number. The mean velocity of strides is shown on the x-axis and their numbers are labeled above the box. Error bars represent standard errors in both dimensions. Significant differences between successive strides are indicated with an asterisk. The two regression lines represent the relationship between stride duration and velocity within the trot (in black) and the canter (in red) based on trials of the same subjects accelerating without transitioning. Also note the significantly shorter stride duration of the dissociating forelimb in stride −1 as compared to the three other limbs.
3.5. Boundary acceleration thresholds In most trials, the measured acceleration matched or even surpassed the critical acceleration, but it was not significant over the entire stance and the timing of the measured acceleration did not consistently coincide with an increase in trunk angle. In addition,
since it is expected that the measured acceleration should exceed a multiple of the critical acceleration in order to have a substantial lifting effect, we tested whether the measured acceleration was larger than 1.5 times the critical acceleration. It was found to be significantly smaller than this new threshold value (alpha = 0.05, power > 0.8).
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Fig. 6. Stride length in meters for each limb in each stride number. The mean velocity of strides is shown on the x-axis and their numbers are labeled above the box. Error bars represent standard errors in both dimensions. Significant differences between successive strides are indicated with an asterisk. The two regression lines represent the relationship between stride length and velocity within the trot (in black) and the canter (in red) based on trials of the same subjects accelerating without transitioning. Also note the significantly smaller stride length of the dissociating forelimb in stride −1 as compared to the three other limbs.
4. Discussion
Fig. 7. Mean minimal and maximal trunk segmental angles with standard error for each stride.
Fig. 8. Mean minimal and maximal neck joint angles with standard error for each stride.
Since the stride duration and stride length of the dissociating fore limb are smaller than those of all the other limbs in stride −1, the first kinematic event that indicates a disruption in the cyclic footfall pattern of the trot is the early touchdown of the dissociating fore limb. It is the limb that is spatially in front of the other fore limb and is therefore often called the leading fore limb. This implies that the transition was initiated during the swing phase of the leading fore limb in stride −1. We therefore suggest calling stride −1 the ‘transition initiating stride’. The limb positioned diagonally to this limb, the dissociating hind limb, is then delayed in its next placement which is associated with increases in stride length and duration for this limb in stride 0, the stride that is defined by its clear dissociation and is therefore called the ‘transition stride’. In stride +1, a further dissociation in the timing of the footfalls of the dissociating limb pair occurs. This stride will be called the ‘transition completion stride’ since it is not until stride +2 that the interlimb differences in stride length and duration disappear (there were statistically significant differences between strides +1 and +2 but variables for strides +2 and +3 were statistically equivalent, power > 0.8). This means that the transition takes about 2.5 strides to complete. This agrees with the prediction of Raibert (1990) that a robotic quadruped is able to transition between symmetrical gaits during the swing phase of a single stride but transitions from a symmetrical to an asymmetrical gait require at least two strides. Transition initiation seems to involve a reorientation of the girdles to accommodate the different amounts of protraction in the leading versus trailing limbs that are characteristic of an asymmetrical gait. By the time the transition is completed, the leading fore and hind limbs have significantly increased both their protraction and retraction angles. Consequently, the entire cycle of rotation of these limbs is more cranial in canter than in trot. In the trailing fore and hind limbs the most obvious change is a decrease in retraction of the trailing hind limb, which is retracted approximately 10◦ further than the other three limbs. The consequent changes in rotational movement of the girdles in the dorsal plane seem to initiate a disruption in the footfall pattern that does not affect the progression of the movements of the center of mass. Indeed, as opposed to transitions in humans from walk to run, no jump in COM velocity was found in transitioning horses. This means that there is no detectable cost in kinetic energy involved in transitioning from trot
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Fig. 9. Maximal (protraction) and minimal (retraction) limb angle per degree for each stride number and each limb. The mean velocity of strides is shown on the x-axis and their numbers are labeled above the box. Error bars represent standard errors in both dimensions. Significant differences between successive strides are indicated with an asterisk. Increasing protraction is indicated by an increase in positive angle, increasing retraction by a larger negative angle.
