Why trot when you can walk? An Investigation of the Walk-Trot Transition in the Horse
A Thesis
Presented to the
Faculty of
California State Polytechnic University, Pomona
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
In
Biological Sciences
By
Devin A. J. Johnsen
2003 SIGNATURE PAGE
THESIS: Why trot when you can walk? An investigation of the Walk-Trot Transition in the Horse
AUTHOR: Devin A. J. Johnsen
DATE SUBMITTED: ______
Department of Biological Sciences
Dr. Donald F. Hoyt ______Thesis Committee Chair Biological Sciences
Dr. Steven J. Wickler ______Animal & Veterinary Sciences
Dr. Edward A. Cogger ______Animal & Veterinary Sciences
Dr. Sepehr Eskandari ______Biological Sciences
ii Abstract
Parameters ranging from energetics to kinematics, from muscle function to ground reaction force, have been theorized as triggers for a variety of terrestrial gait transitions. The walk-trot transition represents a change between gaits governed by very different mechanics, as the walk is modeled by the inverted pendulum, while the trot is modeled by the spring-mass model. A set of five criteria was established in order to determine a parameter as a trigger of the walk-trot transition in the horse. In addition, these mechanical models can provide specific predictions about the change in leg length during the stride. Six horses walked and trotted over a range of speeds on a high-speed treadmill. Stride parameters were measured using accelerometers, while sonomicrometry and electromyography measured muscle function of the vastus lateralis.
Kinematics of the coxofemoral, femorotibial, tarsal, and metatarsophalangeal joints as well as leg length were determined using a high-speed (125 Hz) camera. Leg length at the walk was not constant, as predicted by the inverted pendulum model. While leg length at the trot did not “land short, take off long,” it did conform to the other predictions based on the spring-mass model. Of the parameters studied, only a limited number of kinematic variables, including peak angular acceleration and velocity at the tarsal joint were found to be possible triggers of the walk-trot transition. It could not be determined if these 19 variables conformed to all five transitional trigger criteria because of the limitations of this study. The increased peak angular acceleration and velocity at the tarsal joint at the walk compared to the trot suggests the tibialis anterior m. could be a trigger of the walk-trot transition, while the increased ranges of motion at the coxofemoral joint point to a possible change in the activity of this joint’s extensor muscles as the trigger.
iii Acknowledgements
I would like to thank the academy … no that’s not it … wrong acknowledgements.
I would like to thank my major professor, Don Hoyt, for all of his help and support in the writing of this thesis and my understanding of locomotion in general and for being a mentor to me. A special thanks to Gwenn Catterfeld for graphics and graphical support as well as providing a sense of direction and organization for gigantic mess of the first draft of my discussion, Jen Trilk for support, being an editing guru, and helping me through the next week cause I know I’m going to go nuts. I would like to thank Wick for his comments, help and sense of humor, Sep for his presence on my committee even though locomotion is just a wee bit removed from his field of interest, Darren for help in sorting out some of my data because he is a “real” biomechanist, Holly Greene for her help with stuff, Dr. Cogger for assistance with my stats. A gigantic thanks Debbie Mead and Shannon Garcia for training the horses, to everyone who collected my muscle function data before I was even a student in the lab, to Tim Griffin for suggesting the project that would eventually become mine, to Jessica, Brian, Shannon, Debbie and Eric for their help in the collecting of the kinematic and incline and walk-trot transition data, to my family for their support, to the ERC late night and weekend crew for sanity and camaraderie. And finally and most especially, thank you Katie, thank you for your love and support and for coping with a long distance relationship so I could finish this illustrious thesis.
iv Table of Contents SIGNATURE PAGE ...... ii Abstract ...... iii Acknowledgements ...... iv Table of Contents ...... 1 Introduction...... 2 Materials and Methods ...... 7 Muscle Function ...... 7 Kinematics...... 13 Incline & W-T Transition Speed...... 17 Results ...... 19 Stride Parameters...... 19 Muscle Function Parameters...... 21 Kinematics...... 23 Incline & W-T Transition Speed...... 28 Discussion ...... 29 Muscle Function ...... 29 Kinematics...... 30 Stride Parameters...... 36 Conclusion...... 38 Appendix A ...... 40 Calculation of the Coxofemoral Joint...... 40 Calculation of the Femorotibial Joint ...... 40 References ...... 42 Figures ...... Error! Bookmark not defined.
Introduction
A central question in the study of locomotion is what triggers an animal to switch from one gait to another. Gait transitions have been investigated for a variety of forms of locomotion, including terrestrial (Farley and Ko, 1997; Hreljac, 1995; Blickhan et al.,
1993; Hoyt and Taylor, 1981), flying (Hedrick et al., 2002; Brown, 1953), aquatic
(Korsmeyer et al., 2002; Merz and Edwards, 1998; Drucker and Jensen, 1996), and brachiation (Bertram et al., 1999). For terrestrial locomotion in particular, hypothetical triggers include peak ankle angular velocity (Hreljac, 1995), critical angle between the thighs (Minetti et al., 1994), energetics (Hoyt and Taylor, 1981; Mercier et al., 1994), rating of perceived exertion (Borg et al., 1973; Noble et al., 1973), the peak vertical ground reaction force (Farley and Taylor, 1991), bone strain (Biewener and Taylor,
1986), muscle activation of stance- or swing-associated muscles (Prilutsky and Gregor,
2001), mathematical instability (Schoner et al., 1990), and the inverted pendulum model
(Kram et al., 1997). Many of these investigators have come to different conclusions on transitional triggers even with similar results because of different methods in determining gait transition speeds (Kram et al., 1997).
Due to its value in racing and other sports, the horse has primarily been studied at higher speeds (trotting, galloping) as well as the trot-gallop transition. It has been suggested that the trot-gallop transition occurs more abruptly than the walk-trot transition, making it more straightforward to study, however, there are conflicting views
(c.f. Vilensky et al., 1991; Wetzel et al., 1976; Aflet et al., 1983). While there are some data on the walk (e.g., Clayton et al., 2001; Hodson et al., 2001), there is little information on the walk-trot transition in the horse and other quadrupeds.
2 Not all of the potential triggers of terrestrial gaits listed above are valid for all transitions. For example, rating of perceived exertion is a subjective measurement provided by the individual subjects. While this can be considered a valid variable in humans, there is not yet a working system for a non-human subject, such as the horse, that can provide the researchers with this type of subjective input. It is also unlikely that forces are a trigger for the walk-trot transition as they are hypothesized to be for the trot- gallop transition (c.f. Farley and Taylor, 1991; Wickler et al., 2003), because bouncing gaits such as trotting and running are associated with higher forces than those found in walking (Cavanga et al., 1977; Hreljac, 1993a). Similar to forces, bone strain increases across the walk-trot transition in horses and dogs (Rubin and Lanyon, 1982), although it decreases across the trot-gallop transition in dogs, horses, and goats (Biewener and
Taylor, 1986).
Gait transitions have long been tied to energetics (Margaria 1938; Hoyt and
Taylor, 1981; Mercier et al., 1994; Wickler et al., 2003) though more recent investigations in horses (Farley and Taylor, 1991) and humans (Hreljac, 1993b; Noble et al., 1973) have provided conflicting evidence. Griffin et al. (2000) showed that horses do change from a walk to trot at the energetically optimal transition speed, but many investigators have wondered if the body possibly senses oxygen consumption over the short amounts of time in which transitions are made (Thorstensson and Roberthson,
1987; Farley and Taylor, 1991). Griffin et al. (2000) also found that the walk-trot transition occurred at nearly the same Froude number (0.34) for the horses studied, which were composed of breeds over an 8-fold range of mass, and 2-fold range of leg length. This Froude number is lower than the 0.5 associated with the walk-run transition in humans and bipedal birds (Kram et al., 1997; Diedrich and Warren, 1995) and the walk-hop transition of crows (Hayes and Alexander. 1983), but is within the range found 3 for the gait transition in brachiating white-handed gibbons (Chang et al., 2000), and the walk-trot transition in dogs and sheep (Jayes and Alexander, 1978). While the Froude number provides a biomechanical correlation of gait transition, there is not yet a good explanation as to how it could be sensed by the body. Thus, there are likely a variety of muscloskeletal factors that accompany changes in Froude number, which can be sensed by the body.
The limb musculature is thought to behave differently at the walk and trot, based on the mechanical models. It is believed that, in order to maintain the mechanics of an inverted pendulum, the muscles of the limb acts to maintain the leg as a stiff strut, while at the trot the spring-mass model dictates that the muscles will behave as active springs, storing energy while actively lengthening and dispersing this energy as it shortens
(Taylor, 1985). Changes in muscle function have been implicated as a trigger of gait transition in humans (Prilutsky and Gregor, 2001; Hreljac, 2001) and has been observed across the trot-gallop transition in the horse (Taylor, 1985). Various kinematic variables have been determined to be triggers of the walk-run in humans (Minetti et al., 1994;
Hreljac 1995).
Although criteria for a trigger of a gait transition vary between investigators, the most extensive and specific set of criteria was formulated by Hreljac (1995). These four criteria were: 1) the variable must change abruptly with gait -- if it was increasing during the walk, it must decrease when gait shifts to a run, or vice versa; 2) after switching from a walk to a run, the variable must be within values seen during slower speed walking; 3) the variable must be able to be sensed by the body; 4) the variable must elicit a change in gait, even if the condition is changed.
This fourth criterion (condition), which includes incline (e.g., Minetti et al., 1994;
Hreljac, 1995; Wickler et al., 2000) and load (e.g., Farley and Taylor, 1991; Kram et al., 4 1997), has often been used to determine a trigger's validity. It has been theorized that a trigger will occur at the same value regardless of condition although usually at a different speed. The walk-run transition in humans and the trot-gallop transition in horses are affected by condition with transition speed decreasing on the incline (Minetti et al., 1994;
Wickler et al., 2002) and with load (Farley and Taylor, 1991; Kram et al. 1997). The speed of the human walk-run transition increased on decline (Minetti et al., 1994). The walk-trot transition in the horse is thought to be unaffected by load (Hoyt, pers. comm.) but no data on the effect of incline have been published.
One criticism of Hreljac's (1995) criteria is that they do not take into account the decelerating transition, i.e. the run-walk as well as the walk-run transition. Until recently, this was very common as most investigators focused on the accelerating, e.g. the walk- run, transition but not the decelerating, e.g. run-walk, transition. Prilutsky and Gregor
(2001) relied heavily on the differences between the ascending and descending gait transitions in their model of an ideal gait transition trigger. Their model assumed that the run-walk transition occurred at a slower speed than the walk-run transition (also observed by Thorestesson and Roberthson, 1987; Dendrich and Warren, 1995). It also predicted that a run-walk trigger would be larger in the run than the walk at walking speeds below the transition speed, while a walk-run trigger would be larger in walk than the run at running speeds above the transition speed. These triggers took place when a threshold-level difference between the values of the variable at each gait was reached.
