Velocity-dependent changes of time, force and spatial parameters in Warmblood horses walking and trotting on a treadmill

Authors


email: mweishaupt@vetclinics.uzh.ch

Summary

Reasons for performing study: Gait analysis parameters are sensitive to alterations in velocity. For comparison of nonspeed-matched data, the velocity dependency needs to be known.

Objectives: To describe the changes in gait pattern and determine the relationships between stride duration, vertical impulse, contact time and peak vertical force within a range of walking and trotting speeds.

Methods: Thirty-eight nonlame Warmblood horses were subjected to an incremental speed test. The spans of speed were adjusted individually to each horse and ranged from 1.1–2.1 m/s at walk and from 2.5–5.8 m/s at trot. Time, force and spatial parameters of each limb were measured with an instrumented treadmill and analysed with regression analysis using velocity as the independent variable.

Results: At a slow walk the shape of the force curve was generally single-peaked in the fore- and trapezoidal in the hindlimbs. With increasing speed, the curves turned into the typical double-peaked shape with a higher second peak in the fore- and a higher first peak in the hindlimbs. With increasing velocity, stride duration, stance durations and limb impulses of the fore- and hindlimbs decreased in both gaits (r2>0.92). Increasing speed caused a weight shift to the forehand (walk: from 56 to 59%; trot: from 55 to 57%). Despite decreasing limb impulses, peak vertical forces increased in both gaits (r2>0.83). The suspension duration of the trot increased with faster velocities and reached a plateau of around 90 ms at the highest speeds. At a slow trot, the forelimbs impacted first and followed the hindlimbs at lift-off; with increasing speed, the horses tended to impact earlier with the hindlimbs. Contralateral symmetry indices of all parameters remained unchanged.

Conclusions: Subject velocity affects time, force and spatial parameters. Knowing the mathematical function of these interdependencies enables correction of nonspeed-matched data.

Introduction

The high-speed treadmill is widely accepted as a useful tool in equine exercise physiology and locomotion research and plays an increasingly significant role in clinical investigations. It enables clinical examinations to be combined with sophisticated measurement equipment such as gait analysis systems for assessing gait performance and lamenesses. A further step towards its implementation in an orthopaedic-oriented clinical setting is to instrument the treadmill with a force measuring system (Weishaupt et al. 2002). Ground reaction force (GRF) data of all limbs can offer valuable additional information to the subjective visual evaluation and has the potential to identify abnormalities of locomotor performance prior to the appearance of overt clinical signs.

Speed is known to be the critical variable influencing the kinematics and kinetics of a gait. Different investigators consistently found that, independent of the gait, increasing velocity prolongs stride length, shortens stride and stance duration, decreases limb impulses and increases peak vertical forces (McLaughlin et al. 1996; Khumsap et al. 2001a, 2002; Dutto et al. 2004). Reliable inter- or intraindividual comparisons of gait parameters therefore require speed-matched data. This prerequisite is difficult to meet, especially when using force plates or kinematic systems, which cover only a limited calibrated space and several trials are necessary to obtain a sufficient number of representative strides. To overcome the difficulties of standardising moving velocity in the over ground situation, mathematical correction procedures based on regression analyses and ‘body size-normalised’ data were proposed (Hof 1996, 2001; Khumsap et al. 2001a,b, 2002).

Although speed can be controlled easily on the treadmill, certain experimental set-ups may include factors, such as varying the head-neck position, that limit the horses’ ability to move at a required velocity, thus preventing the experimental standardisation of velocity (Weishaupt et al. 2006a; Waldern et al. 2009). The same applies for the evaluation of individual gait performance and abnormalities, which necessitates a comparison with reference values of clinically normal horses moving at the same gait and velocities.

From the perspective of metabolic cost and mechanics of locomotion, several studies pointed out that treadmill data are comparable to but not directly equivalent to over ground data (Buchner et al. 1994; Sloet van Oldruitenborgh-Oosterbaan and Barneveld 1995; Courouce et al. 1999). Consequently, treadmill-specific reference values need to be determined for the various test modalities including gait analysis.