to canter other than the increase due to acceleration and a transition is only visible at the second level of the hierarchy, the limbs. One mechanism to account for the sudden increase in trunk angle amplitude would be the use of the relatively heavy neck–head segment. It is often reported by experienced riders that horses lift their head and neck into the transitions. However, neck joint angle patterns were highly variable between and within horses and the head was not raised consistently either overall or within certain individuals. Therefore, the neck–head raising was not retained as an explanatory factor in our study. Since the horse is accelerating and the pitch angles change in the transition, we tested whether the change in pitch up of the trunk during stride zero could be just a passive effect of the forward acceleration of the horse, which would mean that it is not necessarily controlled through a change in the CPGs of the individual limbs. Applying the boundary acceleration theory (Aerts et al., 2003; Williams et al., 2009) it was shown that the boundary acceleration was only just exceeded. Studies in lizard and horse locomotion showed that significant pitching requires multiples of this boundary acceleration (Aerts et al., 2003; Curtin et al., 2005). Therefore, it was concluded that it is not possible for the pitch up of the trunk to be a purely passive event. The underlying mechanism would be first a push-up coming from the fore limb that lands earlier and then a drop of the rear activated by the gluteal and/or epaxial muscles with the lumbosacral and hip joints flexed. Another important aspect of locomotion that explains the existence of different gaits is the presence or absence of mechanisms to decrease collisional losses (Ruina et al., 2005). Trot is a gait that contains high collision losses which are highly reduced during galloping (Ruina et al., 2005; Lee et al., 2011). When speeding up the trot, collision losses increase and this greatly influences the cost of transport. By transitioning from a two-beat to a three-beat gait, each collision is divided over 1.5 sub-collisions, reducing the costs to 4/9th of the cost of a two-beat gait (Ruina et al., 2005). To reduce the amount of energy wasted in the collision, animals tend to avoid sudden changes in the direction of the velocity vector of the COM (Lee et al., 2011). It is likely that collisional loss reduction plays a role in the causality of the transition itself. A sudden change in pattern, perhaps even as subtle as putting a limb on the ground earlier than expected, might lead to a sudden change in collisional losses, thereby changing the dynamics of the cyclically moving system. Most of the previous studies that have tried to explain why gait transitions occur inferred what happens in the transition by
comparing between different gaits performed at steady-state speed (Hoyt and Taylor, 1981; Biewener and Taylor, 1986; Farley and Taylor, 1991; Wickler et al., 2003; Griffin et al., 2004). However, an important aspect of gait transitions is the discontinuity that occurs while varying the speed of progression (Ivanenko et al., 2011). The abruptness of this phenomenon is particularly intriguing. So far, studies of the mechanics during steady acceleration throughout a gait transition are scarce. Most of the information describes the walk to run transitions in humans (Thorstensson and Roberthson, 1987; Diedrich and Warren, 1995, 1998; Li, 2000; Li and Hamill, 2002; Segers et al., 2006, 2007), but some information is available on transitions in dogs (Afelt et al., 1983; Maes, 2009). Vilensky et al. (1991) wrote a review paper on the trot to gallop transitions in cats, dogs and monkeys. Even though they found interspecific differences in how the transitions were achieved, they also noted that changes occurred primarily during the swing phase. During a trot to transverse gallop transition, cats and velvet monkeys both showed a sudden decrease in swing duration of the dissociating fore limb together with an increased swing duration of the dissociating hind limb, similar to our findings in horses. Even though the horses transition to a canter, it seems that at least the initial part of the transition is consistent with other species’ transitioning to a gallop, which seems to confirm the fact that canter can be considered to be a slow gallop. Similar results were found in dogs (Afelt et al., 1983; Maes, 2009). New information on the transition coming from the present study is the realization that transitions take more than two strides to complete and that this transition does not seem to be visible as a disruption in the continuity of forward speed progression of the COM. We found considerable variation in transition speeds, both within and between individuals. This perhaps unexpected variation could be due to the fact that we did our experiments overground instead of on a treadmill. Optical flow could possibly play a role in this (Mohler et al., 2007). Another source of variation could be the differences in acceleration between the trials. Also, the fact that horses can be trained to trot at higher velocities or to canter at lower velocities than expected by their preferred transition speeds seems to point to a reasonable assumption that at least part of the decision to transition can be overruled or suppressed and therefore flexibility in the transition speed may not be overly surprising. In this context, it may be important to note that the horses used were not specifically trained to transition but training was rather focussed on the horse keeping up with the runner.
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Apart from the straightforward explanation that transitions occur to allow adjustment of locomotor speeds, all explanations on why transitions occur have in common that the transition is meant to reduce certain “costs” of locomotion. Even though this explains why transitions occur (ultimate cause), it does not provide a framework to predict how such transitions (proximate cause) would occur. This study is a first step in unraveling how transitions occur by describing which kinematic events occur during a transition in a specific and consistent order. Acknowledgments The authors would like to thank Sheila Boyer, Alexia Heney, and Dan and Bess Ohlgren-Miller, the owners of the horses for allowing their horses to participate in this study. A lot of students worked hard on the experiments and on tracking the kinematics data: Nathalie Cousin, Rachel Wright, Jasmine Lane, Rachel Buchholz, Katherine O’Connor, Lila Zarski, Andrea Lawrence and Erin Tans. This study was funded by the McPhail Endowment and a postdoctoral research grant and travel grant from the Flemish Science Foundation FWO-Flanders, both to S.N., and a FWO-Flanders project grant G.0183.09N and a grant from the European Community’s Seventh Framework Program FP7/2007–2013 – Future Emerging Technologies, Embodied Intelligence, under grant agreement no. 231688, both to P.A.
