Relationships of Body Weight, Body Size ... - Wiley Online Library

Relationships of Body Weight, Body Size, Subject Velocity, and Vertical Ground Reaction Forces in Trotting Dogs Katja Voss1, Dr med vet Diplomate ECVS, Luca Galeandro1, Dr med vet, Thomas Wiestner2, BS El Eng, Michael Haessig3, Prof Dr med vet, and Pierre M. Montavon1, Prof Dr med vet 1

Small Animal Clinic, Vetsuisse Faculty University of Zurich, Zurich, Switzerland, 2Section Sports Medicine of the Equine Department, Vetsuisse Faculty University of Zurich, Zurich, Switzerland and 3Clinic for Farm Animals, Vetsuisse Faculty University of Zurich, Zurich, Switzerland

Corresponding Author Katja Voss, Faculty of Veterinary Science, University Veterinary Teaching Hospital Sydney, 65 Parramatta Road, Camperdown NSW 2006, Australia E-mail: [email protected] Submitted: December 2007 Accepted: June 2009 DOI:10.1111/j.1532-950X.2010.00729.x

Objective: To evaluate the relationship of body weight (BW) and size, dog velocity, and vertical ground reaction forces (GRF) from a large number of dogs of various sizes. Study Design: Clinical research. Animals: Orthopedically healthy dogs (n = 129) Methods: BW and dog size, represented as height at the withers (WH), were obtained. Stance times (ST), vertical impulses (VI), and peak vertical forces (PVF) of thoracic and pelvic limbs were measured on a force plate at controlled trotting speed. They were evaluated against BW and WH using linear regression analysis in absolute (nonnormalized) values, and when normalized to BW and/or body size according to the theory of dynamic similarity. Relative velocities were calculated for each dog. Results: Absolute ST, VI, and PVF showed strong positive correlations with BW and/or body size. When GRFs were normalized to BW, correlations with body size were markedly reduced, but remained positive for VI, and turned negative for PVF. Normalizing the time-dependent variables (ST and VI) also to WH eliminated most size influence. A small dependency of fully normalized GRF on body size remained that was because of differences in relative velocity between dogs of different sizes. Reference values for the fully normalized data are given. Conclusions: The inherent relationship between BW, body size, dog velocity, and vertical GRF was demonstrated. Clinical Relevance: BW, body size, and relative dog velocity must be accounted for when wanting to obtain GRF variables that are comparable between different dogs.

Force plate gait analysis is an objective, sensitive and accurate method to evaluate limb loading in dogs1,2 that is increasingly used in clinical studies to objectively demonstrate outcome after medical or surgical treatments of various orthopedic diseases. One problem with force plate gait analysis is the large variation of normal ground reaction forces (GRF) that prevents meaningful direct comparison of data between different dogs or dog groups. GRF are highly dependent on body mass and traveling velocity.3–5 Comparing GRF variables from different sized dogs, between unequal subject velocities, as well as between various study protocols necessitates some kind of standardization. Because GRFs are closely related to body mass, force variables are usually normalized to body mass (N/kg) or body weight (BW) (N/N), the latter often expressed in percentage of BW. To account for the velocity dependency of GRFs most authors limit dog velocities ranges to o 0.3–0.4 m/s and make an effort to keep the horizontal acceleration o 0.4–0.5 m/s2.2,3,6 Habituation7 to the guided experiments on runways with integrated

force plates, and nonspecific day-dependent variations8 also play a role in GRF variability. These factors are more difficult to control, especially in clinical studies where patients are usually only measured on a single occasion. Despite attempts to reduce GRF variability by normalizing the forces to BW, considerable variation was observed comparing dogs with different BWs to each other.9 BW and peak vertical forces (PVF) had a negative correlation and BW and vertical impulses (VI) a positive correlation at the walk.9 This finding however, that heavier or larger dogs appear to have smaller PVF and larger VI compared with smaller dogs, is not caused by BW itself but is rather related to differences in relative dog velocity; small dogs will travel at a relatively faster velocity than large dogs when they are measured at the same absolute dog speed.10 Larger Greyhounds, for example, used fewer and longer strides than smaller Labrador Retrievers when traveling at the same absolute velocity across 4 force platforms, but these differences mostly disappeared when the variables were evaluated at a similar relative dog velocity.10 For the GRFs this implies

c Copyright 2010 by The American College of Veterinary Surgeons Veterinary Surgery 39 (2010) 863–869