The aim of this study was to establish normative standards of time, force and spatial variables in Warmblood horses moving on a treadmill over the full range of walking and trotting speeds and to compare the velocity-dependencies measured on the treadmill with those reported in the literature for the over ground situation.

Materials and methods

Animals

Thirty-eight Warmblood riding horses were selected on the basis of their representative natural gait pattern and physical soundness (age range 3–18, mean 7.3 years; mean ± s.d. bwt 565 ± 51.8 kg; withers height 1.68 ± 0.06 m). The orthopaedic examination included the inspection and palpation of the limbs and a careful visual assessment of their gait at the walk and trot on hard surface, before and after flexion tests, on the lunge, and on the treadmill. The horses were ridden on a daily basis and competed intermittently to regularly in jumping and dressage events of different levels. Beforehand, the horses were accustomed to walk, trot and canter on the treadmill (Mustang 2200)1 and trained to easily adjust their speed of movement to a range of velocities within each gait.

Data acquisition and analysis

The horses were warmed-up for 20 min at walk and trot. Data were collected over a range of individually adjusted velocities starting in each gait with the slowest speed at which the horse showed a regular pace. The velocity was incrementally increased up to the point at which the horse was not able to hold the preset speed and made the transition to the higher gait. Speed increments were 0.1 m/s at walk and 0.3 m/s at trot. Gait parameters of each limb were measured using an instrumented treadmill (Weishaupt et al. 2002).

Data sampling was started as soon as the horse was moving at a regular pace and in a straight head-body position. The sampling frequency was 433 Hz. The recording time of each velocity step lasted 30 s, which resulted in 22 ± 1.6 motion cycles at the walk and 38 ± 1.9 at the trot. Measurements during which the horse stumbled or visibly changed its relative position on the treadmill were rejected. Force-time series were analysed with in-house developed software (HP2)2, which allowed the automatic extraction of temporal, force and spatial data for each limb separately. The terminology refers to the one proposed by Deuel (2001). Discrete values of each stride cycle were averaged per horse and speed increment. On condition that horses were nonlame, data of contralateral limbs were pooled. Temporal parameters were normalised to stride duration. Force and impulse parameters were normalised to the subject's body mass.

Further analyses were based on ‘mean-normalised data’; i.e. for each parameter, gait and horse the mean value over the full range of velocities was computed and the velocity-dependent changes were expressed as delta values to this mean. Delta velocities were calculated in the same way. This procedure enabled the investigation of the velocity dependency of each parameter regardless of the individual levels of the absolute data. For each horse, the best matching regression function was determined visually and based on the coefficient of determination (r2) using the mean-normalised data of the respective variables vs. speed changes as the independent variable. Depending on this assessment, a linear or 2nd order polynomial regression was calculated for the data set of the whole group.

Contralateral limb and cycle asymmetries were assessed with the asymmetry index (ASI) according to (Herzog et al. 1989).

Statistics

Descriptive statistics and polynomial regression analyses were performed in Excel 20033. The functional relationship between velocity and time, force and spatial parameters was qualified with the r2 and the P value of the F test. Level of significance was set at P<0.05.

Ethical review

The experimental protocol had been approved by the Animal Health and Welfare Commission of the Canton of Zurich.

Results

The walking speed ranged from 1.1–2.1 m/s (mean 1.54 m/s) and trotting speed from 2.5–5.8 m/s (mean 3.88 m/s). In the extreme cases, the span accounted for ±30 and ±35% around the horse's individual mean value of walking and trotting speed, respectively.

Shape transformation of the vertical GRF curve at walk

In contrast to the trot, where the shape of the vertical force curve maintained its characteristic one-peak outline over the entire velocity range, the typical double-peaked force curve of the walk developed only at faster speeds (Fig 1). First indications of the double-peaked curve were observed at 1.43 ± 0.08 m/s; peaks were clearly developed at 1.58 ± 0.10 m/s with a higher second peak in the fore- and a higher first peak in the hindlimbs. Two-thirds of the horses first developed a distinct hindlimb force curve. In general, the shape of the force curves evolved asymmetrically between contralateral limbs.

Figure 1.