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Zoology journal homepage: www.elsevier.com/locate/zool
Spatio-temporal gait characteristics during transitions from trot to canter in horses Sandra Nauwelaerts a,b,∗ , Peter Aerts a,c , Hilary Clayton b a b c
Functional Morphology Laboratory, Department of Biology, Antwerp University, Universiteitsplein 1, B-2610 Wilrijk, Belgium McPhail Equine Performance Center, Michigan State University, 736 Wilson Road, East Lansing, MI 48824, USA Department of Movement and Sport Sciences, University of Ghent, Campus HILO, Watersportlaan, B-9000 Ghent, Belgium
a r t i c l e
i n f o
Article history: Received 10 October 2012 Received in revised form 6 March 2013 Accepted 20 March 2013 Available online 15 June 2013 Keywords: Gaits Gait transition Locomotion Limb kinematics Quadrupeds
a b s t r a c t Gaits can be defined based upon specific interlimb coordination patterns characteristic of a limited range of speeds, with one or more defining variables changing discontinuously at a transition. With changing speed, horses perform a repertoire of gaits (walk, trot, canter and gallop), with transitions between them. Knowledge of the series of kinematic events necessary to realize a gait is essential for understanding the proximate mechanisms as well as the control underlying gait transitions. We studied the kinematics of the actual transition from trot to canter in miniature horses. The kinematics were characterized at three different levels: the whole-body level, the spatio-temporal level of the foot falls and the level of basic limb kinematics. This concept represents a hierarchy: the horse’s center of mass (COM) moves forward by means of the coordinated action of the limbs and changes in the latter are the result of alterations in the basic limb kinematics. Early and short placement of the fore limb was observed before the dissociation of the footfalls of one of the diagonal limb pairs when entering the canter. Dissociation coincided with increased amplitude and wavelength of the oscillations of the trunk in the sagittal plane. The increased amplitude cannot be explained solely by the passive effects of acceleration or by neck and head movements which are inconsistent with the timing of the transition. We propose that the transition is initiated by the fore limb followed by subsequent changes in the hind limbs in a series of kinematic events that take about 2.5 strides to complete. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Gaits can be defined by having specific interlimb coordination patterns that are used within a limited range of speeds and show discontinuous changes in one or more defining variables at a transition (Hildebrand, 1965; Abourachid, 2003; Robilliard et al., 2007). Each species performs a repertoire of gaits with transitions between gaits usually being performed when increasing or decreasing locomotor speed. Horses have become a paradigm in the gait literature because they exemplify the use of three main gaits: horses walk at low speed, trot at moderate speed and burst into a gallop at higher speeds. A wealth of experimental studies analyzing the kinematics and dynamics of equine gait patterns exists (e.g., Buchner et al., 1994; Minetti et al., 1999; Clayton, 1994a,b, 1995; Dutto et al., 2004) but the understanding of the mechanical events involved
∗ Corresponding author at: Functional Morphology Laboratory, Department of Biology, Antwerp University, Universiteitsplein 1, B-2610 Wilrijk, Belgium. Tel.: +32 3 265 2119. E-mail address: [email protected] (S. Nauwelaerts). 0944-2006/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.zool.2013.03.003
in transitions between the gaits is limited (Argue and Clayton, 1993a,b; Tans et al., 2009). Transitions from one gait to another are said to occur abruptly at a critical speed (Alexander, 1989). Several hypotheses on the ultimate causes of gait transitions have been tested. The most recognized hypotheses are the minimization of the energetic costs of locomotion (Hoyt and Taylor, 1981) and the minimization of the loading of the musculoskeletal system (Farley and Taylor, 1991). In addition, suggestions about the proximate mechanisms that may trigger gait changes have been put forward (Biewener and Taylor, 1986; Farley and Taylor, 1991). However, a striking lack of knowledge on the series of kinematic events occurring during a gait transition has remained. This is likely a consequence of the fact that only a few studies were designed with an experimental protocol that allowed investigation of what actually happens throughout the transition itself (Segers et al., 2006, 2007; Diedrich and Warren, 1995; Vilensky et al., 1991). Insights from such studies are essential for a better understanding of the proximate mechanisms as well as the control underlying gait transitions. Spinal interneurons play a key role in determining the form of rhythmic limb movements within a gait that determine the temporal characteristics of the stride (Grillner, 2002). The four central
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pattern generators (CPGs), one controlling each limb, coordinate the rhythmic patterns of the limb movements that characterize the different gaits. Transitions involve a change in coordination of these rhythmic movements. We studied the kinematics of the transition from trot to canter during accelerating locomotion in miniature horses. In the idealized trot, diagonal limb pairs move in phase (right fore together with left hind and left fore together with right hind), whilst both contralateral (left–right, within a girdle) and ipsilateral (fore–hind on the same side of the body) pairs move maximally out of phase. This means that time-symmetrical footfalls are present between the girdles and between the body sides. During the transition to canter one of the diagonal pairs de-synchronizes to produce the typical threebeat rhythm of canter. As a result, the phasing between both the contra-lateral and the ipsilateral limb pairs changes. Investigating the transitions thus combines a focus on maximized alterations in contra- and ipsilateral interlimb coordination with the pragmatic advantage of keeping a cyclic time reference – the synchronized footfalls of one diagonal pair throughout the transition – bearing in mind, though, the possibility that neither the neural control nor the mechanics of the system make use of this reference system. The kinematics were characterized at three different levels: (i) the whole-body level (center of mass, COM), (ii) the spatiotemporal level of the foot falls (interlimb coordination) and (iii) the level of basic limb kinematics (overall flexion–extension; oscillations with respect to the trunk). This concept represents a hierarchy: the horse’s COM moves forward by means of the coordinated action of the limbs quantified by their spatio-temporal events and changes in these events are the result of alterations in the basic limb kinematics. In the present study, we investigated which kinematic events occur in a specific and consistent order during a transition from trot to canter. We measured the limb movements, more specifically, how the horse changes footfall coordination pattern by altering limb kinematics. We tested how abrupt transitions occur at each of the hierarchical levels when changing from trot to canter using thresholds. Apart from the limbs, movements of the head–neck segment could potentially influence the COM mechanics. We therefore tested the involvement of neck and head movements in the transition. Because some trunk kinematic events could be caused by a passive acceleration effect, we also tested whether the boundary acceleration threshold (e.g., Aerts et al., 2003) is reached during transitions.
