Fourier Analysis of Horse feet

7/30/2019 Fourier Analysis of Horse feet

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Journal of Biomechanics 35 (2002) 11731182

Fourier analysis of trunk displacements: a method to identify the

lame limb in trotting horses

Fabrice Audigi!ea,*, Philippe Pourcelotb, Christophe Degueurceb, Didier Geigerc,Jean Marie Denoixa

aCIRALE-IPC-UMR INRA-ENVA Biom !ecanique et Pathologie Locomotrice du Cheval-RN 17514430 Goustranville, FrancebUMR INRA-ENVA Biom!ecanique et Pathologie Locomotrice du Cheval-Ecole Nationale V!et!erinaire dAlfort-7,

Av du Gal de Gaulle 94704 Maisons-Alfort Cedex, FrancecE.A. CNRS 7052-Laboratoire de M!ecanique Physique-Universit!e Paris XII-Av du Gal de Gaulle 94000 Cr !eteil, France

Accepted 8 May 2002

Abstract

The aim of this paper is to present a method allowing the identification of the lame limb in trotting horses. Using a 3-D kinematic

analysis system, 13 sound and 25 lame horses fitted with 4 skin markers placed on the dorsal midline of their trunk were recorded

while trotting on a track in the conditions of the routine lameness examination. The vertical displacements of the trunk markers

underwent Fourier analysis. Results indicated that these displacements could be represented using only the first and second

harmonics. From these two harmonics, indices were then developed. The sensitivity of these indices to the different types of

experimental errors was also studied. Results showed that the values of the indices of the lame horses were relatively unaffected by

the experimental errors. In lame horses, these indices allowed the quantification of the degree of the lameness, the identification of

lame limb with a reliability >95% and the characterisation of the type of trunk movements. These indices could be easily

implemented in a computer program to provide objective information to the clinician or to be used as a first step in the development

of an expert system. Moreover, these clinical tools may also be extended to other quadrupedal or bipedal locomotions. r 2002

Elsevier Science Ltd. All rights reserved.

Keywords: Kinematics; Fourier series; Lameness; Trunk; Symmetry

1. Introduction

The diagnosis of equine lameness is an intricate task,

even for trained clinicians. During the traditional

clinical lameness examination, the veterinarian evaluates

the locomotion pattern of the horse at trot to score

subjectively the severity of the lameness, to identify the

lame limb and to hypothesise the anatomical location of

the locomotor injury. To achieve these aims, evaluation

of the asymmetry in head and trunk movements has a

major role. Because of Newtons second law and the fact

that trunk contains most body mass, asymmetries in

head and trunk movements allow lame horses to reduce

the vertical ground reaction force in their painful limb

(Vorstenbosch et al., 1997). Therefore several methods

have been developed to quantify objectively the severity

of equine lamenesses using head and trunk kinematic

data (Buchner et al., 1993, 1996; Keegan et al., 2001;

May and Wyn-Jones, 1987; Peham et al., 1996, 1999,

2001; Uhlir et al., 1997).

Fourier analysis of kinematic variables has proved to

be an effective tool for the study of cyclic live motion

pattern (Cappozzo and Gazzani, 1983). In human

studies, Fourier analysis has been used previously to

decompose trunk movements into an intrinsic pure form

of movement pattern (the stereotype) eventually de-

formed by some extrinsic causes such as locomotor

asymmetries or environmental disturbances (Cappozzo,

1981, 1984; Cappozzo et al., 1982; Crowe et al., 1995).

Recently, Fourier analysis of the vertical movements of

the head and sacral bone has been used in fore- and

hindlimb lame horses to quantify the lameness degree

(Keegan et al., 2001; Peham et al., 1996) and to compare

the subjective judgement of a clinician with the

computerised symmetry measurements (Peham et al.,

1999, 2001). In these last studies, authors used also

*Corresponding author. Tel.: +33-2-31-27-85-53; fax: +33-2-31-27-

85-57.

E-mail address: [email protected] (F. Audigi!e).

0021-9290/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 2 1 - 9 2 9 0 ( 0 2 ) 0 0 0 8 9 - 1


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Fourier analysis to assign the lameness to the lame limb.

Several studies (Buchner et al., 1996; Peham et al., 1996,

1999, 2001; Uhlir et al., 1997) have also proposed

kinematic parameters to identify the lame limb. Never-

theless in these studies, the discrimination between fore-

and hindlimb lame horses was based on the decision of

the clinician. Therefore, to the authors knowledge, nomethod allowing an entirely automatic identification of

the lame limb in a fore- or hindlimb lame horse has been

reported. Consequently, the purpose of this paper was

to adapt Fourier analysis to the trunk displacements of

trotting horses in order to: (1) quantify the lameness

degree, (2) identify the lame limb and (3) characterise

using numerical data the pattern of trunk displacements.

In the long term, such numerical data would make it

possible to determine whether or not a particular injury

of the locomotor apparatus generates a particular

pattern of trunk displacement.

2. Materials and methods

2.1. Horses

Two groups of horses were studied. The reference

group consisted of 13 sound French Warmblood horses

(3 females and 10 geldings, ranging in age from 6 to 13

years) from the R!egiment de Cavalerie de la Garde

R!epublicaine. A detailed clinical examination confirmed

that each horse was clinically free of lameness.