Representative transformation of the vertical force curve with increasing velocity at walk. Slowest speed 1.06 m/s (17 stride cycles), fastest speed 1.95 m/s (25 stride cycles). FL, left forelimb; HR, right hindlimb; FR, right forelimb; HL, left hindlimb.

At the slow, collected walk, the forelimb force curve showed a single maximum around 60% of stance. The hindlimb force curve had a trapezoidal shape with hardly recognisable peaks. At medium walk, the first force peak of the forelimb curve appeared around 39% and in the hindlimbs around 32% of stance. At extended walking speeds both peaks became distinct and moved to the onset and end of stance (forelimb, 24 and 70%; hindlimb, 17 and 78% of stance, respectively), indicating a higher rate of loading and unloading. The time of peak force at the trot was speed-independent and was located at 48–52% of stance.

Velocity dependencies of selected gait parameters are illustrated in Figures 2 and 3.

Figure 2.

Walk: Velocity dependencies of selected time, force and spatial parameters at walk. Dependent and independent variables are delta to the respective mean value (305 measurement points). The variable's mean values and the respective regression coefficients are listed inTable 1. TFP1, time of the first vertical force peak; TFP2, time of the second vertical force peak; for remaining abbreviations seeTable 1.

Figure 3.

Trot: Velocity dependencies of selected time, force and spatial parameters at trot. Dependent and independent variables are delta to the respective mean value (300 measurement points). The variable's mean values and the respective regression coefficients are listed inTable 2. For abbreviations seeTables 1 and 2.

The coefficients of the linear or 2nd order polynomial regressions are listed together with the mean values and r2 in Tables 1 and 2, for walk and trot, respectively.

Table 1. Walk: Functional relationship of time, force and spatial variables to velocity (38 horses, 305 measured trials in total). The dependent and independent variables are expressed as differences to the respective mean (ΔVar, Δv); mean ± s.d. velocity, 1.54 ± 0.07 m/s
  Mean ± s.d.a0a1a2r2
  1. Polynomial regression function: ΔVar = a0+ a1Δv + a2Δv2; r2, coefficient of determination. Significant regressions (P<0.001) are marked with an asterisk (*). SD, stride duration; SR, stride rate; StDabs, stance duration; StDrel, duty factor (StDabs relative to SD); StpDdiag, diagonal step duration; StpDipsi, ipsilateral step duration; OD2F1H, overlap duration of tripedal support – 2 fore-, one hindlimb; ODlat, overlap duration of lateral bipedal support; OD2H1F, overlap duration of tripedal support – 2 hind-, one forelimb; ODdiag, overlap duration of diagonal bipedal support; IzSD, vertical stride impulse (sum of the 4 vertical limb impulses during an entire motion cycle); Iz, vertical limb impulse; Izfore, proportion of diagonal vertical impulse carried by the forelimbs; Fzmean, mean vertical force during StD; FzP1, first vertical force peak; FzP2, second vertical force peak; Fzdip, vertical force dip; SL, stride length; StLabs, stance length; StLrel, StL relative to SL; StpW, step width; OR, overreach distance. Unless stated differently, time parameters are expressed as percentage of SD (%SD).