2. Materials and methods 2.1. Experiments Five miniature horses (mass: 116 ± 38 kg; mean ± SD) were used in this study. Thirty-four reflective markers of 6 mm were attached to the skin over anatomical landmarks on the body and limbs of each animal using adhesive tape while the horse was standing square (see Fig. 1). Eight Eagle infrared cameras (Motion Analysis Corp., Santa Rosa, CA, USA) operating at 120 Hz were used to cover a capture volume of 1 m × 1 m × 8 m. The capture volume was calibrated using a wand technique that yielded an error in linear measurement of 1 mm. We chose to work with the breed of miniature horses in order to obtain a larger number of strides within the restrictions of a capture volume using eight cameras. A runner led the horses in hand in a straight line through the capture volume using a loose lead rope while accelerating at trot with the intention of stimulating a transition from trot to canter. No direct cues to change gaits were given so the transitions were initiated by the horses. Data collection continued until a minimum of 15 trials that included a trot–canter transition had been recorded from each horse. In order to be retained for analysis, the
Fig. 1. Positions of markers: three markers on the head (forehead, distal end of left and right facial crests), four markers on the neck (wings of the atlas (C1) and caudal part of the left and right transverse processes of C6), six lateral markers on each forelimb (tuber spinae scapulae (scapula), greater tubercle of humerus (shoulder), lateral epicondyle of humerus (elbow), ulnar carpal bone (carpus), lateral condyle of third metacarpus (fore fetlock), and midlateral hoof wall), two markers on the back (withers (T6) and croup (S2)) and six markers on each hind limb (ventral part of tuber coxae (pelvis), greater trochanter of femur (hip), lateral condyle of the femur (stifle), talus (hock), lateral condyle of third metatarsus (hind fetlock) and midlateral hoof wall). Measured angles are indicated as shaded arcs. The trunk angle (˛) is the sagittal plane angle between the trunk segment and the horizontal; the value is positive when T6 is higher than S2 and negative when T6 is lower than S2. Neck angle (ˇ) was measured between the neck segment and the back segment (T6–S2) on the ventral aspect. Limb angles ( and ı) were calculated as the angle between the limb axis (from either scapula or hip to the lateral hoof marker) and an axis perpendicular to the trunk axis. In the left corner, the drawing is placed on a picture of one of the miniature horses used in the present study to demonstrate its similarity in proportions to averaged-sized horses.