Hreljac's (1995) criteria and Prilutsky and Gregor's (2001) model are not necessarily mutually exclusive. Each has strengths and drawbacks, but also represent the development of our perceptions. For the determinant of a transitional trigger in this study, a combination of these two ideas of gait transition will be used in the horse for the walk-trot (w-t) transition and is outlined as follows: 1) the variable should change with 5 speed; 2) at the transition the variable should show an abrupt change with gait, and the variable should be larger in the "faster" gait (e.g. trot) than the "slower" gait (e.g. walk) in the decelerating transition, and vice versa, 3) after transition, the variable should return to levels seen in the previous gait, 4) the variable should be able to be sensed by the body, and 5) the threshold at which a transition occurs should remain constant, independent of condition. This model also assumes the decelerating transition occurs at a slower speed than the accelerating transition.
The walk and the trot are described by two different mechanical models, the inverted pendulum (Alexander, 1977) and the spring-mass model (McMahon and Cheng,
1990; Farley et al., 1993), respectively. The spring-mass model describes a running subject as a point of mass supported by a single mass-less leg acting as a spring
(Blickhan, 1989; McMahon and Cheng, 1990; Farley et al., 1993). This spring is most compressed at midstance, and least compressed when the foot touches and lifts off the ground. It also predicts that the leg will "land short, take off long" (Iverson and McMahon,
1992), that is that maximum at liftoff is longer than the maximum at contact. This hypothesis, however, has been disproved in the horse at higher trotting speeds (Hoyt et al., 2002). We can therefore predict that leg length will have one minimum (50% of stance) and two maxima (0% and 100% of stance) with the maximum at liftoff being longer than that at contact. The inverted pendulum model describes the subject as a point of mass vaulting over by a single stiff leg (Alexander, 1977) and predicts that the length of the leg will remain constant throughout stance phase.
During low-speed trotting, including speeds near the walk-trot transition speed, peak vertical ground reaction force and duty factor in the hind limb show a different trend than at higher trotting speeds (Catterfeld et al., 2002). These kinetic changes could affect how joints function. Linkages between the tarsal and femorotibial joint have been 6 identified in many quadrupeds including, cats, dogs (Gregerson et al., 1998) and horses
(Back et al., 1996b). In horses, a mechanical basis for this linkage has been identified
(Back et al., 1995b). Due to the changes in peak vertical ground reaction force and duty factor, the linkage between the tarsal and femorotibial joints could be adversely affected by low-speed trotting.
The purpose of this study was to determine if any of the parameters measured
(stride, muscle and kinematic) are triggers of the walk-trot transition in the horse. In addition, we tested if the walk and trot at transition speeds conform to certain leg length parameters that are predicted by the inverted pendulum and the spring-mass models.
This was also the first study to determine if the walk-trot transition speed is affected by incline.
Materials and Methods
Muscle Function
Horses
Three horses (additional characteristics are listed in Table 1) were obtained from the Arabian Horse Center of California State Polytechnic University, Pomona or private owners. The University Animal Care and Use Committee approved the use of the animals in this research. For at least three months prior to this study, the horses were physically conditioned on a high-speed treadmill (Säto I; Säto AB, Knivsta, Sweden).
Each exercise session lasted 30 minutes and occurred 5 times a week. The training regime was designed for a study that was performed concurrently with the present study.
The horses were conditioned to trot and gallop on both level and 10% incline conditions, 7 as well as trained to extend these gaits, e.g., trot at speeds above the speed that they would normally trot at 100% of the time.
Table 1: Characteristics of the horses in 2000 used in the muscle function and stride parameter study. Averages are given plus or minus standard deviation. Arab = Arabian.
Horse Sex Age in 2000 (years) Breed Weight (kg) Gentle Touch Female 4 Arab 408 Red Gelding 8 Arab 437 Reign Female 5 Arab 448 Average -- 5.7 ± 2 -- 431 ± 21
Surgery and Implantation
On the morning of the surgery, the horse was initially tranquilized with xylazine
(xylazine HCl, Fermenta Animal Health Co., Kansas City, MO; 0.2-1mg/kg) intravenously and a catheter was placed aseptically. At the beginning of surgery, the horse was sedated intravenously with butorphanol (butorphanol tartrate, Fort Dodge Animal Health,
Fort Dodge; IA0.025-0.1mg/kg) and detomidine hydrochloride (detomidine hydrochloride,
Pffiezer Animal Health, Exton, PA; 10-20 µg/kg). This anesthesia was administered as needed throughout the surgery to maintain sedation. The location of the vastus lateralis was determined by palpation of the lateral condyles of the femur, the cranial and caudal aspects of the greater trochanter and the 3rd trochanter. A 7.5 cm incision was made in
the right hind limb over the vastus lateralis. Lidocaine (lidocaine hydrochloride, Pro Labs
Ltd., St. Joseph, MO) administered subcutaneously was used as a local anesthetic. After
the removal of subcutaneous fat, two stab incisions were made in the fascia
approximately 10-15 mm apart. One pair of omnidirectional, spherical, piezoelectric
sonomicrometry crystals (Sonometrics Corporation, London, Ontario, Canada) was
implanted. Including epoxy, the diameter of the crystals was 2 mm. The crystals were
8 positioned 10-15 mm apart, 2 cm deep, and parallel to the long axis of the muscle fibers using a polyethylene introducer. A 0-silk suture was used to anchor the crystals to the muscle, with an additional suture for a 5 cm loop of wire acting as tension relief. EMG wires (Carrier, 1996b) were inserted into the muscle parallel to and 1 cm away from the sonomicrometry crystals. The absence of a second silastic patch to anchor the EMG wire to the fascia represented the only deviation from Carrier’s method. This change was thought to eliminate muscle tearing caused by two fixed anchors. A ground wire was implanted subcutaneously into the dorsal aspect of the horse’s sacral region (Biewener et al., 1998b). The incision was closed loosely with 2-0 silk. Flunixin meglumine
(Schering-Plough Animal Health Corp., Union, NJ; 20-40 mcg/kg) was administered post-surgically to reduce inflammation.
Data Collection
Horses were given a minimum of 90 minutes to recover after surgery. A lameness exam was performed to determine if any lasting effects of the surgery were present. Heart rate was monitored (Polar Vantage XL, Polar CIC Inc., Port Washington,
New York, USA) and compared to pre-surgical values to give an objective measurement of whether the horse had fully recovered from surgery. Once the horse had fully recovered from surgery, it was placed on the treadmill. A surcingle was positioned on the thorax in order to hold data cables secure. Once on the treadmill, the horse under went a brief warm-up, walk (1.7 m/s) for three minutes followed by a five-minute trot (3.0 m/s).
Horses performed ten trials: walking at five speeds (1.2, 1.4, 1.6, 1.8, and 1.9 m/s), and trotting at five speeds (1.8, 1.9, 2.0, 2.2, and 2.5 m/s). Each condition was maintained for approximately 30 seconds, prior to 15 seconds of data collection, and the order of gait and speed were randomized. All trials for one horse were completed in one day but
9 completed in an alternating fashion with the concurrent trot-gallop study. After the last trial, the horse was again sedated in order to remove the sonomicrometer crystals and
EMG wires. Phenylbutazone (one gram, BID, for three days) was given post-surgically to reduce pain and inflammation. Horses were hand walked for a week and then sutures were removed.
Data Acquisition
A biaxial accelerometer (±50×g, CXL25M2, Crossbow Technology, Incorporated,
San Jose, California) was taped to the lateral aspect of the right hind hoof.
Accelerometer data were collected at 3704 Hz with an analog to digital card (PCI 1200,
National Instruments, Austin, Texas) using a data acquisition Virtual Instrument (VI) created with LabVIEW® (LabVIEW®, National Instruments, Austin, Texas) software on a
PC (Microsoft Windows, 1995). Contact (when the hoof first impacted the tread) and liftoff (when the hoof left the tread) were recorded using the x-axis of the accelerometer signal (Figure 1). These data were used to subdivide the sonomicrometry and EMG records. The exact location of liftoff within the accelerometer records was determined in a separate study using a force plate.
Sonomicrometer measurements were made with Sonometrics Corporation hardware on a PC (Microsoft Windows, 95). The sonomicrometry crystals were sampled at 231.5 Hz, converted to analog signal and output to the data acquisition VI, which sampled at 3704 Hz. The conversion to this high rate of sampling was required because the sonomicrometry signals were sampled using the same program as the EMGs (which were sampled at 3704 Hz to assure a sufficiently high frequency for subsequent analysis). The speed of sound in vertebrate skeletal muscle was assumed to be 1540 m/s (Goldman and Richards, 1954; Hatta et al., 1988).
10 Each of the two EMG electrodes had 7 mm of bared wire and the two segments were separated by 1.5 cm. The EMG signal was amplified (1,000 to 10,000- depending on signal strength) and filtered (60 Hz notch and 100 to 1,000 Hz bandpass) with a
Grass model P511K preamplifier, and sampled at 3704 Hz by the A/D system.
Data Processing
Initial processing of accelerometer, sonomicrometry, and EMG records was accomplished using LabVIEW® VI’s designed by Dr. Edward Cogger (California
Polytechnic State University, Pomona). Ten consecutive strides of the accelerometer record were analyzed using the autodetect VI in order to mark contact and liftoff. When the autodetect VI failed to correctly place contact and liftoff the Manual Adjust VI was used for correct placement and thus divide the stride into stance and swing phases. The marked files were sent through the Points Processor VI to determine temporal parameters, including stride frequency and duty factor. The temporal parameters (mean
± SD for the ten strides) were exported to an Excel® database (Microsoft Corp.,
Redmond, Washington).
The sonomicrometer records were first processed with the Chopping VI, which decremented the sonomicrometer record from 3704 to 231.5 Hz by retaining every sixteenth point. The files were converted from volts to length (mm) using an empirically derived equation and smoothed using a third rank butterworth filter. For each horse a normalizing factor was determined from the data collected when the animal was standing square (which gives the resting length of muscle or Lo). Normalized muscle length (L/ Lo) was determined by taking L (the actual length of the muscle at any given point) and dividing by Lo for each point for the ten consecutive strides. Each stride was fit
to a 201-point waveform using a cubic spline interpolation of the normalized muscle
11 length data in order to temporally normalize the data. Each increment of the cubic spline interpolation corresponded to 0.5% of the stance phase. Taking the average of 10 waveforms yielded normalized muscle length vs. relative time for the stance phase.
Similar processing was performed for the strain rates: taking the difference between two consecutive non-normalized muscle lengths (∆L/Lo) and dividing by the non-normalized time interval between the two points (∆t) yielded a strain rate vs. time waveform. A cubic spline interpolation was then used to normalize for time. This manipulation gave 10 strain rate vs. percent stance phase waveforms, which were averaged to generate one strain rate vs. percent stance phase curve for each trial.
Normalized muscle lengths and strain rates were exported to Microsoft Excel® for further processing. For total positive and negative strains, the stance phase was divided into quartiles. Total positive strains for each quartile were calculated by summing all positive (shortening) length changes during that quartile. A similar calculation was performed for total negative strains using negative length changes. Total positive and negative strains were divided into quartiles. The first two quartiles represent the approximate time when the muscle was active. The beginning of stance was used as a starting point because the femorotibial joint exhibits an extensor moment during this time
(Clayton et al., 2001) and 45% of stance was 45 ms (assumed to be the relaxation time of the muscle) after the average cessation of muscle activity. One horse had multiple bursts of EMG activity within stance. In order to compute the average cessation of muscle activity for this horse, the middle burst in a walk (which best corresponded to what was seen in the other animals) and the average of the two bursts for trot was used.