SD (s) 1.210 ± 0.0740.000−0.352 0.92 *
SR (1/min) 50.0 ± 3.00.00014.060 0.93 *
StDabs (s)Forelimbs0.775 ± 0.053−0.005−0.3360.0920.95 *
 Hindlimbs0.766 ± 0.048−0.006−0.2880.1150.95 *
StDrel (%SD)Forelimbs63.9 ± 1.0−0.179−8.9123.1640.97 *
 Hindlimbs63.2 ± 1.0−0.351−5.2276.2180.92 *
StpDdiag (%SD) 26.0 ± 1.80.000−0.394 0.01
StpDipsi (%SD) 24.0 ± 1.80.0000.384 0.01
OD2F1H (%SD) 13.9 ± 1.00.000−8.899 0.96 *
ODlat (%SD) 12.1 ± 2.20.3918.519−6.9260.88 *
OD2H1F (%SD) 13.2 ± 1.0−0.349−5.2196.1740.92 *
ODdiag (%SD) 10.8 ± 1.80.0005.597 0.75 *
IzSD (Ns/kg) 11.87 ± 0.720.000−3.447 0.92 *
Iz (Ns/kg)Forelimbs3.44 ± 0.200.000−0.903 0.88 *
Hindlimbs2.50 ± 0.190.000−0.820 0.93 *
Izfore (%IzSD) 57.9 ± 1.10.1401.550−2.4720.52 *
Fzmean (N/kg)Forelimbs4.46 ± 0.110.0180.733−0.3210.94 *
Hindlimbs3.27 ± 0.100.0070.150−0.1210.58 *
FzP1 (N/kg)Forelimbs5.66 ± 0.19−0.0290.563 0.39 *
Hindlimbs4.62 ± 0.230.0001.762 0.88 *
FzP2 (N/kg)Forelimbs6.60 ± 0.240.0001.501 0.88 *
Hindlimbs4.38 ± 0.220.0000.405 0.43 *
Fzdip (N/kg)Forelimbs5.05 ± 0.300.041−0.812 0.51 *
Hindlimbs2.96 ± 0.180.002−1.986 0.96 *
SL (m) 1.848 ± 0.1250.0000.686 0.95 *
StLabs (m)Forelimbs1.167 ± 0.0800.0110.275−0.1880.92 *
Hindlimbs1.132 ± 0.0720.0070.322−0.1330.94 *
StLrel (%SL)Forelimbs63.3 ± 0.90.000−8.678 0.94 *
Hindlimbs61.4 ± 0.9−0.205−5.4773.6290.85 *
StpW (m)Forelimbs0.151 ± 0.0330.0000.016 0.14 *
Hindlimbs0.173 ± 0.0390.0000.027 0.22 *
OR (m) 0.166 ± 0.1030.0000.533 0.92 *
Table 2. Trot: Functional relationship of time, force and spatial variables to velocity (38 horses, 300 measured trials in total). The dependent and independent variables are expressed as differences to the respective mean (ΔVar, Δv); mean ± s.d. velocity, 3.88 ± 0.23 m/s
  Mean ± s.d.a0a1a2r2
  1. Polynomial regression function: ΔVar = a0+ a1Δv + a2Δv2; r2, coefficient of determination. Significant regressions (P<0.001) are marked with an asterisk (*). TAP, time of diagonal advanced placement (time dissociation between diagonal limbs at initial ground contact); TAC, time of diagonal advanced completion (time dissociation between diagonal limbs at toe-off); SpD, suspension duration; Fzpeak, peak vertical force. Unless stated differently, time parameters are expressed as percentage of SD (%SD). For remaining abbreviations see Table 1.

SD (s) 0.742 ± 0.0350.000−0.049 0.93*
SR (1/min) 81.3 ± 3.90.0005.367 0.92*
StDabs (s)Forelimbs0.302 ± 0.018−0.006−0.0590.0130.97*
Hindlimbs0.269 ± 0.014−0.003−0.0350.0050.97*
StDrel (%SD)Forelimbs40.6 ± 2.3−0.734−5.3251.4590.96*
Hindlimbs36.2 ± 1.9−0.294−2.3540.5850.90*
TAP (%SD) −0.07 ± 1.070.3602.186−0.7150.87*
TAC (%SD) 4.37 ± 1.080.000−0.783 0.58*
SpD (%SD) 8.49 ± 1.960.7664.303−1.5220.92*
IzSD (Ns/kg) 7.28 ± 0.340.000−0.476 0.93*
Iz (Ns/kg)Forelimbs2.05 ± 0.090.000−0.120 0.93*
Hindlimbs1.59 ± 0.090.000−0.118 0.90*
Izfore (%IzSD) 56.3 ± 1.00.0000.397 0.38*
Fzmean (N/kg)Forelimbs6.88 ± 0.360.0730.944−0.1440.98*
Hindlimbs5.95 ± 0.360.0360.332−0.0710.86*
Fzpeak (N/kg)Forelimbs11.56 ± 0.730.1301.571−0.2590.97*
Hindlimbs9.99 ± 0.550.0360.469−0.0720.83*
SL (m) 2.853 ± 0.2340.0000.548 0.98*
StLabs (m)Forelimbs1.114 ± 0.0670.0000.068 0.93*
Hindlimbs0.972 ± 0.0500.0000.123 0.98*
StLrel (%SL)Forelimbs39.7 ± 2.3−0.767−5.2091.5240.95*
Hindlimbs34.4 ± 1.8−0.236−2.2320.4690.89*
StpW (m)Forelimbs0.148 ± 0.0510.000−0.004 0.05
Hindlimbs0.124 ± 0.0550.000−0.001 0.00
OR (m) 0.099 ± 0.0920.0000.208 0.98*