transition trials had to fulfill two selection criteria: (i) the hoof markers were visible for a minimum of two strides before and two strides after the transition, which was necessary for construction of the gait diagrams; (ii) all markers were visible for at least three successive strides including the transition stride (stride zero: defined in Section 2.2), which was necessary for the COM analysis. 40 trials met these criteria and were retained for further analysis. Even though data were more difficult to obtain overground, we decided it was important to retain the effects of overall body inertia during acceleration as opposed to performing experiments on a treadmill (Van Caekenberghe et al., 2010a,b). To compare some of the spatiotemporal changes with changes due to increases in speed, 5 trials for each horse were recorded with the horse accelerating in trot and canter without transitioning. 2.2. Gait diagrams and spatio-temporal gait parameters Temporal and spatial footfall diagrams were constructed from the timing and position of the four hoof markers. To visualize temporal changes during the transitions more clearly, quadrilaterals were drawn on the gait diagrams by connecting the touchdowns and lift-offs of each diagonal pair. Stance durations and hoof heights for each hoof were determined for each stride. Stride length and stride duration were calculated separately for each limb as the distance and time, respectively, between successive footfalls. Speed was determined as the stride average of the instantaneous velocity of the COM. The four limbs of the horse were named (i) according to the anatomical girdle they belong to (fore or hind limb), (ii) according to the timing of the diagonal limb pair during the canter: the dissociating limb pair is the diagonal pair that is dissociated during the canter, while the non-dissociating limb pair is the other diagonal
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pair and (iii) according to their spatial orientation during the canter (leading or trailing limb of a contralateral pair; the former being the limb always kept in front of the other during a canter). As illustrated in Fig. 2, the first stride for which one diagonal pair of footfalls clearly deviated from an in-phase pattern was the first transition stride and it was assigned the stride zero number. This was done by visual examination of the vertical coordinates of the lateral markers over time for each trial. After detecting a continuous dissociation (pattern does not return to an in-phase pattern, point 1 in Fig. 2), the start of stride zero was determined as the contact of the dissociating fore limb prior to this dissociation. The strides preceding and following stride zero were designated negative and positive, respectively, and were numbered from the transition outwards. 2.3. Center of mass (COM) Since miniature horses have roughly similar proportions to normal-sized horses (insert in Fig. 1) and no specific data on inertial properties for this breed are available, COM position was calculated using the mass distribution and position of segmental COMs based on anatomical data from Buchner et al. (1997) and Van den Bogert (1989). COM velocities and accelerations were obtained from numerical differentiation of the positional data in the vertical and forward directions by calculating the incremental difference between two successive positions divided by the time interval. Time was set to zero at the start of stride zero. Intercepts of two linear regressions of the COM velocity against time through the velocity profile (i) prior to time zero (trots) and (ii) after time zero were compared to test whether the change in forward velocity at the transition was significantly different from zero (cf. transitions in humans; see Segers et al., 2007; example in Fig. 3). 2.4. Kinematics The trunk is considered the reference segment with regard to which limbs move. Trunk angle was defined as the angle between the line drawn from the marker on the withers to the one on the croup and the horizontal such that the angle increases when the front of the horse pitches up and decreases when it pitches down (˛ in Fig. 1). For every stride, minimal and maximal angles of the trunk were determined. Neck angle (representing the position of the head–neck segment) was defined as the ventral angle between a line connecting the C1 and C6 markers with a line connecting the T6 and S2 markers (ˇ in Fig. 1). Instantaneous limb length was calculated for each limb as the 3D distance between the positions of the scapula (or hip) marker and the lateral hoof marker (i.e., the limb longitudinal axis), while limb angles (fore limb: ␥; hind limb: ␦ in Fig. 1) were calculated as the angle between the limb longitudinal axis and an axis perpendicular to the trunk axis in the sagittal plane. This definition ensures that an increase in angle corresponds with protraction of the limb with respect to the trunk segment while a decrease in angle implies retraction (zero is always perpendicular to the trunk). Overall limb kinematics were assessed by measuring maximal and minimal limb lengths, maximal limb protraction angle and its timing with respect to touchdown, and maximal limb retraction angle and its timing with respect to lift-off. 2.5. Boundary acceleration threshold Aerts et al. (2003) described a method of estimating the accelerative conditions that would have to occur in order for the forces on the fore limbs to become zero. This rough estimate of the minimal acceleration (a) necessary to lift the trunk is based on the ratio of the averaged craniocaudal position of the hind limbs when in contact with the ground with respect to the COM (x) against the absolute
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height of the COM (y) taking the gravitational acceleration (g) into account: a = x/y g. This ‘critical acceleration’ was then compared to the actual forward acceleration in order to test the hypothesis that the increase in trunk elevation could potentially be a passive effect of the acceleration of the COM.
2.6. Statistics A paired t-test was used to test for differences between the intercepts of the regression lines of velocity against time. Since the Shapiro–Wilk test did not detect violations of normality (n = 147) for any of the variables tested, repeatedmeasures multivariate analyses of variance (MANOVA) were used to determine differences in spatio-temporal gait characteristics and kinematic variables between successive stride numbers and between limbs. Tukey-B post hoc comparisons were used to detect grouping between the stride numbers and limbs (P < 0.05). Chi square tests were used to test the acceleration threshold hypothesis.
3. Results 3.1. Velocity profile of the COM No sharp change in forward velocity of the COM was observed during trot to canter transitions. The intercepts of the velocities during trot did not significantly differ from those in canter and they did pass the equivalence test (alpha = 0.05, power > 0.8). There is considerable variation in transition speeds, here defined as the horizontal velocity averaged over stride zero, both within subjects and between subjects: animal 1 (3.14 ± 0.38 m/s, N = 11), animal 2 (2.88 ± 0.09, N = 11), animal 3 (3.97 ± 0.22 m/s, N = 7), animal 4 (4.10 ± 0.13 m/s, N = 4) and animal 5 (3.76 ± 0.28 m/s, N = 5).