The EMG_man VI was used to process the EMGs. Records were corrected for the amplification used during the trial using a calibration pulse produced by the Grass amplifier. EMGs were smoothed with a 3rd or 4th order elliptic filter, and divided into 12 stance and swing phases using the accelerometer records. Onset and offset of EMG activity for each stride were determined manually. The average integrated EMG (iEMG) was calculated by taking the average area under the positive rectified EMG curve for ten consecutive strides. In addition, the total duration of the EMG signal, the duration of the
EMG as percent of stance and the duration of the EMG as a percent of stride were determined for ten consecutive strides.
Statistical Analysis
Coefficients of variation were used to assess the variation in the normalized muscle lengths, within trial, and between and within horses. A repeated measures analysis of variance, with horse as the repeated measure, was run on all stride parameters, sonomicrometry, and EMG data during transition speeds (1.8 and 1.9 m/s) and total positive and negative strains at the trot and walk using the SuperANOVA software (Abacus Concepts Inc., Berkley, CA) with the significance set at p < 0.05. Gait and speed were the two variables tested for stride parameters, strain rate, and EMG data. For positive and negative strain during transition speeds three variables were tested: gait, speed, and quartile. Speed and quartile were the two variables tested for total positive and negative strains during each gait. Standard errors were reported in all graphs and tables displaying average values for all horses.
Kinematics
Horses
A separate study investigated the kinematics of the walk-trot transition. Five horses were used in this aspect of the study (additional characteristics are listed in table
13 2), three of which were horses from the muscle function study. All horses had been conditioned for work on the treadmill in a manner similar to that described for the muscle function study except that there was no training for gait extension.
Table 2: Characteristics of the horses in 2002 used in the kinematic study. Averages are given plus or minus standard error. TB = Thoroughbred, Arab = Arabian.
Horse Sex Age in 2002 (yrs) Breed Weight (kg) Anakin Gelding 6 TB 506 Henry Gelding 8 Arab 397 Gentle Touch Female 6 Arab 443 Red Gelding 10 Arab 459 Reign Female 7 Arab 481 Average -- 7.4 ± 1 -- 457 ± 18
Data Collection
Nine reflective markers were positioned on the horse: 1) tuber coxae, 2) center of rotation (CoR) of the coxofemoral joint, 3) CoR of the femorotibial joint, 4) shaft of the tibia, 5) CoR of the tarsal joint, 6) CoR of the metatarsophalangeal joint, 7) coronary band, 8) anterior distal hoof wall, and 9) posterior distal hoof wall. Most points were in standard palpable locations (Hodson et al., 2001) with the exception of #4, 8 and 9. The anterior (6) and posterior distal hoof (7) wall markers were placed at a 54º angle relative to the marker on the coronary band.
The coxofemoral and femorotibial joints, however, undergo a fair amount of skin displacement during locomotion (van Weeren et al., 1990; van Weeren et al., 1992; Back et al., 1995a; Back et al., 1995b). That is, the skin lateral to the joint (where the reflective markers were placed) moves less than the joint itself (Back et al., 1995a; Back et al.,
1995b). In order to account for this displacement, the positions of the coxofemoral and femorotibial joints were calculated from known morphological distances and the 14 locations of the tuber coxae and two markers on the tibia. It was assumed that during locomotion the lengths of the segments that comprise these joints remain constant and that these anatomical positions undergo little skin displacement. The position of the femorotibial joint was calculated by rotating the segment from the femorotibial point (3) to the CoR of the tarsal joint (5) inline with the imaginary line running through the CoR of the tarsal joint (5) and the shaft of the tibia (4) using polar coordinates. This calculation was achieved such that the distance between the CoR of the tarsal joint (5) and the femorotibial joint remained the same length as determined when the horse was standing square. The position of the coxofemoral joint was calculated by determining the intersection of two circles whose centers are the tuber coxae (1) and the calculated femorotibial point (3a). The radii of these circles are the distance from the tuber coxae
(1) to the CoR of the coxofemoral joint (2) and the distance from the CoR of the femorotibial joint (3) to the CoR of the tarsal joint (5) while the horse was standing square (Figure 2). The two points of intersection of these two circles were determined, and the caudal point was taken to be the coxofemoral joint. The equations used in the calculation of these joints can be found in Appendix 1. Figure 3 shows the location of all points used in the kinematic analysis.
Once on the treadmill, the horse under went a brief warm-up, walk (1.7 m/s) for three minutes, followed by a three-minute trot (2.5 m/s). Horses walked on the treadmill at 1.6-1.9 m/s, and trotted at 1.7-2.0 m/s, at 0.1 m/s intervals. Each trial was maintained for one minute, and once all combinations were completed the horse walked a three minute 1.7 m/s cool-down. Order of speed and gait were randomized, except if two gaits were performed at one speed they were performed sequentially. This assured that the treadmill speed was exactly the same for both gaits
15 Data Analysis
Five consecutive strides were captured and digitized using the Motus® software
(Peak Performance Technologies, Englewood, CO) for each horse at each trial. A complete stride was defined as starting at the moment when the hoof first contacted the tread surface and ending with the same hoof making a second contact. Stance phase is a subset of a complete stride and begins with the first contact of the hoof to the treadmill and ends with liftoff. Liftoff occurred when the toe had lifted off the tread. All contacts and liftoffs were determined visually with the aid of the posterior lateral hoof wall marker.
Two-dimensional angles were calculated for four joints: coxofemoral (CF), femorotibial (FT), tarsal, and metatarsophalangeal (MP). All angles were defined so the value decreased when the joint was flexed (Figure 4). The angular data were smoothed using a cubic spline filter and normalized for time using a cubic spline fit. Angular velocities (ωt) and angular accelerations (αt) were also calculated for the tarsal joint.
The angular values for the five joints, as well as tarsal angular velocities and
accelerations, were exported from Motus® software to Microsoft Excel®. The liftoff data
were used to divide the stride into stance and swing phases. Only values during stance
phase were analyzed because it is only during this time when the muscles are
generating force to support the animal’s mass.
Joint angles were determined at initial contact and endstance. In addition, the
maximum extension and/or flexion during stance and the timing of maximum extension
and/or flexion as a percent of stance were also determined for each joint based on the
time-angle diagrams for each joint. Ranges of motion (ROM) were determined from
contact to maximum extension/flexion and from this time to endstance, e.g. range of
motion from contact to maximum extension (ROMc-me) and range of motion from
16 maximum extension to endstance (ROMme-e) for the coxofemoral joint. Leg length was calculated by determining the distance from the anterior hoof marker to the midpoint between the tuber coxae and coxofemoral points. The maximum length during the first
25% of stance, the last 25% of stance, and the minimum leg length during the middle
50% of stance were calculated. These time frames were used because of the multiple points of interest and the specific times predicted by the spring-mass model.
Statistical Analysis
Angles, ROMs, maximum flexion and extension, the time of maximum flexion and extension as a percent of stance, peak tarsal angular velocity, and peak tarsal angular acceleration at transition speeds were analyzed with a two within factor repeated measures analysis of variance using the SuperANOVA software. Kinematic transition speeds were defined as speeds with walking and trotting trials, 1.7, 1.8 and 1.9 m/s. The repeated measures were the horses and the two within factors were gait and speed. A 1- tailed t-test was used to determine if the maximum and minimum leg lengths occurred at the predicted time. Comparisons between maximum and minimum leg length during the trot were also tested using a repeated measures ANOVA. A regression analysis was used to determine if leg length remained constant during the walk. A standard alpha probability of 0.05 was used for statistical significance of all tests.
Incline & W-T Transition Speed
Horses
Four Arabians and two Hackneys (additional characteristics can be found in
Table 3) were used in this study. Two of these horses (GT and Reign) were also used in
17 the muscle function and kinematic studies, and one horse (Henry) was also used in the kinematic study. All horses were housed in and acclimated to work on the treadmill in a manner similar to that of the muscle function study. No special training was required of these horses.
Table 3: Characteristics of the horses in 2002/2003 used in the incline and transition speed study. Averages are given plus or minus standard error. Arab = Arabian, Hkny = Hackney. Horses measured in 2003 are marked by an *.
Horse Sex Age (yrs) Breed Weight (kg) Henry Gelding 8 Arab 397 Donald Gelding 13 Hkny 455 Gentle Touch Female 6 Arab 481 Reign* Female 8 Arab 482 Charlie* Female 7 Arab 425 Nick* Gelding 21 Hkny 447 Average -- 11 ± 3 -- 439 ± 19
Data Collection
Horses were warmed up with three minutes walk at 1.5 m/s on the flat, followed by a trot for three minutes at 2.5 m/s on flat, and finally a walk for three minutes at 1.5 m/s on the incline. Walk-trot transition speed was determined by beginning with a 1.6 m/s walk and incrementally increasing the speed 0.1 m/s every 60 seconds and noting at what speeds the transitions occurred. Trot-walk transition speeds were ascertained in a similar manner but began with a trot at 2.2 m/s with speed decreased incrementally.
Most horses have a range of speeds between the speed where they will walk 100% of the time and trot 100% of the time. If a horse exhibited this behavior, the average of these two speeds was used as the walk-trot or trot-walk transition. The order of condition
(incline vs. flat) and which transition (walk-trot vs. trot-walk) was randomized. The overall
18 transition speed for each condition was the average of the walk-trot and trot-walk transition speeds.
Statistics
The average of the two transition speeds was taken for each condition. These averages were compared with a 1 factor repeated measures ANOVA using the
SuperANOVA software with the significance set at p < 0.05. Condition was the only variable tested.
Results
Stride Parameters
Stride Parameters at 1.8 and 1.9 m/s
All stride parameters, except the duration of swing phase (Figure 4), showed a change with gait at 1.8 and 1.9 m/s. Stride period decreased 25% (P=0.0130) and duration of stance phase decreased 35%(P=0.0113) when changing from a walk to a trot
(Figures 5 and 6). Duty factor also was 12% smaller (P=0.0337) at the trot compared to the walk (Figure 7). Step length (35%, P=0.0115) and stride length (25%, P=0.0132) both decreased as a function of gait (Figures 8 and 9). Only the rate of force application
(P=0.0126) and stride frequency (P= 0.0131) were higher at the trot than the walk, 53% and 34%, respectively (Figure 10 and 11). Most stride parameters also changed with speed at 1.8 and 1.9 m/s, with exceptions being duration of swing phase, step length, and stride frequency. Stride period (P=0.0466, Figure 5), stance (P=0.047, Figure 6),
and duty factor (P=0.0207, Figure 7) decreased with speed, while stride length
19 (P=0.0367, Figure 9) and rate of force application (P=0.0171, Figure 10) increased with speed. It is important to note that only stride period, stance phase, and swing phase were calculated directly from the accelerometers. The other stride parameters were calculated from one or more these three variables.