With the exception of the contralateral step duration in both gaits, the diagonal and lateral step duration at walk and the step width at trot, all F tests had P values of <0.001 confirming a highly significant functional relationship between the dependent variables and velocity.

Temporal parameters as function of speed

In both gaits, stride duration (SD), absolute (StDabs) and relative stance durations (StDrel) of fore- and hindlimbs decreased with increasing velocity (r2>0.90). At the trot, forelimb StDabs and StDrel decreased at a faster rate than in the hindlimbs resulting in contact times of similar duration between fore- and hindlimbs at higher speeds (Figs 2 and 3).

At the walk, contralateral step duration as well as absolute diagonal and lateral step durations decreased proportionally to SD. Consequently, the half and quarter subdivision of the stride, i.e. the ratio between half cycles as well as between relative diagonal (StpDdiag) and lateral step durations (StpDlat), did not change with speed. In contrast, the proportions between the overlap times of the tripedal and bipedal support phases were speed-dependent. With increasing velocity, the tripedal support phases decreased whereas the bipedal support phases increased (Fig 2).

At the trot, relative suspension duration (SpD) increased with faster velocities in a strong (negative) quadratic fashion and in absolute terms approached an upper limit of approximately 90 ms (Fig 3). At slow trotting speeds, the forelimbs impacted first at onset of diagonal stance (negative time of advanced placement, TAP) and followed the hindlimbs at lift-off (positive time of advanced completion, TAC; Fig 3). With increasing speed, first contact and lift-off of the diagonal limb pair occurred gradually more simultaneously with the hindlimbs preceding the forelimbs by a few milliseconds (Fig 3, Table 2).

Force parameters as function of speed

In both gaits, vertical stride (IzSD) and limb impulses (Iz) of fore- and hindlimbs decreased linearly with increasing speed (r2>0.88). Conversely, all mean vertical limb forces (Fzmean), the principal peak forces at walk (second peak forelimbs, first peak hindlimb) and the peak vertical forces (Fzpeak) of fore- and hindlimbs at trot increased (r2>0.83). However, the rate of increase in hindlimb Fzmean in both gaits and hindlimb Fzpeak at trot was markedly lower than in the forelimbs (Figs 2 and 3). At walk, the force dip between peaks decreased with increasing speed in the fore- (r2= 0.51) and particularly in the hindlimb force curve (r2= 0.96; Fig 2). With increasing speed the horses’ centre of mass shifted towards the forehand (Izfore walk: from 56 to 59%; trot: from 55 to 57%; Figs 2 and 3); however, the speed-dependency was weak because of considerable individual variation (r2 walk: 0.52; trot: 0.38).

Spatial parameters as function of speed

Stride length (SL) and absolute stance length (StLabs) increased in fore- and hindlimbs in both gaits with increasing velocity; nevertheless, stance length relative to SL (StLrel) decreased with increasing velocity (Fig 3). Step width (StpW) remained unchanged between fore- and hindlimbs at trot. At faster walking speeds, horses walked wider with fore- and hindlimbs; although significant, in absolute terms the changes were small and ranged from 15–20 mm.

Over-reach distance (OR) increased linearly in both gaits with increasing velocity (Figs 2 and 3).

Contralateral symmetry

The average contralateral symmetry indices of all parameters remained unchanged. However, accentuation or reduction of asymmetry as a function of speed was observed on an individual basis.

Discussion

The analysis of the GRF represents a very useful technique for characterising the mechanics of a specific gait. Gait parameters measured with an instrumented treadmill proved to be very sensitive in quantifying weight bearing asymmetries or gait performance (Weishaupt et al. 2004, 2006a,b, 2009). The objective of this study was to establish treadmill-specific reference values over a range of relevant speeds in Warmblood horses and to discuss the functional relationship of gait parameters and velocity with published over ground data.