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that a small dog with fast and short strides will have shorter stance times (ST) and smaller VI compared with a large dog that is traveling at the same absolute velocity.9 A small dog will also have higher PVF because of a more dynamic hit of the foot on the plate.9 Standard normalization of the GRFs to BW therefore seems insufficient to account for differences between body sizes, and relative velocities respectively. Normalizing the temporal gait variables to body size, in addition to normalizing the forces to BW according to the theory of dynamic similarity is a scaling method that produces comparable values between dogs of different sizes.11,12 Re-scaling the gait variables might also reveal information on factors influencing GRFs that are not related to body size and/or relative dog velocity. We evaluated the dependency of vertical GRFs on BW, body size, and absolute velocity at which the dog is lead across the force plate at the trot. A large number of dogs of different body sizes were investigated while strictly controlling dog velocity and acceleration/deceleration during measurements. We hypothesized that vertical GRFs of both the thoracic and pelvic limbs would have a significant dependency on dog size and relative velocity, and that re-scaling the GRFs would produce comparable values between dogs. A second aim was to establish size-adjusted reference values that could be used for comparison in future clinical trials.

MATERIAL AND METHODS Dog Population The study population was 129 orthopedically healthy dogs (31 breeds) aged 4 months to 13 years old (mean SD, 4.1 2.8 years). Dogs belonged to the staff of our institution or were from breeding clubs. Every dog had a complete clinical gait and orthopedic examination. Inclusion criteria were absence of lameness from owner history, absence of clinically detectable lameness, and absence of abnormal findings on orthopedic examination. Absence of lameness was also confirmed after force plate gait analysis by calculating a symmetry index (SI) of PVFs between paired limbs.2,13 Based on a previous study,2 dogs with a SI o 6 were considered to be sound, and were included. Mean SI of the thoracic limbs was 0.46 3.4, and mean SI of the pelvic limbs was 0.26 3.4. BW of each dog was measured, and the height at the withers (WH) was determined with a scale measure of the type used at dog shows and competitions (Meiko AG, Villmergen, Switzerland). BWs were between 13.4 kg and 78 kg (mean, 39.6 14.5 kg). WHs ranged from 0.42 to 0.87 m (mean, 0.66 0.10 m). Force Plate Gait Analysis A force plate (OR6-7 from AMTI with Acquire 7.3 software, Advanced Medical Technologies Inc., Watertown, MA) embedded in an 8 m runway was used to measure GRFs of

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the thoracic and pelvic limbs. Dogs were allowed to explore the environment before measurements started. Dogs were lead across the force plate by their owners who were similarly instructed by 1 investigator. Dog velocity and acceleration/ deceleration were measured with 3 pairs photoelectric cells (1 centered over the force plate, 1 each positioned 1.5 m either side of center). The dogs were lead across the force plate until 5 valid trials had been obtained for each of the left and right thoracic and pelvic limbs. A valid trial needed to have a distinct hit of a front paw on the force plate, followed by a distinct hit of the ipsilateral hind paw. Trotting velocity had to be in the range of 2.0 0.15 m/s with a maximum horizontal acceleration of o 0.3 m/s2.

Data Collection And Processing From the GRF traces ST of the thoracic and pelvic limbs (seconds), PVF of the thoracic and pelvic limbs (Newtons), and VI of the thoracic and pelvic limbs (N s) were determined. Dog mean velocity V (m/s) and acceleration (m/s2) were recorded. Data were then normalized to BW, body size or both, according to the theory of dynamic similarity.11,12 Withers height was used as characteristic length measure to describe body size. Applying this similarity approach results in nondimensional values that account for differences in BW and also for differences in body size. Completely normalized values are indicated with an asterisk (): ST were normalized to body size using the equation ST = ST/(WH/g)1/2, where g is the gravitational acceleration (9.81 m/s2). VI were normalized in 2 ways: First, VI was normalized to BW as VIBW = VI/(m g), where m is body mass (kg). VIBW was expressed as a percentage of BW (% N s/ N = %BW s). Note that by applying this widely used standard procedure, VIBW are not yet completely normalized by not accounting for their time-dependent factor. Secondly, full normalization of VIs according to dynamic similarity was calculated as VI = VI/(m g [WH/g]1/2). PVF were normalized to BW by using the standard method PVF = PVF/(m g), and were also expressed in per cent of BW (% N/N = %BW). Dog velocity was normalized to body size as V = V/(g WH)1/2. This relative, or nondimensional V (also known as Froude number) has the meaning that dogs running at the same V exert similar GRF on the ground and will have equal nondimensional contact times ST.