Stride Parameters as a Function of Speed for Both Gaits
All stride parameters varied significantly with speed at both gaits; the only exceptions were the swing phase and step length while walking. The stride period
(Figure 5) shortened by 15% at the walk (R2=0.884; P<0.0001) and 7% (R2=0.563;
P=0.0013) at the trot. For the trot, swing phase decreased (R2=0.416; P=0.0094), but
appeared to level off between 2.0 and 2.5 m/s (Figure 4). The duration of stance phase
(Figure 6) decreased 21% over the range of both walking speeds (R2=0.867; P<0.0001)
and trotting speeds (R2=0.7761; P<0.0001). Duty factor (Figure 7) decreased 15% at the walk (R2=0.669; P=0.0002), and 7% at the trot, (R2=0.743; P<0.0001). Step length
(Figure 8) increased 10% with speed while trotting (R2=0.340; P=0.022). Stride length
(Figure 9) increased 21% during the walk (R2=0.566; P=0.012), while a slightly larger
increase, 30%, was seen during the trot, (R2=0.943; P<0.0001). The rate of force
application (Figure 10) increased 27% for both the walk (R2=0.834; P<0.0001) and the
trot (R2=0.792; P<0.0001). Stride frequency (Figure 11) increased 18% at the walk
(R2=0.867; P=0.0011) and 7% at the trot, (R2=0.570; P<0.0001).
20 Muscle Function Parameters
Normalized Muscle Length (NML)
Normalized muscle length did not vary a great deal between strides. The coefficient of variation for ten consecutive strides for a representative horse was 5.3% at a 1.4 m/s walk and 5.1% at a 2.5 trot (Figures 12 and 13). Between horses the coefficient of variation was 10.5% and 14.7% at these speeds (Figures 14 and 15). The coefficient of variation for each horse at all speeds and gaits remained similar, 8.0%,
9.5%, and 11.4%. At the walk, the overall coefficient of variation was 10.8%, while it was
13.7% at the trot (Figures 16 and 17). At transition speeds, the coefficient of variation was 13.1% (Figure 18). For all horses at all speeds and conditions, the coefficient of variation was 12.3%.
Muscle Function Parameters at 1.8 and 1.9 m/s
At 1.8 and 1.9 m/s, there was no effect of gait or speed on total positive or negative strain (Figures 19-20). Total positive strain (Figure 20) decreased 58% from the
1st to 4th quartiles (P=0.0261). A means comparison analysis showed the differences were between the 1st and 2nd (P=0.0109), 3rd (P=0.0082), and 4th quartiles (P=0.0207).
Strains for individual horse can be seen in Figure 21. Gait and speed (Figure 22) did not
influence average positive strain rate at 1.8 and 1.9 m/s, (P=0.1925, P=0.4578),
respectively. A closer inspection of the strain rate data, however, indicated that there
was a consistent change in positive strain rate between gaits for each horse (Figure 23).
There was likely a significant difference in positive strain rate (wilcoxon test, P=0.028),
but the small sample size of this study prevented it from being statistically significant with
a repeated measures ANOVA. A wilcoxon test was used to determine if the observed
21 difference was significant because no interaction between gait and speed was seen in the ANOVA (P=0.4578) and a great deal of variability was present in the data. None of the EMG parameters (Figures 24-26), onset, offset, iEMG, EMG duration, EMG duration as a percent of stance or EMG duration as a percent of stride were affected by gait or speed.
Muscle Function Parameters as a Function of Speed for Both Gaits
Total positive strain decreased on average 53% from 1st to 4th quartiles
(P=0.0203) at the walk, while total negative strain was not affected by quartile (Figure
20). A means comparison analysis showed differences in total positive strain between the 1st and 2nd (P=0.0040), 3rd (P=0.0277), and 4th quartiles (P=0.0197). Total positive
strain at the walk (Figures 19-20) was also affected by speed (P=0.0019). At the trot,
total positive and negative strain were affected by quartile (Figure 20), decreasing 80%
(P=0.0291) and increasing 88% (P=0.0273) respectively. A means comparison analysis
of the positive strain at the trot showed differences between the 1st and 2nd (P=0.0089),
3rd (P=0.0169), and 4th quartiles (P=0.0154). A means comparison analysis of the negative strain at the trot showed differences between the 2nd and 4th (P=0.0064) and the 3rd and 4th quartiles (P=0.0156). Average positive strain rate (Figure 22) increased
73% with speed when walking (R2=0.037; P=0.037) but did not change with speed when
trotting. The 73% increase in average positive strain rate at the walk (Figure 22)
occurred between 1.2 and 1.6 m/s and appeared to level off at speeds above 1.6 m/s.
Most EMG parameters (Figures 24-26) were not affected by speed at either gait.
The only exceptions were found for EMG duration, EMG duration as a percent of stance,
and EMG duration as a percent of stride. EMG duration (Figure 24) increased 35% as a
function of speed, (R2=0.194; P=0.028), and EMG duration (Figure 26) as a percent of
22 stride increased 45% with speed (R2=0.335; P=0.0024) over the range of walking
speeds. No difference was seen in these variables at the trot (Figure 24 and 26). EMG
duration as a percent of stance (Figure 26) increased significantly with speed during
both gaits, walk (R2=0.379; P=0.001) and trot (R2=0.236; P=0.035). The magnitude of
this increase was higher in the walk, 48%, than in the trot, 32%. There was a trend for
iEMG (Figure 25) to increase with speed at the walk (P=0.0020), especially at lower
speeds, but not in a linear fashion. A means comparison analysis showed differences
1.2 and 1.6 (P=0.0101), 1.8 (P=0.0012), and 1.9 m/s (P=0.0003), 1.4 and 1.8
(P=0.0162) and 1.9 m/s (P=0.0043).
Kinematics
Coxofemoral Joint
The coxofemoral joint (Figure 27A) underwent primarily extension during stance and flexion during swing. The peak extensions and flexions of the coxofemoral joint appear to be greater in the walk than the trot. All kinematic variables of interest (Table 4) changed as the gait switched from a walk to a trot, most notably decreased maximum extension (Figure 28C) and range of motion throughout stance (Figure 28E-F).
Femorotibial Joint
The femorotibial joint (Figure 29B) underwent flexion with a period of extension occurring at the end of stance in the walk and approximately three-quarters of stance in the trot. During the swing phase of both gaits, the femorotibial joint showed primarily flexion. Only angle of contact (Figure 29A), the timing of maximum flexion (Figure 29D) and ranges of motion (Figure 29E-F) showed changes from a walk to a trot at 1.7, 1.8,
23 1.9 m/s (Table 4). For maximum flexion at the femorotibial joint (Figure 29C), there was also a significant interaction between speed and gait (P=0.0277).
A linkage between the femorotibial and tarsal joints was observed in low speed trotting as well as high speed walking (Figure 30). In low speed trotting, the two angles had a linear relationship of (R2=0.90, P<0.0001) with a slope of 0.78. Fast walking shows
this link but to a lesser extent with a slope of 0.52 (R2=0.62, P=0.0120).
Tarsal Joint
The tarsal joint (Figure 27C) underwent flexion during early stance followed by extension throughout the remainder of stance. During swing, the tarsal joint first undergoes flexion then extension. The angle at contact (Figure 31A) decreased 1%
(P=0.0289) and maximum flexion (Figure 32A) decreased 3% (P=0.0023) when
switching from a walk to a trot at 1.7, 1.8, and 1.9 m/s. The remaining variables either
showed no change or an interaction between speed and gait. Angular acceleration
(Figure 33A) of the tarsal joint (αt) decreased 60% (P=0.0178), while angular velocity
(Figure 33B) of the tarsal joint (ωt) decreased 29% (P=0.0049) when switching from a
walk to a trot during 1.7, 1.8, and 1.9 m/s. No change in ωt or αt was seen at either gait as a function of speed (Figure 33A-B).
Metatarsophalangeal Joint
The metatarsophalangeal (MP) joint underwent extension and then flexion
(Figure 27D) during stance, with the walk showing two peaks of extension while the trot shows a single peak. This joint primarily undergoes extension during swing. At 1.7, 1.8 and 1.9 m/s maximum extension (Figure 34C) increased, while range of motion (Figure
34E-F) increased for the metatarsophalangeal joint (Table 4). The only kinematic
24 variable that showed a significant change with speed was range of motion from maximum extension to endstance at the MP joint (Figure 34F), which increased 40% when comparing a walk to a trot (R2=0.212; P=0.041).
Table 4: Changes in angles and ranges of motion when going from a walk to a trot at 1.7, 1.8, 1.9 m/s. Values are averages for five horses. Positive values indicate increased extension, angles occurring later in stance, or increased range of motions and negative values indicate decreased extension, angles occurring earlier in stance, or decreased range of motion. Cells left empty in table represent parameters not measured. Range of motion from maximum flexion to liftoff for the femorotibial joint was measured but was not significant and thus was not included in this table. Flex. = Flexion, Ex. = extension, % Stn = percent of stance, ROMc-me = Range of motion for contact to maximum extension, ROMme-e = Range of motion from maximum extension to endstance, * indicates a significant gait speed interaction. Results can be seen graphically in figures 28-33.
Parameter Coxofemoral Femorotibial Tarsal Metatarsophalangeal Contact -12% -3% -1% No change (P=0.0270) (P=0.0098) (P=0.0289)
Max Flex. () -- No change No change --
At % Stn -- 14% No -- (P=0.377) change*
Max Ex. () -13% -- -3% 5% (P=0.0114) (P=0.0023) (P=0.0101) At % Stn -25% -- No change No change (P=0.0010) Liftoff () -17% No change No change No change (P=0.0093) ROMc-mf -- 16% No -- (P=0.0423) change* ROMmf-e -- 141% -- -- (P=0.159)
25 ROMmf-me -- -- -18%* -- (P=0.0083)
ROMc-me -47% -- -- 48% (P=0.0131) (P=0.0028)
ROMme-e -265% -- No change 39% (P=0.0131) (P=0.0195)
Leg Length
During stance phase, leg length (Figure 35) followed a sinusoidal pattern during the trot. While, the leg length (Figure 35) at contact was found to be 1.5% greater than that at liftoff (P=0.0057), there was also an interaction between speed and phase of stride (P=0.0182). A means comparison analysis revealed the differences were only at
1.7 and 1.9 m/s. No difference was found between maximum leg length (Figure 35) during the first 25% and last 25% of stance (P=0.6959) at the trot. Average maximum leg length (the average of the maximum leg lengths during the first and last 25% of stance) was 8% greater than the minimum leg length during the middle 50% of stance
(P<0.0001). There was a tendency for these leg lengths to decrease with speed
(P=0.0421), as well as there was an interaction (Figure 37) between the three leg length variables and speed (P=0.0372).
Maximum leg length during the first 25% of stance (Figure 36) occurred at 1% of stance. This was found to be significantly different than the predicted value of 0% of stance (t-test, P=0.0016). Minimum leg length during the middle 50% of stance (Figure
36) occurred at 41% of stance, which was significantly less than the predicted value of
50% (t-test, P<0.0001). Maximum leg length during the last 25% of stance (Figure 36) occurred at 95% of stance, which was significantly less than the predicted value of 100%
26 (t-test, P=0.0003). None of these differences, however, likely represented a biologically significant difference
At the walk, leg length (Figure 35) decreased then leveled off and then increased during stance. Leg length appeared to remain relatively stable from 20 to 80% of stance
(Figure 35). A regression analysis showed leg length did vary as a percent of stance over the range of walking speed (P<0.0001). From 20 to 80% of stance leg length increased 2%. While this value appeared small, leg length only changed 7% from the maximum to minimum leg lengths during stance.