Shape transformation of the vertical GRF curve at walk

Descriptions of differently shaped vertical GRF curves at the walk can be found in the literature (Schryver et al. 1978; Khumsap et al. 2001a). However, these variations were not definitely associated with walking velocity.

At walk, the cranial and caudal segmental halves of the trunk each oscillate in vertical direction twice per stride and out of phase by a quarter stride cycle. The lowest point of this vertical movement is reached by each trunk segment during the tripedal support phases (OD2F1H and OD2H1F) when the pro-retraction angle between the contralateral limbs is maximal; the highest point occurs around midstance with the supporting limb in the vertical.

Functionally, the first peak occurs when the supporting limb props up the respective body part at the moment of weight acceptance accelerating the trunk upwards. The second peak is the result of decelerating the downward movement of the body segment during the last third of stance. During midstance the respective trunk segment reaches its highest point where the upwards directed momentum partly counteracts the gravitational forces; at this instant the supporting limb is slightly unloaded, which is reflected in the characteristic force dip. The extent to which the release of kinetic loading of the elastic limb spring and the upwards momentum of the contralateral limb in its midswing phase (Khumsap et al. 2001a) contributes to this phenomenon, remains unclear.

At the slow walk, the force peaks were not distinctly outlined, indicating that the body centre of mass was transported almost horizontally without large vertical displacement. As the walk got faster, absolute StL increased, accentuating the vertical excursion of the trunk. In combination with the shorter limb contact times the gait became more dynamic because of the higher loading and unloading rates. Consequently, this resulted in higher peak forces separated by an increasingly deeper dip at midstance (Fig 1). The fact that the second force peak in the forelimbs and the first force peak in the hindlimbs are higher may be explained by the position of the respective limbs relative to the horse's centre of mass.

Compensation of inter-individual variability

Horse height affects SL, with taller horses taking longer strides. To compensate for this effect, data can be scaled such that, for animals of different sizes, the acceleration and the gravitational forces are scaled in proportion (Hof 1996; Khumsap et al. 2001a, 2002). The decisive factor of this concept is the ‘body size-normalised’ velocity also called Froude number (Hof 1996). The Froude numbers calculated with the data set of this study amounted in average to 0.381 and 0.956 at walk and trot, respectively. Taking into account the variation in withers height of the study horses (1.56–1.81 m), the Froude number would vary approximately by ± 4%. This variation contrasts to the variation achieved by experimentally changing the velocity by ± 30% around the individual mean velocity.

In this study, a different approach was chosen to reduce inter-individual variation. Instead of submitting the raw data of the various variables to the regression analyses, the differences to the individual means measured within the investigated range of velocities were used. For almost all examined parameters a limited spread of the data points around the regression line was observed. In general, the r2 values were comparable to or higher than previously published values (McLaughlin et al. 1996; Khumsap et al. 2001a, 2002), which might be explained by the procedure of ‘mean-normalisation’ or by the greater number of observations and the finer spacing between speed increments.

Changes of gait parameters as function of speed

The larger part of the velocity-dependent changes observed in the absolute time parameters can be explained by the dependency of those parameters on SD (e.g. for StDabs, approximately 65%); i.e. the main influence of the velocity changes are dictated by the changes in stride cadence. However, looking at the SD-normalised time data, all time parameters except contralateral step duration, StpDdiag and StpDlat still showed a residual direct speed-dependency. This was more prominent at walk than at trot and more evident for the forelimb parameters than for the hindlimb parameters.

As expected from the momentum theorem, IzSD decreased in exactly the same proportion as SD with increasing velocity (Figs 2 and 3). And although Iz in fore- and hindlimbs decreased at faster velocities, Fzmean and Fzpeak increased because of the disproportional shortening of the StD. As described for the compensatory mechanisms of weightbearing lameness (Weishaupt et al. 2004, 2006b) or the changes in movement pattern due to rider interaction (Weishaupt et al. 2006a, 2009), StD plays the decisive tuning factor in regulating how high peak forces raise for a given impulse.