Data Analysis Data were analyzed with statistical software (Stat View 5.1: SAS Institute Inc, Cary, NC). The relationships between BW and WH, and the relationships between those 2 measurements and nonnormalized and normalized ST, VI, and PVF of the thoracic and pelvic limbs were evaluated using linear regression analysis. The relationships between fully


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normalized GRF and relative velocity V were also evaluated. Coefficients of determination (R2) were used to describe strength of the correlations. For each regression slope a t-test was used to determine if a significant (P o 0.05) correlation existed between variables. From regression analysis of the fully normalized data (ST, VI, PVF) versus relative velocity V, the standard error of estimate (SEest) was used to calculate a normal-value band. This band was calculated as 95% confidence interval of the population (95% CI pop = 1.98 SEest) and was overlaid on the respective regression plots. Stance Time

Vertical Impulse 200

y = 0.34x + 0.07 R2 = 0.68

0.2 0.1

120 80

0

VI BW fore (% N s / N) VI* fore (% N s / N s)

ST* fore (s / s)

0.6

0.0 0.4

600 400

40 60 BW (kg)

80

0

20

40 60 BW (kg)

80

160

20 15 10 y = 14.98x + 8.24 R2 = 0.58

5 0.5

0.6 0.7 WH (m)

0.8

0.9

120 80 40 0 0.4

y = –45.17x + 143.78 R2 = 0.18 0.5

0.6 0.7 WH (m)

0.8

0.9

100

0.9

0.3

20

25

0 0.4

1.2

800

0 0

B

y = 9.71x + 52.75 R2 = 0.93

200

40

0.0 0.4 0.5 0.6 0.7 0.8 0.9 WH (m)

1.5

1000

160

0.3

C

Peak Vertical Force

y = 2.19x – 14.71 R2 = 0.97 PVF fore (N)

ST fore (s)

0.4

BW had a positive and strong correlation with WH (P o .001, R2 = 0.72). Regression functions of absolute and normalized vertical GRFs of the thoracic limbs are shown in Fig 1. Each step of normalization reduced the dependency of the GRF variables on body measures. Very similar results were found for the corresponding regression analyses of vertical GRFs of the pelvic limbs (Table 1). Mean ( SD) trotting velocity of the dogs was 1.97 0.04 m/s, and the horizontal acceleration was

PVF* fore (% N / N)

0.5

VI fore (N s)

A

RESULTS

y = 0.46x + 0.82 R2 = 0.21 0.5

0.6 0.7 WH (m)

0.8

0.9

80 60 40 y = 4.56x + 67.02 R2 = 0.01

20 0 0.4

0.5

0.6 0.7 WH (m)

0.8

0.9

Figure 1 Stance times (ST), vertical impulses (VI), and peak vertical forces (PVF) of the thoracic limbs from 129 dogs. Five force plate trails of each dog were averaged, and values of both thoracic limbs were pooled. (A) Regression of absolute values versus withers height (WH) or body mass (BW), respectively. Beside the expected strong dependency of the GRF variables on body mass, the correlation of ST on dog size was also remarkable. (B) Regression of BW normalized PVF and VIBW versus WH. Abscissa values are given as % of BW. It is clearly visible that after normalizing VI to BW a strong positive dependency on WH (body size) remains. In contrast, BW-normalized PVF revealed a slight negative dependency on WH. (C): ST and VI after re-scaling of the abscissas to account for the various body sizes of the dogs. This re-scaling process was based on a dynamic similarity approach (see text) using WH as size quantifier. ST and BW-normalized VI were divided by (WH/g)1/2 to derive the dimensionless values ST and VI. Regression equations and coefficient of determination (R2) are given for each regression. With the exception of VI versus WH (row C) all regression slopes were significant (P o .001).