Table 5: This table shows which criteria (if any) each parameter studied conforms to. All variable could reasonably be hypothesized to be sensed by the body (4th criterion). The 5th criterion (threshold is independent of condition) was unable to be assessed by the current study. Variables that did not conform to any of the first three parameters were ommitted from this table. Kinematic parameters do not include leg length parameters. CF is the coxofemoral joint. FT is the femorotibial joint. T is the tarsal joint. MP is the metatarsaphalangeal joint. * denotes a change in the parameter with speed only at the walk.
Criteria 1st 2nd 3rd (change with speed) (abrupt change with (return to values seen gait) in previous gait) Stride Parameters Stride period X X Stance period X X Swing period X* Duty factor X X Rate of Force App. X X Stride Length X X X Step Length X* X Stride frequency X X
Muscle Parameters Tot. Pos. Strain X* Av. Pos. Strain Rate X* EMG duration X* EMG dur as %stn X EMG dur as %str X*
Kinematic Parameters 27 CF: all X FT:angle at contact X FT: timing max. flex X FT: ROMc-mf X FT: ROMmf-e X T:angle at contact X T: max. flexion; X T: αt; ωt X MP:max. extension X MP: ROMc-me X MP: ROMme-e X* X
Incline & W-T Transition Speed
Incline had no effect on the w-t transition speed (P=0.2062). The average w-t
transition speed was 1.98 m/s on the level and 1.94 m/s on the incline. All horses
exhibited a range of speeds over which neither gait was preferred for at least half of the
trials. Data for individual animals can be found in Table 5.
Table 5: Walk-trot transition speed data on the level and incline for all horses. Horses measured in 2003 are marked by an *.
Incline Level Difference Horse w-t t-w Average w-t t-w Average of Averages Henry 1.85-1.9 1.92 1.895 1.95-2 2-1.9 2.015 -0.120 Donald 1.9-2.0 1.95 1.950 2.05-2.15 2.05-2 2.075 -0.125 GT 1.71 1.8-1.6 1.705 1.7-1.9 1.57 1.685 0.020 Reign* 2.1 1.9 2.000 1.95-2.1 2.05-1.85 1.988 0.013 Charlie* 2.15-2.3 2.2 2.212 2.1-2.4 2.2-2.05 2.186 0.025 Nick* 1.8-2.0 2.05-1.65 1.875 1.75-2.15 2.1-1.75 1.937 0.063 Average -- -- 1.940 -- -- 1.981 -0.042
28 Discussion
Muscle Function
The vastus lateralis, a femorotibial joint extensor, actively shortened during the first 50% of stance (Figures 18, 24, and 26) when this joint was undergoing flexion
(Figure 27B). Thus its tendon probably was being stretched. While gait did not influence the function of the vastus lateralis (Figures 19, 20, and 24-26), the femorotibial joint showed increased ranges of motion (Figures 29E-F), suggesting that there was increased elastic storage at this joint in the trot. The lack of change in any aspect of vastus lateralis function with gait, however, differs from data on the rat (Gillis and
Biewener, 2001). The iEMG data also does not agree with Prilutsky and Gregor’s (2001) hypothesis that the run-walk transition is triggered by the large proximal leg muscle which they theorized to be required to generate more force during slow running than fast walking. The trot-gallop transition in horses also does not elicit a change in the function of the vastus lateralis (unpublished data). While it seems unlikely that the function of the vastus lateralis plays a role in triggering gait transitions in the horse, it is possible that a difference in methodology could affect any comparison between Prilutsky and Gregor
(2001) and the current study. Prilutsky and Gregor (2001) used different variables to quantify EMG function, peak EMG and average EMG over stance and swing, which were normalized to peak EMG at maximal activity, whereas the current study used iEMG, EMG duration, etc, which were normalized to peak EMG activity of an individual animal.
While strain did not change between gaits, it did differ between quartiles of stance (Figure 20). The majority of the shortening occurs during the 1st quartile of stance
when the muscle is active, indicating that the muscle is generating work. A similar 29 amount of lengthening occurs during the last quartile. These results agree with Gillis and
Biewener’s (2001) suggestion that Taylor’s (1994) hypothesis is only correct for the limb overall, as some muscles act to generate or absorb net work while others perform no net work. The overall patterns of strain were not similar to the two burst pattern seen in the rat (Gillis and Biewener, 2001) with one small burst in swing and a much larger burst that encompasses over half of stance. One horse, however, did show a pattern similar to that of the rat at the trot (Red), but since the burst during swing only was present in one horse it was excluded in the overall analysis. The overall patterns of strain were also not similar to that of the dog (Carrier et al., 1998), which showed two patterns, one starting in late swing and continuing through over half of stance and one with a small burst during swing and a larger burst in what would approximately be the second quartile of stance.
The overall duration of activation during the walk (Figures 24, 26) is shorter than what has previously been reported for horses (Wentik, 1978), the dog (Tokurki, 1973a) and the cat (Wetzel, 1981; Trank et al., 1996). For trotting (Figure 24, 26), patterns of activation are similar to those seen in the dog (Tokuriki 1973b; Carrier et al., 1998), but different than those in the cat (Wetzel, 1981) and others studies on horses (Wentik
1978), although a difference in the speeds studied may account for this difference.
Kinematics
In the horse tarsal joint, peak angular acceleration (αt) and velocity (ωt) showed
an abrupt 30-60% (Figure 33A-B) decrease when transitioning from a walk to a trot,
which satisfies the second of Hreljac’s criteria (that the variable changes with gait) and
suggests it could be a trigger for the walk-trot transition. It is uncertain if these variables
conform to the first (the variable changes with speed) and third criteria (the variable 30 returns to level seen in the previous gait). The range of speed studied for kinematic variables was small (0.4 m/s) and may not be large enough to show trends with speed within a gait. ωt and αt could be sensed by the body, (the fourth criterion) in the same manner as Hreljac (1995) described: the ωt and αt are caused by the activity of tarsal joint flexors, which can send information about their function to the central nervous system. We could not test the fifth criterion (the threshold at which a transition occurs is independent of condition because the w-t transition was unaffected by incline (Table 5).
A total of eighteen out of twenty-nine kinematic variables showed changes at the w-t transition (Table 5). Six of these occurred at the coxofemoral joint, four at femorotibial joint, five at the tarsal joint (including ωt and αt), and three at the metatarsophalangeal joint. All eighteen variables satisfy the second criteria, but due to the limitations described earlier it remains unknown if they fit all of the criteria. It is also important to note that Minetti et al.’s (1994) trigger, the angle between the thighs, was not measured in this study, and thus cannot be ruled out as a trigger of the w-t transitions in horses.
Patterns of angle time graphs (Figure 27A-D) were similar to those seen in the horse by other researchers (Wentik 1978; Back et al., 1995b; Back et al., 1996; Hodson et al., 2001). The variation between studies might be explained by speed, breed differences (e.g. Back et al., 1996 used Warmbloods) and differences in angle calculation, smoothing algorithms and other elements of methodology. Some notable differences occurred between the current study and that of Hodson et al. (2001).
Femorotibial patterns (Figure 27B) were similar but the current study showed a more constant rate of flexion throughout mid to late stance. At the tarsal joint (Figure 27C), the current study showed both more flexion and extension in early to midstance, though the second bout of flexion was similar. 31 The coxofemoral joint (Figure 27A) showed extension during most of stance followed by extension, which is similar to the pattern seen for the walking cat (Trank et al., 1996) and the walking and trotting rat (Gillis and Biewener, 2001) and dog (Tokurki,
1973a; Tokurki, 1973b). The pattern of flexion during stance followed by extension during swing seen in the femorotibial joint (Figure 27B) has also been reported for the rat
(Gillis and Biewener, 2001). In the walking dog and cat, however, the femorotibial joint angle decreased slightly in early stance but then remained fairly constant throughout remainder of stance with the only significant burst of flexion in swing (Tokurki 1973a;
Trank et al., 1996). In the trotting dog, a burst of flexion followed by extension was seen during both stance and swing (Tokurki, 1973b). The tarsal joint (Figure 27C) pattern of flexion followed by extension was not similar to those seen in the dog or cat, although the patterns were more similar in the walk. The metatarsophalangeal joint (Figure 27D) of the horse at the walk showed a characteristic ‘M’ shaped pattern with two peaks of extension of the during stance, whereas the dog and cat only show one (Tokurki 1973a;
Trank et al., 1996). The patterns for this joint (Figure 27D) at the trot however were similar to those reported for canines and felines (Tokurki 1973b; Trank et al., 1996). It is possible that these differences in kinematics reflect differences between the digitigrade limb posture of the dog and cat and the unguligrade limb posture of the horse, but more data is needed to test this idea.
A number of kinematic variables were found to be different between the walk and trot by Back et al. (1996): the angle at contact and maximum extension of the coxofemoral joint (Figures 28A and C), angle at contact and maximum flexion of the femorotibial joint (Figure 29A and C), angle at contact of the tarsal joint (Figure 31A), angle at maximum extension of the metatarsophalangeal joint (Figure 34C). The direction and magnitude of these changes, however, were not given. Back et al. (1996) 32 also found significant differences for the angle at maximum flexion of the tarsal joint and angle at contact of the metatarsophalangeal joint. This was not observed in the current study, although there was a difference in maximum extension of the tarsal joint (Figure
32A). These differences are most likely due to the higher trotting speed (4.0 m/s) used by Back et al.
The current study also provides evidence for a linkage between the femorotibial and tarsal joints. In low speed trotting, the two angles (Figure 30) had a linear relationship (slope = 0.78). Fast walking showed this link (Figure 30) but to a lesser degree (slope = 0.52). Back et al. (1996b) found a similar relationship between these joints at 4.0 m/s in the horse with a comparable slope of 0.72. In canines, this mechanical link is apparent in the linear relationship between the angles of the two joints at the trot (Gregerson et al., 1998).
Predictions from Mechanical Models
From the spring-mass model it was predicted that maxima of leg length would occur at 0% and 100% of stance and a single minimum would occur at 50% of stance.
Between observed and expected times, the difference for the maximum at beginning of stance was only 1%, while the maximum at the end of stance only showed a 5% difference (Figure 36). These differences, while statistically significant, do not represent biologically significant differences. The minimum leg length during stance (Figure 36) occurred 9% earlier than what was predicted. We also believe this is not biologically significant, even though it was statistically significant. Thus, our results agree with the predictions from the mechanical model. One possible explanation for the greater discrepancy for the minimum than for the maxima is the presence of double support at
33 low speed trotting (Figure 7). The spring-mass model does accurately describe the movement of the center of mass in humans (Lee and Farley, 1998).
This study used leg length as a substitute for the distance from the ground to the center of mass, for two reasons. One, the center of mass in the horse moves horizontally, vertically, and laterally over the course of the stride, making it difficult to easily quantify (Minetti et al., 1999). This is especially difficult at slower speeds due to the large lateral movements of the center of mass (Minetti et al., 1999). Two, the mechanical models are unipod and for example in a trotting quadruped, even if a symmetrical gait is assumed, there are two limbs to choose between. So, if we had measured the distance from the hind hoof to the approximate center of mass, the pattern of change bears no resemblance to the predicted one. The minimum would have occurred at the beginning of stance and the maximum at the end of stance. The distance from the center of mass to the ground also cannot be calculated from kinetics because all four limbs cannot simultaneously fit on a single force plate. Since it conformed to the predictions of the spring-mass model, our measure of leg length provides a reasonable measure for the calculation of leg length in a large quadruped.