3.2. Discontinuous changes in stride duration and stride length In the temporal gait diagram (Fig. 4A), the quadrilateral shape seen in the dissociating limb pair in the transition stride was an intermediate between the rectangle during trot and the parallelogram during canter. Since no significant differences were found for all variables between strides +3 and +2 or between strides −4, −3 and −2 and the differences passed the equivalence test (alpha = 0.05, power > 0.8), the data were pooled into 5 groups (−2, −1, 0, 1, 2). The change from a gait in which both diagonal pairs are synchronized to a gait in which only one diagonal remains synchronized while the other is dissociated takes two strides to perform (stride 0 and +1). Trot to canter transitions (Fig. 4A and B) can be described by comparing mean stride duration (Fig. 5) and mean stride length (Fig. 6) between successive strides plotted against mean velocity. Comparing the change in stride duration to the expected changes due to the increase in velocity within a trot, the non-dissociating diagonal limb pair seems to follow the expected pattern. This is in sharp contrast to the dissociating limb pair; the fore limb decreases its stride duration while the hind limb stride duration increases in stride 0. This effect is only negated in stride +2. A similar pattern was found for the stride lengths: the dissociating hind limb shows an increase while the dissociating fore limb shows a decrease in stride length in the transition, only to be negated in stride +2. Interestingly, the stride duration of the dissociating fore limb in the stride prior to the transition stride was on average 59 ms shorter and its stride length 20 cm shorter compared to the mean of the three other limbs together.
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Fig. 2. Example trial of how stride zero was defined in the individual trials. Dissociation (1) of the diagonal pair was detected based on the profile of the vertical coordinates of the hoof markers through time. Stride zero started with the start of the stance phase (2) of the forelimb of the diagonal pair that dissociated.
3.3. Non-limb kinematics Maximal trunk angle (pitch up) increased in stride 0 and stride 1, while minimal trunk angle peaks decreased slightly in stride 0, and more obviously in strides 1 and 2 (Fig. 7). No significant changes in maximal and minimal neck–trunk joint angles were found between strides (Fig. 8). No clear patterns were detected between the timing of trunk oscillation and the footfalls. 3.4. Limb pro- and retraction kinematics In the non-dissociating hind and dissociating fore limbs, maximal protraction angles gradually increased by 10◦ over the five strides we examined. While the maximal protraction of the nondissociating fore limb initially also increased, maximal protraction decreased in the transition, causing the two fore limbs to differ in maximal protraction angle by almost 14◦ in the first full canter stride, stride +2 (Fig. 9). Protraction in the dissociating hind limb did not show a consistent trend and seemed to oscillate around the same average value. Minimal limb angle (retraction) of the entire limb remained constant for the non-dissociating fore limb (alpha = 0.05, power = 0.43), and increased (less retraction) after the transition in the
dissociating fore limb. Minimal retraction increased after the transition for the dissociating hind limb. There are small effects of a couple of degrees with the pattern of change being similar for the three limbs (see Fig. 9). Caution is needed in the interpretation of these results because the minimal limb angles were correlated to each other, which might cause issues of multicollinearity with the MANOVA test. Pearson correlations were all higher than 0.9 between the four minimal angles. Retraction increased more dramatically (decreased retraction angles) in the dissociating hind limb prior to the transition, making it the limb with the most pronounced retraction in the canter. Timing of the maximal protraction angle with respect to touchdown was variable and was significantly different between strides only for the dissociating hind limb, with maximal protraction occurring near touchdown in trot and occurring 350 ms prior in the canter. Timing of minimal retraction with respect to lift-off was close to lift-off for all limbs in the canter, while occurring 200 ms earlier for the non-dissociating limb pair in the trot. Maximal limb lengths did not significantly change between strides. Minimal limb lengths changed in the hind limbs with both limbs having smaller minimal lengths in strides −2, −1 and 0 by 2–3 cm, representing about 5% of total limb length.
Fig. 3. Velocity profile of the COM for an example trial of a transition from trot to canter. Time was set to zero at the start of stride zero (see Fig. 2). Linear fits were drawn through the horizontal velocity against time profiles and the intercepts of the two lines were compared to test for a jump in velocity, defined as an abrupt change in the velocity progression in the transition region. Even though there was high variability in the velocities and the acceleration (slope) between the trials, intercepts of the trot and canter regressions were found to be equivalent.
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Fig. 4. (A) Timings of hoof touchdowns and hoof lift-offs based on the average footfalls of all trials. Time in seconds on the x-axis. Horizontal lines indicate the stance phase of each leg; diagonal limbs are connected by vertical lines creating quadrilaterals. When the diagonal pair hits and lifts off the ground simultaneously, this quadrilateral will be rectangular for both diagonals. During a canter, it will be rectangular for the non-dissociating diagonal and a parallelogram for the dissociating diagonal. Limbs are color-coded: black for dissociating fore, red for non-dissociating fore, green for dissociating hind and blue for non-dissociating hind. (B) Example trial of the positions of hoof prints of a horse that is trotting (from left to right) and transitions to canter. The x-axis shows the position in the direction of movement in meters, while the y-axis shows the mediolateral position. Distance between two ticks is 1 m on both axes. Limbs are color-coded: black for dissociating fore, red for non-dissociating fore, green for dissociating hind and blue for non-dissociating hind. Diagonal pairs that hit the ground simultaneously are connected with a black line. When the pair is dissociated, an arrow is drawn from the hoof that makes contact with the ground first to the hoof that hits second. The hoof that hits second is indicated by a slash through its symbol.