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Table 1 Regression Functions of Pelvic Limb Stance Times (ST), Vertical Impulses (VI), and Peak Vertical Forces (PVF) with Body Weight (BW) and Withers Height (WH) of 129 Dogs Absolute Values

Units

Regression Equation

R2

Slope P

ST VI PVF Normalized to BW VIBW PVF Normalized to size (WH) ST VI

seconds Ns Newtons

= 0.313 WH10.057 = 1.29 BW–9.01 = 6.49 BW120.2

0.59 0.96 0.91

o .001 o .001 .01

% N s/N % N/N

= 11.3 WH13.09 = 7.57 WH177.1

0.65 0.00

o .001 .271

s/s % N s/N s

= 0.463 WH10.709 = 13.3 WH132.0

0.17 0.14

o .001 o .001

Regression equations, coefficients of determination (R2), and t-test probability for slope (slope P) are reported. Results are summarized as (1) absolute values (no normalization), (2) BW-normalized GRFs, and (3) size-normalized ST and VI (time-dependant variables). As for the thoracic limbs (Fig 1), absolute values strongly correlated with BW and WH, respectively. After normalizing VI to BW a strong positive dependency on body size (represented by WH) remained, whereas BW-normalized PVF was no longer size dependant. Re-scaling VI and ST to body size (WH) according to the dynamic similarity approach markedly reduced dependency of ST and VI on body size. A small positive correlation remained.

0.14 0.04 m/s2. When the fully normalized GRF variables were analyzed against relative dog velocity V, the regression slopes changed direction (Fig 2). This occurred because smaller dogs with higher relative velocities were now represented on the right instead of the left side of the ordinate. Regression slopes were significant (P o .001), with the exception of those of thoracic limb VI, and Stance Time

0.5 y = –0.80x + 1.75 R2 = 0.23 0.7 V*

ST* hind (s / s)

0.8

(ms–1

/

0.9

60 45 30 15 0 0.6

1.0

ms–1) 90

1.3 1.0 0.8 0.5 y = –0.85x + 1.68 R2 = 0.21

0.3 0.7

0.8

0.9

V* (ms–1 / ms–1)

y = –12.82x + 80.06 R2 = 0.02 0.7 V*

1.5

0.0 0.6

75

1.0

75

0.8

(ms–1

/

0.9

40

30 15 0.9

V* (ms–1 / ms–1)

y = 62.65x + 65.12 R2 = 0.12 0.7 V*

45

0.8

80

ms–1)

y = –23.45x + 59.06 R2 = 0.16

0.7

120

0 0.6

1.0

60

0 0.6

PVF* fore (% N / N)

0.8

160

1.0

160 PVF* hind (% N / N)

1.0

VI* fore (% N s / N s)

1.3

0.0 0.6

Peak Vertical Force

90

0.3

B

Vertical Impulse

1.5

VI* hind (% N s / N s)

ST* fore (s / s)

A

pelvic limb PVF, but the remaining correlations were weak. Because of the quasiconstant absolute velocity, the alteration of V is predominantly caused by different dog sizes. The smallest dog with a WH of 0.42 m and a dimensionless V of 0.95 is trotting 45% faster than the largest dog that was twice as tall (WH, 0.87 m; V of 0.65).

0.8

(ms–1

/

0.9

1.0

ms–1)

y = 15.31x + 60.17 R2 = 0.01

120 80 40 0 0.6

0.7

0.8

0.9

1.0

V* (ms–1 / ms–1)

Figure 2 Nondimensional stance times (ST), vertical impulses (VI) and peak vertical forces (PVF) as they depend on relative velocity V. (A) = thoracic limbs (B) = pelvic limbs. V is a normalized velocity which accounts for the size of the dogs. Animals moving at an equal V (equal Froude number) will have equal normalized limb impulses as well as the same normalized ST. Note that the regression slopes have changed direction because the smaller patients with a higher V are now represented on the right side of the regression line. Regression lines and equations are given together with a 95% confidence band of the observations; by a 95% probability further observations will be expected to lie within this band. Regression slopes were significant (P o .001) with the exception of those of thoracic limb VI and pelvic limb PVF.