As found with higher speed trotting (Hoyt et al., 2002), low speed trotting does not "land short, take off long". It seems possible that the "land short, take off long" hypothesis is a prediction of the spring-mass model that is descriptive of humans
(Iverson and McMahon, 1992) and other bipeds (Cavanga et al., 1977) but does not extend to horses and other quadrupeds. Further studies on other quadrupeds are needed to test the validity of these ideas.
While leg length during walking increased very slowly from 20-80% of stance, it lengthened almost a third of the total leg length change during stance (Figure 35). While this 2% change is relatively small, it represents a fairly constant rate of extension. During 34 this time, the leg extended until approximately 65% of stance, and then compressed. For the first 20% of stance the leg compressed as the limb began to support the weight of the animal. As the hoof prepares to lift off in the last 20% of stance, the leg extended, though to a lesser extent than the compression of early stance. This extension could be due to a reduction in the amount of body weight this limb was supporting. There are three possible explanations of why the inverted pendulum model did not accurately describe the movement of the horse. First, the increased phase discrepancies at fast or slow walking speeds deviate more from the inverted pendulum model than those at moderate walking speeds (Cavanga et al., 1977). Second, while our use of leg length instead of distance to the center of mass conformed to the predictions of the spring- mass model, it may not be suitable for walking. Third, Alexander's (1977) model may not be complex enough to describe the motion of a quadruped at faster walking speeds.
Researchers have theorized increasingly complex models of the walk employing bipeds with limbs containing a spring (Alexander, 1992) or a single joint (Minetti and Alexander,
1997), which were not used in this study as we were investigating only the most basic mechanical models. In humans, the virtual stance limb, from the center of mass to the point of ground contact, compresses substantially during walking, especially at fast walking speeds (Lee and Farley, 1998). Virtual stance limb compression may reduce the feasibility of gravitational-kinetic energy exchange of inverted pendulum mechanics, but may increase elastic energy storage and act to reduce peak muscloskeletal forces associated with contact (Lee and Farley, 1998). Thus, the inverted pendulum model did not reasonably predict leg length during the walking speeds measured in the horse.
35 Stride Parameters
Except for swing, the overall patterns of stride parameters for both gaits showed linear changes with speed and a significant difference between the walk and the trot at the same speeds (Figures 5-14) (Figure 4). These patterns were similar to those found in humans at the walk-run transition (Nilsson et al., 1985; Nilsson and Thorestensson,
1987; Minetti et al., 1994). Stride frequency at the trot-gallop transition in horses (Wickler et al., 2003) also shows a similar pattern. Stance at the trot-gallop transition in horses
(Wickler et al., 2003) and the walk-run transition in birds (Gatesy and Biewener, 1991), however, show similar changes with speed but no abrupt change with gait. In birds, however, the slope of relative stride length does change at the walk-run transition. This difference between walk-run transition of birds and those in other animals can be attributed in part to the smooth walk-run transition in birds, their crouched posture, and their hypothesized need for stability (Gatesy and Biewener, 1991). While stride parameters in humans show an abrupt change between walking and running, the walk and run curves usually overlap at extremely low running or high walking speeds (Nilsson et al., 1985; Nilsson and Thorestensson, 1987; Minetti et al., 1994), which were speeds well beyond the speeds currently studied. Thus, the differences in stride parameters between trot-gallop and walk-trot or equivalent transitions may represent fundamental differences in these transitions. There are data on stride parameters at transitions for only a few animals (most notably the horse and humans), so more data on other quadrupeds at both transitions is needed to explore this possibility.
While all stride parameters changed with gait (Table 5), they did not return to levels seen in the previous gait (third criterion). It is possible that step length during the
36 trot might have returned to levels seen in the walk at higher speeds, but it is unknown at this time if this is the case.
The change in duration of stance when switching from a walk to a trot (Figure 6) means that there will be a difference in step length, which was observed (Figure 8). A change in step length indicates an alteration in the range of motion from contact to endstance of one or more joints. A change in the range of motion from contact to endstance can be measured directly or be determined if all of the ranges of motion (as measured in the current study) change in the same direction. In the coxofemoral (Figure
28E-F) and femorotibial (Figure 29E-F) joints, the changes in the ranges of motion were consistent with the change in step length. The increased flexion at the coxofemoral joint at contact (Figure 28A, Table 4) is offset by the greater increase in flexion at liftoff
(Figure 28B, Table 4). The metatarsophalangeal joint also showed changes in ranges of motion (Figure 34E-F) but this joint is primarily passive and any change in it cannot be actively contributing to the change in step length.
Within a single gait, however, the patterns of stride parameters (Figure 4-14) were similar to those seen for a variety of animals. The linear decrease of the duration stance with speed for both gaits (Figure 6) were similar to the linear decreases seen in the dog (Roush et al., 1994; McLaughlin and Roush, 1994), rat (Gillis and Biewener,
2001), and previous studies of the horse (McLaughlin et al., 1996; Khumsap et al.,
2001b). It is important to note that once a sufficiently large range of speed is investigated, the duration of stance decreases as a power range of speed in the trotting horse (Hoyt et al., 2000). The range of speeds used in the current study was not large enough to detect a difference between power and linear functions of speed for the duration of stance.
37 Stride length in the horse (Figure 9) showed a linear increase with speed, which is similar to data on the mouse, rat, and dog (Heglund et al 1974). Stride frequency
(Figure 11) also matched the linear patterns seen in many other quadrupeds, including lion (Chassin et al., 1996), mice, rats and dogs (Heglund et al., 1974), and wild African artiodactyls (Heglund and Taylor, 1988). The change in stride parameters with speed at the walk and trot also showed similar patterns (Figures 5-7 and 11) to those seen in humans: stance (Nilsson et al., 1985; Nilsson and Thorestensson, 1987), stride period
(Nilsson et al., 1985; Nilsson and Thorestensson, 1987;), duty factor (Nilsson et al.,
1985;) and stride frequency (Minetti et al., 1994).
The duty factor for the trotting speeds studied did exceed 0.5 at speed slower than 2.0 m/s, indicating periods of double support. This is common at low running and trotting speeds and has been documented in humans (Nilsson et al., 1985). In the rat, duty factor exceeds 0.5 at trotting speeds (Gillis and Biewener, 2001), though this may mostly be due to the crouched posture of the rat.
Conclusion
While the function of the vastus lateralis does not appear to be a trigger of the walk-trot transition, the differences in the kinematics of the coxofemoral joint suggests a difference in the function of muscle acting at this joint. The increased range of motion at the femorotibial joint without a change in muscle function of the vastus lateralis suggests an increase in elastic storage in this muscle at the trot, which agrees with the spring- mass model. The differences in ωt and αt suggest that the activity of the ankle flexors
(e.g. tibialis anterior m.) may be a walk-trot transition trigger. The activity of the
extensors of the coxofemoral joint (e.g. gluteus maximus m.) might also show 38 differences between the walk and the trot. Future studies should focus on these areas to better understand the walk-trot transition in horses, as well as its relation to transitions in other animals.
39 Appendix A
Calculation of the Coxofemoral Joint
CFxx'1=[cos(θ −×+θ2) R1] CF
CFyy'1=[sin(θ −×+θ2) R1] CF where CFx’ is the new coxofemoral x component, CFy’ is the new coxofemoral y component, d is the distance between the tuber coxae (1) and the calculated femorotibial point (3a), R1 is the distance from the tuber coxae (1) to the CoR of
coxofemoral joint (2) during standing square, R2 is the distance from the calculated
femorotibial point (3a) to the CoR of coxofemoral joint (2), CFx is the original coxofemoral x component, CFy is the original coxofemoral y component (Figure 2b). R1,
R2, and d are used in the calculation of Θ1 and Θ2.
Since this method of calculation yield two possible solutions, the tuber coxae was set as the origin and the solution with a positive x component was used for subsequent analysis. In order to obtain the position of the calculated coxofemoral point, the x and y solutions generated were added to the position of the tuber coxae
Calculation of the Femorotibial Joint
FTxm' =+[cos(θ esθ sq)×r]+FTx
FTym' =+[sin(θ esθsq)×r]+FTy
where FTx’ is the new femorotibial x component, FTy’ is the new femorotibial y
component, Θmes is the angle between the lines through the CoR of the tarsal joint (5) and the shaft of the tibia (4) and the CoR of the tarsal joint (5) and the CoR of the femorotibial joint (3), and Θsq is this angle during the standing square, r is the distanced 40 from the CoR of the tarsal joint (5) to the CoR of the femorotibial joint (3) during standing square, FTx is the original femorotibial x component, and FTy is the original femorotibial y component
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49
Figure 1: Accelerometer Record at 2.5 m/s
Contact
Liftoff
Figure 1: The x-axis component of the accelerometer signal was used to determine contact and liftoff. The accelerometer was positioned so that the x-axis component was the fore-aft component with forward acceleration equaling position. Red dots denote contact and green dots denote liftoff. Location of contact and liftoff within a record was determined from the timing of force generation in a separate force plate study. Contact and liftoff were used to determine all other stride parameters and subdivide the sonomicrometer and electromyography records.
50 Figure 2: Determination of Calculated Femorotibial Joint
(xt, yt)
(xcf, ycf)
(xft, yft)
Figure 2: The position of the coxofemoral joint was calculated by determining the intersection of two circles whose centers are the tuber coxae (xt, yt) and the calculated femorotibial point (xft, yft). The radii of these circles were the length of the pelvis (the distance from the tuber coxae to the CoR of the coxofemoral joint) and the thigh (the distance from the CoR of the coxofemoral to the CoR of the femorotibial joints) while the horse was standing square. This yields two possible points where the circles intersect (or one if the thigh and pelvis segments form a straight line). The position of the coxofemoral joint was taken to be the caudal point of intersection. This image was used with the permission of Darren Dutto.
51 Figure 3: Location of Kinematic Anatomical Landmarks
1 2/2a
3/3a
4
5
6 7
9 8
Figure 3: Kinematic markers were placed at palpable locations: 1) Tuber coxae, 2) Center of rotation (CoR) of the coxofemoral joint, 2a) Calculated coxofemoral joint, 3) CoR of the femorotibial joint, 3a) Calculated femorotibial joint, 4) Shaft of the tibia, 5) CoR of the tarsal joint, 6) CoR of the metatarsophalangeal joint, 7) Coronary band, 8) Anterior distal hoof wall, and 9) Posterior distal hoof wall. Most points were in standard palpable locations (Hodson et al., 2001) with the exception of #4, 8 and 9. The anterior (6) and posterior distal hoof (7) wall markers were placed at a 54º angle relative to the marker on the coronary band. The reflective marker model horse was Gentle Touch. Image credit: Gwenn Catterfeld.
52 Figure 4: Swing Phase versus Speed
500 Trot 480 Walk 460 440 420 400 380 360 Swing (msec) 340 320 300 0 0.01.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Speed (m/s)
Figure 4: Over the range of trotting speeds, swing phase increased 9% (P=0.0094), but levels off at approximately 400 ms between 2.0 and 2.5 m/s. Standard error bars are present for all points but some are so small as to be eclipsed by each point, N=3.
Figure 5: Stride Period versus Speed
1300 Trot 1200 Walk 1100 1000 900 800 Period (msec) 700 600 0 1.00.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Speed (m/s)
Figure 5: Stride period (P=0.0130) decreased 25% at 1.8 and 1.9 m/s. As speed increased, the stride period shortened 15% (P<0.0001) for the walk and 7% (P=0.0013) for the trot. Standard error bars are present but are so small as to be eclipsed by each point, N=3.