At the trot, SL is composed by the distances covered during the diagonal stance phases and the airborne phases (SpD) of both half-cycles. With increasing speed, StL increased and SpD extended. Interestingly, SpD approached a plateau at the fastest trotting velocities (Fig 3). To achieve an airborne phase, an extra impulse equal in amount to bwt ×g× SpD (where ‘g’ is the gravitational acceleration) has to be generated by the diagonal limb pairs. The maximal duration of the flight phase depends on the achievable muscular power and how fast the force is transmitted to the ground, thus on the muscular fibre type composition. Whether the muscle power itself is the decisive factor limiting SpD or the speed of force generation, which also depends on the limits of shortening StD, is difficult to decide. However, the regression function of StDrel indicated clearly that fore- and hindlimb contact times approaches a minimum at higher velocities (Fig 3). This is not surprising as with increasing velocity, limb impulses decreased and therefore StD had to shorten over-proportionally to maintain the required force rates. Interestingly, the synchronicity of the ground contacts of the diagonal limbs increased as well at higher velocities, which may be part of the strategy to optimise the maximal flight time.

Velocity is the product of stride rate (SR) and SL. In the present study SR and SL changed in a linear fashion with velocity. At walk, faster velocities were achieved by increasing SR and SL almost proportionally (44 and 56%). At trot, SL was clearly the main variable, contributing 74% to the increase in velocity. In the over ground situation, SL was the primary contributor to changes in speed at walk (Clayton 1995). The ratio between SR and SL at a given speed and consequently the entire gait pattern of the horse is very sensitive to external factors such as ground surface properties, handler and rider interaction or agitating stimuli. Individual factors such as the horse's conformation, the level of schooling and suppleness or its mental state at the moment of assessment primarily affect SR.

Difference between treadmill and over ground situation

This study presents for the first time a comprehensive description of velocity-dependent changes and functional relationship between GRF and time parameters of fore- and hindlimbs. The study was conducted on a treadmill, taking advantage of the possibility of precisely determining and varying velocity in fine increments within an extended range of walking and trotting speeds adapted to Warmblood sport horses. Together with the data normalisation concept, this resulted in reliable regression equations of which the majority had r2 of >0.85.

In principle, the velocity-related tendencies of time (SD, StDrel, TAP, TAC, SpD), force (Iz, Fzpeak, Fzdip, Izfore) and spatial (SL, OR) variables found in different over ground studies (Clayton 1994, 1995; McLaughlin et al. 1996; Khumsap et al. 2001a, 2002; Dutto et al. 2004) were also observed on the treadmill. However, taking a closer look at the detailed regression functions, differences were noted and reflected in varying orders of polynomial regression. Most notably, the hindlimb peak force variables behaved differently in the over ground and the treadmill situations. In contrast to the over ground situation where hindlimb FzP2 at walk (Khumsap et al. 2001a) and Fzpeak at trot (Dutto et al. 2004) did not change significantly, peak force parameters showed speed-dependent increases on the treadmill (Figs 2 and 3).

Conclusion

The velocity-dependency of time, force and spatial parameters measured on an instrumented treadmill is very close to the functional relationship reported for the over ground situation. It has to be emphasised that the reported functional relationships are only valid for the reported range of velocities and for horses of similar conformation, gait capacity and training level. Leach and Drevemo (1991) showed in trotters that the functional relationship may differ depending on the span of velocities and type of horses. And even though an individual's gait pattern can be as characteristic as a fingerprint, specific training was able to change basic gait parameters such as StD (Back et al. 1995). This set of reference values with the respective regression equations might be useful for adjusting speed differences where standardisation of movement velocity is not feasible despite the use of the treadmill.

Acknowledgements

The authors wish to thank the horse owners and particularly the Swiss National Equestrian Centre, Berne, for kindly leaving their horses at the study's disposal, as well as the various assistants of the Equine Performance Centre for technical assistance.

Conflicts of interest

The authors have declared no potential conflicts.

Manufacturers’ addresses

1 Kagra AG, Fahrwangen, Switzerland.

2 University of Zurich, Zurich, Switzerland.

3 Microsoft, Redmond, Washington, USA.

Ancillary