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Table 2


Stance times (ST), Vertical Impulses (VI), and Peak Vertical Forces (PVF) of Thoracic and Pelvic Limbs from 129 Dogs at the Trot Thoracic Limbs

Pelvic Limbs

Absolute Values

Units

Mean SD

cv (%)

95% CI pop

Mean SD

cv (%)

95% CI pop

ST VI PVF Normalized to BW VIBW PVF Normalized to size ST VI

seconds Ns Newtons

0.291 0.039 72.1 32.2 437.1 145.4

14 45 33

0.213–0.368 8.4–135.9 149.3–724.9

0.261 0.039 42.2 19.0 277.2 98.3

15 45 35

0.185–0.338 4.5–79.9 82.5–471.9

% N s/N % N/N

18.0 1.9 114.2 10.1

10 9

14.3–21.8 94.1–134.3

10.5 1.3 72.2 7.4

13 10

7.9–13.2 57.5–86.8

1.12 0.10 70.0 4.8

8 7

0.94–1.31 60.6–79.4

1.01 0.10 40.7 3.3

10 8

0.81–1.22 34.1–47.2

s/s % N s/N s

Means SD, coefficients of variation (cv), and, and a 95% confidence interval of the population (95% CI pop) are reported. Results are summarized as (1) absolute values (no normalization), (2) BW normalized GRFs, and (3) size normalized ST and VI (time-dependant variables). Note that the cvs, and the ranges of the 95% CI pop were large for absolute values, were markedly reduced after normalization of GRFs to BW, and got again smaller after normalization of time-dependent variables to body size. The asterisk () indicates variables fully normalized to BW and/or body size (see text).

Means SD, coefficients of variation (cv), and 95% CI pop of ST, VI, and PVF (absolute values, normalized to BW, and normalized to size) are summarized in Table 2.

DISCUSSION Our results demonstrate the influence of body mass, body size, and dog velocity on ST and vertical GRFs at the trot. In contrast to other studies,3–5,9,10,14 timing and force data of a large group of dogs with various body sizes were examined concurrently. We found that standard normalization of GRFs to BW is insufficient to account for differences in body size when evaluating time-dependent variables. At a given velocity, small dogs need to travel at a relatively higher speed than large dogs to cover the same distance over the same time.10 Time-associated variables are therefore largely dependent on dog size and relative velocity; neglecting normalization of ST and VI to dog size will result in false positive differences between dogs. Normalizing ST and VI to body size, the latter in addition to BW, eliminated most differences between dogs in our study. Full data normalization was based on the theory of dynamic similarity,11,12 and the respective variables are labeled with an asterisk () in this report. A small dependency of the fully normalized ST, VI, and PVF on dog size remained, with the exception of thoracic limb VI, and pelvic limb PVF. This effect was caused by differences in relative velocities between dogs. Larger dogs had longer ST than smaller dogs. Dependency of ST on dog size decreased after normalization to body size (Fig 1); coefficients of variation of thoracic and pelvic limb STs decreased from 14% to 8%, and from 15% to 10% respectively (Table 2). Body size was then still responsible for 20% of the remaining variability (R2: 0.21 in Fig 1C). This is caused by differences in relative velocities between small and large dogs, and by the close relation of dog velocity and ST.4,5,9,10 Because of the strong dependency of ST and dog velocity, the use of ST as a control

variable has been suggested to be as, or even more, useful than absolute dog velocity in study design.4,5,15 Although ST would provide a good indirect description of relative dog velocity in sound animals, there are drawbacks of using this method. First, it is technically more difficult to aim at similar STs between dogs than it is to aim at similar dog velocities. Secondly, and more importantly, use of ST as a control variable when investigating lame dogs is questionable because lameness would naturally influence ST. In horses with an experimentally induced thoracic limb lameness, impulse is redistributed to the sound contralateral limb, and ST of both the lame and sound limb are distinctly prolonged to avoid possible overload of the compensating sound limb.16 Coefficients of variation decreased from 45% (absolute VI) to 10% and 13% for the thoracic and pelvic limbs, respectively, when VI was normalized to BW according to the standard procedure. Despite this markedly reduced dependency on dog size, 58% of the remaining variability could still be attributed to dog size (R2: 0.58; Fig 1B). Very similar correlations strengths have been observed previously at the walk using standard normalization.9 The dependency of VI on dog size was completely eliminated (thoracic limbs) or markedly reduced (pelvic limbs) after additionally normalizing the VI to body size. This is an expected finding because the impulse is the average force times the ST, and normalizing VI to body mass only does not account for the time-associated fraction. The usual standard normalization of PVF to body mass was able to eliminate most of the differences between dogs of different sizes. For PVF, normalization to BW is also the normalizing procedure that entirely fulfils the dynamic similarity approach. Coefficients of variation decreased from 34% to 10% after BW normalization. From this remaining variability another 18% of the variability of PVF of the thoracic limbs (R2: 0.18, Fig 1B) could still be attributed to differences in body size, whereas in the pelvic limbs PVF was no longer size dependant. The remaining dependency of fully normalized PVF of