53 Figure 6: Stance Phase versus Speed 900 Trot 800 Walk 700 600 500 400 300 Time of Contact (msec) 200 1.00.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Speed (m/s)
Figure 6: Stance phase (P=0.0113) decreased 35% at 1.8 and 1.9 m/s. The duration of stance phase decreased 21% over the range of walking speeds (P=0.00000049) and trotting speeds (P=0.000016). Standard error bars are present but are so small as to be eclipsed by each point, N=3.
Figure 7: Duty Factor versus Speed
0.70 Trot 0.65 Walk
0.60
0.55
0.50 Duty Factor
(Stance/Period) 0.45
0.000.40 1.00.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Speed (m/s)
Figure 7: Duty factor (P=0.0337) decreased 12% at the trot compared to the walk and decreased with speed (P=0.0207) at 1.8 and 1.9 m/s. Duty factor decreased 15% for the walk (P=0.0002) and 7% for the trot (P<0.0001). Standard error bars are present for all points but some are so small as to be eclipsed by each point, N=3.
54 Figure 8: Step Length versus Speed 1.4 Trot 1.3 1.2 Walk 1.1 1 0.9 0.8 0.7
Step Length (m) 0.6 0.5 0.00.4 0.01.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Speed (m/s)
Figure 8: Step length (P=0.0115) decreased 35% at 1.8 and 1.9 m/s. Over the range of trotting speeds, step length lengthened 10% with speed (P=0.022). No difference was found during the walk, which was most likely due to the large amount of variation at a 1.2 walk. Standard error bars are present for all points but some are so small as to be eclipsed by each point, N=3.
Figure 9: Stride Length versus Speed
2.3 Trot 2.1 Walk 1.9 1.7 1.5 1.3 1.1 Stride Length (m) 0.9 0.00.7 0.01.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Speed (m/s)
Figure 9: Stride length (P=0.0132) decreased 25% at the trot compared to the walk at 1.8 and 1.9 m/s. Stride length increased 21% during the walk (P=0.012), and 30% during the trot, (P<0.0001). Standard error bars are present for all points but some are so small as to be eclipsed by each point, N=3.
55 Figure 10: Rate of Force Application versus Speed 3.5 3 2.5 2 1.5 1 1/tc (1/msec) Trot 0.5 Walk 0.00 10.0 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 Speed (m/s)
Figure 10: The rate of force application (P=0.0126) increased 53% at a trot compared to a walk and increased with speed (P=0.0171) at 1.8 and 1.9 m/s. The rate of force application increased 27% for both the walk (P<0.0001) and for the trot (P<0.0001). Standard error bars are present but are so small as to be eclipsed by each point, N=3.
Figure 11: Stride Frequency versus Speed 90
80
70
60
50 Trot Stride Frequency Walk 40 1.00.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Speed (m/s)
Figure 11: Stride Frequency (P=0.0131) increased 34% at a trot compared to a walk and increased with speed (P=0.0367) at 1.8 and 1.9 m/s. Stride frequency increased 18% for the walk (P=0.0011) and 7% for the trot, (P<0.0001). Standard error bars are present but are so small as to be eclipsed by each point, N=3.
56 Figure 12: Normalized Muscle Length versus Percent Stance Phase for 10 strides at a 1.4 Walk for One Horse (Red) Stride 1 1.20 Stride 2 1.15 Stride 3 Stride 4 1.10 Stride 5 Stride 6 1.05 Stride 7 1.00 Stride 8
NML Stride 9 0.95 Stride 10 0.90 Average 0.85 0.800.00 0 102030405060708090100 Percent Stance Phase
Figure 13: Normalized Muslce Length versus Percent Stance Phase Stride 1 Stride 2 1.10 for 10 Strides at a 2.5 Trot for One Horse (Red) Stride 3 1.05 Stride 4 Stride 5 1.00 Stride 6 Stride 7 0.95 Stride 8 Stride 9 NML 0.90 Stride 10 Average 0.85
0.80
0.750.00 0 102030405060708090100 Percent Stance Phase
Figures 12-13: Within an individual horse at a given speed, the coefficients of variation of normalized muscle lengths were small. The coefficient of variation for this variable for one horse (Red) was 5.34 for the 1.4 walk and 5.1 for the 2.5 trot. Normalized muscle lengths were for one horse at two speeds, 1.4 m/s walk (Figure 12) and 2.5 m/s trot (Figure 13). Normalized muscle lengths are of ten consecutive trials and their average. The coefficient of variation was 5.34 for the 1.4 walk and 5.1 for the 2.5 trot.
57 Figure 14: Normalized Muscle Length for all Horses at 1.4 m/s Walk
1.15 Red GT 1.10 Reign 1.05
1.00
NML 0.95
0.90
0.85
0.0.8000 0 102030405060708090100 Percent Stance Phase
Figure 15: Normalized Muscle Length for all Horses at 2.5 m.s Trot
1.30 Red GT 1.20 Reign
1.10
L 1.00 NM
0.90
0.80
0.700.00 0 102030405060708090100 Percent Stance Phase
Figures 14-15: The coefficients of variation for normalized muscle lengths between horses at a given speed were within what would be expected from a biological parameter. These normalized muscle lengths were for individual horses at two speeds, 1.4 m/s walk (Figure 14) and 2.5 m/s trot (Figure 15). The coefficient of variation was 14.7 for the 2.5 trot and 10.5 for the 1.4 walk. Normalized muscle lengths are averages of ten consecutive trials.
58 Figure 16: Normalized Muscle Function versus Percent Stance Phase for all Walking Speeds 1.05
1.00
0.95
NML Walk 1.2 Walk 1.4 0.90 Walk 1.6 Walk 1.8 Walk 1.9 0.850.00 0 20406080100 Percent Stance Phase
Figure 17: Normalized Muscle Function versus Percent 1.05 Stance Phase for All Trotting Speeds
1.00
0.95
NML Trot 1.8 Trot 1.9 0.90 Trot 2.0 Trot 2.2 Trot 2.5 0.850.00 0 20406080100 Percent Stance Phase
Figures 16-17: Within a gait, normalized muscle function had small coefficients of variation. Normalized muscle lengths as averages of all horses over range of speed of each gait, walk (Figure 16) and trot (Figure 17). The coefficient of variation was 14.7 for the trot and 10.5 for the walk. During trotting, the vastus is functioning relatively isometrically from approximately 40-90% of stance phase. At lower speed walking, 1.2- 1.6 m/s, the vastus lateralis also appears to be functioning isometrically. The normalized muscle function of walking at 1.8 and 1.9 m/s deviate from this pattern by continuously lengthening until approximately 70% of stance and then shortening for the remainder of stance with no period of isometric function.
59 Figure 18: Normalized Muscle Length versus Precent Stance Phase 1.05 for Walking and Trotting at 1.8 & 1.9 m/s
1.00
0.95
NML Walk 1.8 Walk 1.9 0.90 Trot 1.8 Trot 1.9
0.0.8500 0 20406080100 Percent Stance Phase
Figure 18: The NML for walking and trotting were similar over 0-40% of stance phase, which include the range strains and strain rates were determined. Over this range the muscle shortened during the first 5-10% of stance and then slowly lengthens until 40% of stance. From 40-80% the two gaits were different. NMLs of the trot were isometric during this time, while those of the walk increased in length up until 70% of stance and then shortened from 70-80%. Over the last 20% of stance the muscle is behaving isometrically for both gaits.
60 Figure 19: Total Positive Strain versus Speed 0.40 Trot 0.35 Walk 0.30 0.25 0.20 0.15 0.10 0.05 Total Positive Strain 0.00 1.00.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Speed (m/s)
Figure 19: Total positive strain was not affected by speed during the range of trotting speeds and showed a great deal of variability. Total positive strain was calculated as an average of the 3 horses over the range of muscle function speeds. Total positive strain was not affected by gait or speed at 1.8 and 1.9 m/s. Total positive strain increased 35% with speed during the walk (P=0.017).
61 Figure 20: Total Positive and Negative Strains of the Vastus Lateralis
GaQ 0.25 0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 12341234123412341234 1.2 Walk 1.4 Walk 1.6 Walk 1.8 Walk 1.9 Walk
0.25 0.2 0.15 0.1 neagative strain 0.05 0 positive strain -0.05 -0.1 -0.15 -0.2 12341234123412341234 1.8 Trot 1.9 Trot 2.0 Trot 2.2 Trot 2.5 Trot
Figure 20: At 1.8 and 1.9 m/s, there was no effect of gait or speed on total positive or negative strain. At these speeds, in both the walk and the trot, the 1st quartile of total positive strain was greater than the remaining three. At the trot, total negative strain in the 4th quartile was different from the second and third. Total average and positive strains were divided in quartiles and were averages of the three horses.
62 Figure 21: Total Positive and Negative Strains of the Vastus Lateralis for Individual Horses
Figure 21: Total positive and negative strains of the vastus lateralis. Total average and positive strains were divided in quartiles and were for individual horse. GT is red, Red is purple, and Reign is orange. While Reign did drive the absolute values of the averages for the three horses seen in Figure 19, the trends over quartile were similar between animals. 63 Figure 22: Average Positive Strain Rate versus Speed 4.0 Trot 3.5 Walk 3.0 2.5 2.0 1.5 1.0
Positive Strain Rate (1/s) 0.5 0.0 0.01.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Speed (m/s)
Figure 23: Average Positive Strain Rate of Individual Horses Red walk versus Speed 4.5 GT walk 4 Reign walk 3.5 Red trot 3 GT trot 2.5 Reign trot 2 1.5 1 0.5 0 1.000.0 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 Speed (m/s) Average Positive Strain Rate (1/s)
Figures 22-23: An ANOVA analysis did not find any influence of gait (P=0.1925) or speed (P=0.4578) on average positive strain rate at 1.8 and 1.9 m/s. Total positive strain rate was calculated as an average of the 3 horses (Figure 22) and for individual horse (Figure 23) over the range of muscle function speeds. Average positive strain rate increased 73% with speed during the walk (P=0.037) but not the trot. This increase in average positive strain rate at the walk is not constant and appears to level off after 1.6 m/s. A closer inspection of the strain rate data, however, indicated that there was a consistent change in positive strain rate between gaits for each horse, which a Wilcox on test confirms (P=0.028). Thus, there was likely a significant difference in positive strain rate with gait at 1.8 and 1.9 m/s but the small sample size of this study prevented it from being detected using a repeated measures ANOVA.
64 Figure 24: Onset, Offset, and Duration of EMG signals versus Speed 600 offset 500 Walk 400 Trot n 300 io 200 durat . onset Time (ms) 100 0 -100 0.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Speed (m/s)
Figure 24: While neither onset, offset, or duration showed any difference at 1.8 and 1.9 m/s, onset and offset tended to occur earlier at the trot, regardless of speed. EMG duration increased 35% (P=0.028) over the range of walking speeds. If an individual horse had more than one burst of EMG activity, the values of EMG parameters for that horse were averages of all bursts of activity. N=3.