Fig. 5. Stride duration in seconds for each limb in each stride number. The mean velocity of strides is shown on the x-axis and their numbers are labeled above the box. Error bars represent standard errors in both dimensions. Significant differences between successive strides are indicated with an asterisk. The two regression lines represent the relationship between stride duration and velocity within the trot (in black) and the canter (in red) based on trials of the same subjects accelerating without transitioning. Also note the significantly shorter stride duration of the dissociating forelimb in stride −1 as compared to the three other limbs.
3.5. Boundary acceleration thresholds In most trials, the measured acceleration matched or even surpassed the critical acceleration, but it was not significant over the entire stance and the timing of the measured acceleration did not consistently coincide with an increase in trunk angle. In addition,
since it is expected that the measured acceleration should exceed a multiple of the critical acceleration in order to have a substantial lifting effect, we tested whether the measured acceleration was larger than 1.5 times the critical acceleration. It was found to be significantly smaller than this new threshold value (alpha = 0.05, power > 0.8).
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Fig. 6. Stride length in meters for each limb in each stride number. The mean velocity of strides is shown on the x-axis and their numbers are labeled above the box. Error bars represent standard errors in both dimensions. Significant differences between successive strides are indicated with an asterisk. The two regression lines represent the relationship between stride length and velocity within the trot (in black) and the canter (in red) based on trials of the same subjects accelerating without transitioning. Also note the significantly smaller stride length of the dissociating forelimb in stride −1 as compared to the three other limbs.
4. Discussion
Fig. 7. Mean minimal and maximal trunk segmental angles with standard error for each stride.
Fig. 8. Mean minimal and maximal neck joint angles with standard error for each stride.
Since the stride duration and stride length of the dissociating fore limb are smaller than those of all the other limbs in stride −1, the first kinematic event that indicates a disruption in the cyclic footfall pattern of the trot is the early touchdown of the dissociating fore limb. It is the limb that is spatially in front of the other fore limb and is therefore often called the leading fore limb. This implies that the transition was initiated during the swing phase of the leading fore limb in stride −1. We therefore suggest calling stride −1 the ‘transition initiating stride’. The limb positioned diagonally to this limb, the dissociating hind limb, is then delayed in its next placement which is associated with increases in stride length and duration for this limb in stride 0, the stride that is defined by its clear dissociation and is therefore called the ‘transition stride’. In stride +1, a further dissociation in the timing of the footfalls of the dissociating limb pair occurs. This stride will be called the ‘transition completion stride’ since it is not until stride +2 that the interlimb differences in stride length and duration disappear (there were statistically significant differences between strides +1 and +2 but variables for strides +2 and +3 were statistically equivalent, power > 0.8). This means that the transition takes about 2.5 strides to complete. This agrees with the prediction of Raibert (1990) that a robotic quadruped is able to transition between symmetrical gaits during the swing phase of a single stride but transitions from a symmetrical to an asymmetrical gait require at least two strides. Transition initiation seems to involve a reorientation of the girdles to accommodate the different amounts of protraction in the leading versus trailing limbs that are characteristic of an asymmetrical gait. By the time the transition is completed, the leading fore and hind limbs have significantly increased both their protraction and retraction angles. Consequently, the entire cycle of rotation of these limbs is more cranial in canter than in trot. In the trailing fore and hind limbs the most obvious change is a decrease in retraction of the trailing hind limb, which is retracted approximately 10◦ further than the other three limbs. The consequent changes in rotational movement of the girdles in the dorsal plane seem to initiate a disruption in the footfall pattern that does not affect the progression of the movements of the center of mass. Indeed, as opposed to transitions in humans from walk to run, no jump in COM velocity was found in transitioning horses. This means that there is no detectable cost in kinetic energy involved in transitioning from trot
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Fig. 9. Maximal (protraction) and minimal (retraction) limb angle per degree for each stride number and each limb. The mean velocity of strides is shown on the x-axis and their numbers are labeled above the box. Error bars represent standard errors in both dimensions. Significant differences between successive strides are indicated with an asterisk. Increasing protraction is indicated by an increase in positive angle, increasing retraction by a larger negative angle.