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the thoracic limbs on body size is again an indirect effect caused by differences in relative velocities. Smaller dogs running at high relative velocities V had shorter relative ST, thus presumably also longer suspension times that resulted in a more dynamic hit of the foot on the force plate, and as a consequence higher PVF. A similar relationship between PVF normalized to BW and body size has been described previously at a walk, using bone length as characteristic length measure.9 Variability in gait variables is problematic when comparing values between different dogs or dog groups and precludes the formulation of reference values to which a single dog can be compared. As seen above, the theory of dynamic similarity enables re-scaling of gait variables to body mass and size to derive comparable results. Although full normalization of gait variables to BW and WH results in marked reduction of gait parameter variability between dogs of different sizes when compared with standard normalization to BW alone (Fig 1), the importance of the theory of dynamic similarity is that only gait variables derived at equal dimensionless velocities V are similar and directly comparable.11,12 Relative velocity V has a close relationship with body size of the dog. This means that when dogs of different sizes are trotted across the force plate at a set subject velocity, their relative velocities V will be different and their gait variables are therefore still not perfectly comparable. The best guess to account for relative velocity V is creating a reference band for the normalized GRF variables that is dependent on the relative velocity V (Fig 2). Future gait data from trotting dogs could then be compared with this reference-band after normalization of data to BW and body size. Although dog size ranges nearly doubled from the smallest to the largest dog, there was only a narrow range of V in the present data. Relative velocity V was mainly altered according to the different WH of the dogs, because absolute dog speed was strictly controlled. Within the observed range, 0–12% of the PVF variability, 0–16% of the VI variability, and 20% of the ST variability were caused by differences in V. When planning investigations with dogs of different sizes it would be preferable to lead each dog at an individual velocity Vind = V (WH g)1/2 that accounts for its own size. Thus, the dogs would all run at the same relative velocity V. Assuming a V = 0.8 (this was the mean V in our investigation), then the largest dog (WH: 0.87 m) should had run with a Vind = 2.34 m/s, and the smallest dog (WH: 0.42 m) with a Vind = 1.62 m/s to get identical normalized values. The remaining variability in the normalized variables that could not be explained by alterations in relative velocity is because of unknown factors. In gait analysis, besides velocity variables, limb length is the most dominant measure that influences stride and ST. Unfortunately, the exact length of the limb is hard to determine especially in the thoracic limb, thus WH was used as size measure in our study because it is easy to obtain. Other authors have used functional limb length10 or bone length9 to describe body size. Whatever length measure is used, it can only provide a

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crude description of body size. Factors, such as general body build, head and neck length, thoracic and pelvic muscle mass are ignored in the calculations, but they could possibly cause distinctively different gaits patterns between dogs or dog breeds.10 These potential relationships should be evaluated and applying the dynamic similarity approach would be useful to gain insight into possible influences of these variables. Summarily, we found that normalization of forces to BW eliminates most of the size-dependent variability. Time-associated GRF variables must also be normalized to body size to control for variation in body size. To do this, WH or another characteristic length measure must be measured and declared. Some size-dependent variability ( o 23% for all variables) remains even after full normalization of vertical GRF, which is caused by differences of relative velocity between dogs.

ACKNOWLEDGMENTS This work was performed at the University of Zurich.

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15. Renberg EC, Johnston SA: Comparison of stance time and velocity as control variables in force plate analysis in dogs. Am J Vet Res 1999;60:814–819 16. Weishaupt MA, Wiestner T, Hogg HP, Jordan P, Auer JA: Compensatory load redistribution of horses with induced weight-bearing forelimb lameness trotting on a treadmill. Vet J 2006;171:135–146


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