Figure 25: Normalized iEMG versus Speed 0.7
0.6 b 0.5 b 0.4 b 0.3 a 0.2 Trot iEMG (Volts) a 0.1 Walk 0 0.01 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 Speed (m/s)
Figure 25: Normalized iEMGs are the sum of all iEMG for all activity bursts that occurred during stance phase for an individual horse divided by the maximum iEMG for that horse. No change in iEMG was seen at 1.8 and 1.9 m/s. Speed did not have an effect on normalized iEMG at either gait. Letters represent differences in iEMG at the walk as determined by a means comparison analysis. N=3.
65 Figure 26: EMG Duration as a Percent of Stance and Stride 100 100 Percent Stride Trot 90 90 Percent Stride Walk 80 80 Percent Stance Trot
70 Percent Stance Walk 70 Percen 60 60 50 50 t Stan 40 40 30 30 ce Percent Stride 20 20 10 10 0 0 0.01 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 Speed (m/s)
Figure 26: No difference in EMG duration as percent of stride or stance was seen at 1.8 and 1.9 m/s. EMG duration as a percent of stride increased 45% with speed (P=0.0024) over the range of walking speeds. EMG duration as a percent of stance increased significantly with speed during both gaits, 48% for the walk (P=0.001) and 32% for the trot (P=0.035). Standard errors bars are present for all data, although some are so small as to be eclipsed by the data point itself, N=3.
66 Figure 27: Angle-Time Diagrams for the Four Joints
A B 1.6 Walk 1.7 Trot 130 1.7 Walk 1.8 Trot 170 1.8 Walk 1.9 Trot ) 160 1.9 Walk 2.0 Trot 110 150
90 140 130
70 120 Angle (degrees 110 Angle (degrees) 50 100 0 0 25 50 75 100 0 0 25 50 75 100 Percent Stride Percent Stride
C D 180 250 170 230 160 210
150 190
140 170 130 150 Angle (degrees) Angle (degrees) 120 130 0 0 25 50 75 100 0 0 25 50 75 100
Figure 27: Angle-time diagrams for the coxofemoral (A), femorotibial (B), tarsal (C), and metatarsophalangeal (D) joints. Angles are averages of the 5 horses and are defined so that flexion is a decreasing angle. Blue arrows denote the average end of stance for all trotting speeds and green arrows denote the same for all walking speeds. The coxofemoral joint undergoes primarily extension during stance and flexion during swing. The peak extensions and flexions of the coxofemoral joint appear to be greater in the walk than the trot. The femorotibial joint undergoes flexion with a period of extension occurring at the end of stance in the walk and approximately three-quarters of stance in the trot. Both gaits showed mostly flexion at the femorotibial joint during swing. The tarsal joint undergoes flexion during early stance followed by extension throughout the remainder of stance. During swing, the tarsal joint first undergoes flexion then extension. The metatarsophalangeal joint undergoes extension and then flexion during stance, with the walk showing two peaks of extension and the trot shows a single peak. This joint primarily undergoes extension during swing.
67 Figure 28: Kinematic Parameters for the Coxofemoral Joint
A B 90 140 80 120 70 100 60 80 50 600
Liftoff (degrees) Contact (degrees) 0 1.50.0 1.7 1.9 2.1 1.5 1.7 1.9 2.1 0.0 Speed (m/s) Speed (m/s)
B D Trot 150 140 Walk
120 100 100 50
80 0 ME as %st. Max Extension 0.0 0
E F 64 0
56 -2 48 -4 40 -6 32 ROMme-e ROMc-me 24 -8 16 0 -10
Figure 28A-F: Coxofemoral joint angles at contact (A), liftoff (B), and maximum extension (C), the timing of maximum extension (D), range of motion (ROMc-me) from contact to maximum extension (E), and range of motion (ROMme-e) from maximum extension to endstance. At 1.7, 1.8, and 1.9 m/s, when switching from a walk to a trot the angle of contact decreased 12% (P=0.0270), maximum extension decreased 13% (P=0.0114), the timing of maximum extension decreased 25% (P=0.0010), angle at liftoff decreased 17% (P=0.0093), and range of motion from contact to maximum extension decreased 47% (P=0.0131) and from maximum extension to endstance (P=0.0131) decreased 265%. This data provides further evidence of the greater demands placed on the coxofemoral joint during walking at 1.7, 1.8, and 1.9 m/s.
68 Figure 29: Kinematic Parameters for the Femorotibial Joint
A Trot B 180 160 Walk 170 140 160 150 120 140 130 0 0 100 Contact (degrees)
0.1.05 1.7 1.9 2.1 Liftoff (degrees) 1.0.50 1.7 1.9 2.1
Speed (m/s) Speed (m/s)
C D 150 120 140 100 130 120 80
110 60
MF as %st Max Flexion 10 0 0 40 0
E F 0 10
-10 5
-20 0
ROMmf-e ROMc-mf -30 -5
-40 -10
Figure 29A-F: Femorotibial joint angles at contact (A), liftoff (B), and maximum extension (C), the timing of maximum extension (D), range of motion (ROMc-mf) from contact to maximum flexion (E), and range of motion (ROMmf-e) from maximum flexion to endstance. At 1.7, 1.8, and 1.9 m/s, when switching from a walk to a trot, the angle at contact decreased 3% (P=0.0098), the timing of maximum flexion increased 14% (P=0.0377), range of motion from contact to maximum flexion decreased 16% (P=0.0423), and range of motion from maximum flexion to endstance increased 141% (P=0.0159).
69 Figure 30: Femorotibial-Tarsal Linkage 240
230
220
210
200
190
180 Tarsal Angle (Degrees) Walk 170 Trot
160 0 10203040506070 Femorotibial Angle (Degrees)
Figure 30: A linkage between the femorotibial and tarsal joints was observed in low speed trotting as well as high speed walking. In low speed trotting, the two angles had a linear relationship of (R2=0.90, P<0.0001) with a slope of 0.78. This pattern was nearly identical to the one observed in higher speed trotting by Back (1996b). Fast walking shows this link but to a lesser extent with a slope of 0.52 (R2=0.62, P=0.0120).
70 Figure 31: Kinematic Parameters for the Tarsal Joint
A B 172 165 170 160 168 155 166 150 164 145 162 160 140
Liftoff (degrees) Contact (degrees) 158 0 135 0 0.01.5 1.7 1.9 2.1 1.50.0 1.7 1.9 2.1 Speed (m/s) Speed (m/s)
C D 164 50 40 160 30 156 20 Trot 152 MF as %st.
Max Flexion 10 Walk 0 148 0
Figure 31A-D: Tarsal joint angles of contact (A), liftoff (B), maximum flexion (C) and the timing of maximum flexion (D). At 1.7, 1.8, and 1.9 m/s, when switching from a walk to a trot the angle at contact decreased 1% (P=0.0289). While the timing of maximum flexion changed with gait (P=0.0344), there was also an interaction between gait and speed (P=0.0007).
71 Figure 32: Kinematic Parameters for the Tarsal Joint
A B 100 180 80 175 Trot 60 Walk 170 40 165 20 ME as %st.
Max Extension 160 0 0 0.01.5 1.7 1.9 2.1 0.01.5 1.7 1.9 2.1
Speed (m/s) Speed (m/s)
C D 0 25
-5 20 15 -10 10 -15 ROMc-mf 5 ROMmf-me -20 0
E 0
-5
-10 ROMme-e -15
Figure 32A-E: Tarsal joint maximum flexion (A), the timing of maximum flexion (B), range of motion (ROMc-mf) from contact to maximum flexion (C), range of motion (ROMmf- me) from maximum flexion to maximum extension (D), and range of motion (ROMme-e) from maximum extension to endstance (E). Maximum extension was 3% smaller (P=0.0023) at the trot than the walk. The ranges of motion each showed an interaction between gait and speed. Since many tarsal joint variable show interaction between and gait and speed, it is difficult to interpret the happenings at this joint.
72
Figure 33: Peak Ankle Angular Acceleration (A) and
Velocity (B) versus Speed
1500 A Trot 2 1000 Walk
500
0
Peak Ang. Accel. (m/s )
140 B
120
100
80
60
Peak Ang. Vel. (m/s) 40 0 1.0.50 1.6 1.7 1.8 1.9 2.0 2.1
Speed (m/s)
Figure 33: At speeds of 1.7, 1.8, 1.9 m/s, peak angular acceleration (A) and velocity (B) at the tarsal joint decreased 60% (P=0.0178) and 29% (P=0.0148), respectively as a function of gait. No change in either variable was seen at either gait as a function of speed.
73 Figure 34: Kinematic Parameters for the Metatarsophalangeal Joint
A B 204 180 202 170 200 198 160 196 150 194 0 140 0 Liftoff (degrees) Contact (degrees) 0.0 1.5 1.7 1.9 2.1 1.50.0 1.7 1.9 2.1
Speed (m/s) Speed (m/s)
C D 80 250 240 60 230 Trot 40
220 Walk 20
ME as %st. 210 0 Max Extension 0
E F 50 0
40 -20
30 -40 20 -60 ROMme-e ROMc-me 10 0 -80
Figure 34A-F: Metatarsophalangeal joint angles at contact (A), at liftoff (B), and maximum extension (C), the timing of maximum extension (D), range of motion (ROMc- me) from contact to maximum extension (E), and range of motion (ROMme-e) from maximum extension to endstance. At 1.7, 1.8, and 1.9 m/s, when switching from a walk to a trot maximum extension decreased 5% (P=0.0101), range of motion from contact to maximum extension decreased 48% (P=0.0028), and range of motion from maximum extension to endstance decreased 39% (P=0.0195).
74 1.7 Trot Figure 35: 1.8 Trot Leg Legnth versus Percent Stride 1.9 Trot 2.0 Trot 135 1.6 Walk 1.7 Walk 1.8 Walk 1.9 Walk 130
125
120 Leg Length (cm)
115 0-25% 25-75% 75-100%
110 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 Percent Stride
Figure 35: While length appeared to remain relatively constant form 20-80% of stance at the walk, a regression analysis showed that it did increase 2% over this time (P<0.0001). This increase was almost 1/3 of the change in leg length seen at the walk during stance. Leg length was calculated by taking the distance between the anterior hoof marker and the average of the coxofemoral joint and tuber coxae points. The black lines mark the different portions of stance phase at the trot.
75 Figure 36: Maximum and Minimum Leg Lengths as a 120 Function of Stance for the Trot 100 100 1.7 m/s 80 1.8 m/s 1.9 m/s
60 2.0 m/s 50 Expected 40 Percent Stance 20 0 0 0-25 25-75 75-100 Percent Stance
Figure 36: The timing of maximum and minimum leg lengths as an average of the 5 horses for the trot. The occurrence of the maxima and minimum agreed with the prediction from the spring mass model, as the statistics are not likely biologically relevant. The occurrence of the first maximum occurred at 1% of stance, the minimum at 41% of stance, and the second maximum at 95% of stance. All maximum and minimums appeared to the consistent between animals and speeds.
Figure 37: Average Maximum and Minimum Leg Lenghts for the Trot 140 1.7 m/s 1.8 m/s 135 1.9 m/s 130 2.0 m/s
125
120 aa bc
Leg Length (cm) dd'ef 115
110 Average Maximum Minimum
Figure 37: Average maximum and minimum leg lengths as an average of the five horses. Letters represent differences between speed-length combination, e.g. a and b are significantly different. For d and d’, they are not different from each other but each are different from all other speed-length combinations.
76