to canter other than the increase due to acceleration and a transition is only visible at the second level of the hierarchy, the limbs. One mechanism to account for the sudden increase in trunk angle amplitude would be the use of the relatively heavy neck–head segment. It is often reported by experienced riders that horses lift their head and neck into the transitions. However, neck joint angle patterns were highly variable between and within horses and the head was not raised consistently either overall or within certain individuals. Therefore, the neck–head raising was not retained as an explanatory factor in our study. Since the horse is accelerating and the pitch angles change in the transition, we tested whether the change in pitch up of the trunk during stride zero could be just a passive effect of the forward acceleration of the horse, which would mean that it is not necessarily controlled through a change in the CPGs of the individual limbs. Applying the boundary acceleration theory (Aerts et al., 2003; Williams et al., 2009) it was shown that the boundary acceleration was only just exceeded. Studies in lizard and horse locomotion showed that significant pitching requires multiples of this boundary acceleration (Aerts et al., 2003; Curtin et al., 2005). Therefore, it was concluded that it is not possible for the pitch up of the trunk to be a purely passive event. The underlying mechanism would be first a push-up coming from the fore limb that lands earlier and then a drop of the rear activated by the gluteal and/or epaxial muscles with the lumbosacral and hip joints flexed. Another important aspect of locomotion that explains the existence of different gaits is the presence or absence of mechanisms to decrease collisional losses (Ruina et al., 2005). Trot is a gait that contains high collision losses which are highly reduced during galloping (Ruina et al., 2005; Lee et al., 2011). When speeding up the trot, collision losses increase and this greatly influences the cost of transport. By transitioning from a two-beat to a three-beat gait, each collision is divided over 1.5 sub-collisions, reducing the costs to 4/9th of the cost of a two-beat gait (Ruina et al., 2005). To reduce the amount of energy wasted in the collision, animals tend to avoid sudden changes in the direction of the velocity vector of the COM (Lee et al., 2011). It is likely that collisional loss reduction plays a role in the causality of the transition itself. A sudden change in pattern, perhaps even as subtle as putting a limb on the ground earlier than expected, might lead to a sudden change in collisional losses, thereby changing the dynamics of the cyclically moving system. Most of the previous studies that have tried to explain why gait transitions occur inferred what happens in the transition by
comparing between different gaits performed at steady-state speed (Hoyt and Taylor, 1981; Biewener and Taylor, 1986; Farley and Taylor, 1991; Wickler et al., 2003; Griffin et al., 2004). However, an important aspect of gait transitions is the discontinuity that occurs while varying the speed of progression (Ivanenko et al., 2011). The abruptness of this phenomenon is particularly intriguing. So far, studies of the mechanics during steady acceleration throughout a gait transition are scarce. Most of the information describes the walk to run transitions in humans (Thorstensson and Roberthson, 1987; Diedrich and Warren, 1995, 1998; Li, 2000; Li and Hamill, 2002; Segers et al., 2006, 2007), but some information is available on transitions in dogs (Afelt et al., 1983; Maes, 2009). Vilensky et al. (1991) wrote a review paper on the trot to gallop transitions in cats, dogs and monkeys. Even though they found interspecific differences in how the transitions were achieved, they also noted that changes occurred primarily during the swing phase. During a trot to transverse gallop transition, cats and velvet monkeys both showed a sudden decrease in swing duration of the dissociating fore limb together with an increased swing duration of the dissociating hind limb, similar to our findings in horses. Even though the horses transition to a canter, it seems that at least the initial part of the transition is consistent with other species’ transitioning to a gallop, which seems to confirm the fact that canter can be considered to be a slow gallop. Similar results were found in dogs (Afelt et al., 1983; Maes, 2009). New information on the transition coming from the present study is the realization that transitions take more than two strides to complete and that this transition does not seem to be visible as a disruption in the continuity of forward speed progression of the COM. We found considerable variation in transition speeds, both within and between individuals. This perhaps unexpected variation could be due to the fact that we did our experiments overground instead of on a treadmill. Optical flow could possibly play a role in this (Mohler et al., 2007). Another source of variation could be the differences in acceleration between the trials. Also, the fact that horses can be trained to trot at higher velocities or to canter at lower velocities than expected by their preferred transition speeds seems to point to a reasonable assumption that at least part of the decision to transition can be overruled or suppressed and therefore flexibility in the transition speed may not be overly surprising. In this context, it may be important to note that the horses used were not specifically trained to transition but training was rather focussed on the horse keeping up with the runner.
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Apart from the straightforward explanation that transitions occur to allow adjustment of locomotor speeds, all explanations on why transitions occur have in common that the transition is meant to reduce certain “costs” of locomotion. Even though this explains why transitions occur (ultimate cause), it does not provide a framework to predict how such transitions (proximate cause) would occur. This study is a first step in unraveling how transitions occur by describing which kinematic events occur during a transition in a specific and consistent order. Acknowledgments The authors would like to thank Sheila Boyer, Alexia Heney, and Dan and Bess Ohlgren-Miller, the owners of the horses for allowing their horses to participate in this study. A lot of students worked hard on the experiments and on tracking the kinematics data: Nathalie Cousin, Rachel Wright, Jasmine Lane, Rachel Buchholz, Katherine O’Connor, Lila Zarski, Andrea Lawrence and Erin Tans. This study was funded by the McPhail Endowment and a postdoctoral research grant and travel grant from the Flemish Science Foundation FWO-Flanders, both to S.N., and a FWO-Flanders project grant G.0183.09N and a grant from the European Community’s Seventh Framework Program FP7/2007–2013 – Future Emerging Technologies, Embodied Intelligence, under grant agreement no. 231688, both to P.A.
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