The group of lame horses consisted of 25 horses

presented to the Veterinary School of Alfort for a

lameness (Table 1). All horses underwent a detail clinicalexamination which showed that 12 horses presented a

unilateral forelimb lameness and 13 horses presented a

unilateral hindlimb lameness. The degree of lameness

was scored by an experienced clinician on a scale of 04

(0=sound; 1=mild; 2=moderate; 3=severe; 4=non-

weightbearing lameness; Dyson, 1991).

2.2. Data acquisition

Four retroreflective skin markers were placed on the

dorsal midline of the trunk of each horse (Fig. 1) over

the sixth thoracic vertebra (i.e. top of the withers), the

13th thoracic vertebra, the first lumbar vertebra and

over the lumbosacral junction (i.e. tuber sacrale). One

additional marker was glued to the dorsolateral wall of

each fore hoof. Fore hoof landing defined as the instant

when the hoof marker passed the horizontal velocity

limit of 0.1 m/s (Buchner et al., 1993) was used to

determine the stride duration and to identify the left (left

Table 1

Characteristics of the 25 lame horses

Horse Age (years) Breed Sex Lameness degree Lame limb Diagnosis

Forelimb lameness1 4 FT F 1 LF Osteoarthritis shoulder

2 6 FW G 1 RF Tendinitis extensor carpi radialis

3 7 AA G 1 RF Podotrochlear syndrome

4 9 FW F 1 RF Osteoarthritis carpal joint

5 12 A S 1 RF Tendinitis deep digital flexor tendon

6 8 FW F 2 LF Distal enthesopathy of the biceps brachii

7 12 FW G 2 LF Osteoarthritis distal interphalangeal joint

8 14 FW G 2 LF Podotrochlear syndrome

9 8 FW G 2 RF Podotrochlear syndrome

10 10 AA G 2 RF Osteoarthritis shoulder+elbow

11 12 FW G 3 LF Tendinitis superficial digital flexor tendon+desmopathy of the palmar ligament

12 6 FW F 3 RF Tendinitis third interosseous muscle

Hindlimb lameness

13 11 FW G 1 RH Osteoarthritis knee+osteochondrosis tibial cochlea

14 9 T G 1 RH Infection of the hoof 15 6 FW F 1 LH Osteoarthritis tarsal joint+cunean bursitis

16 7 AA G 1 LH Osteoarthritis tarsal joint

17 8 FW G 1 LH Osteoarthritis metatarsophalangeal joint

18 9 T G 2 RH Old metacarpal wound

19 14 FT G 2 RH Osteoarthritis tarsal joint

20 4 FW F 2 LH Osteoarthritis hip

21 10 FW G 2 LH Osteoarthritis tarsal joint

22 17 AA F 2 LH Osteoarthritis knee+meniscal injuries

23 8 FW G 3 RH Neurologic disorder (stringhalt)

24 13 FW F 3 RH Tendinitis superficial digital flexor tendon (tarsal level)

25 9 FW G 3 LH Tendinitis third interosseous muscle

A: Arabian; AA: Anglo-Arabian; FT: French trotter; FW: French warmblood; T: thoroughbred; F: female; G: gelding; S: stallion; LF: left forelimb;

RF: right forelimb; LH: left hindlimb; RH: right hindlimb.

F. Audigi!e et al. / Journal of Biomechanics 35 (2002) 117311821174


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forelimbright hindlimb) and right (right forelimbleft

hindlimb) diagonal stance phases.

Horses were guided by hand on an outdoor examina-

tion track 20 m long until at least 5 correct runs were

done (Drevemo et al., 1980). Horses were trotted at their

own comfortable speed, ranging from 3.0 to 3.5 m/s in

sound horses and from 2.9 to 3.6 m/s in lame ones.

Recordings were realised as previously described (Pour-

celot et al., 1997a) using four 8 mm video cameras (Sony

FX 700, 50 Hz) placed in such a way that each side of

the horse was filmed by 2 cameras. The cameras werefocused to image a 5.50 m long field of view. After

digitisation of the 2-D video recordings, the 3-D

trajectories of the markers were calculated using the

Direct Linear Transformation technique (Abdel-Aziz

and Karara, 1971).

2.3. Harmonic analysis of vertical displacements of trunk

markers

For each horse, five runs were analysed. For each

trial, harmonic analysis was carried out on the stride

placed in the centre of the recording field of view. Forthis stride, the experimental vertical displacement (Zexp)

of each trunk marker was used to calculate the following

function of time (t):

ZFt A0 Xi2i1

Ai cos i2p

Tt fi

;

where A0 is the mean value of the displacement over the

stride period (T), Ai and fi are the amplitude and phase

of the ith harmonic, respectively (Fig. 2). The assump-

tion of taking into account only the first and second

harmonics of Fourier series to represent the experi-

mental vertical displacement was evaluated by calculat-

ing for each trial and each trunk marker the following

ratio (Hottinger et al., 1996):

%Reconstruction

1

PFrame tTFrame t0 Zexp ZF

2PFrame tTFrame t0 Zexp A0

2

! 100:

The value of this ratio represents the percentage of

reconstruction of the experimental displacement ob-

tained with A0 and the first and second harmonics.

Thus, this ratio measures the closeness of fit.

Three types of errors may alter the previous harmonic

analysis: (1) the experimental vertical coordinates of the

trunk markers are affected by random errors introduced

during the digitisation process. In our experimental set-

up, these errors were estimated normally distributed

with a zero mean and a standard deviation (sd) of 1 mm.

(2) The experimental vertical coordinates of the trunk

markers are affected by systematic errors due to lens

distortions and other comparator deformations. These

errors were modelled by a second-order polynomial

function (Chen et al., 1994) with a magnitude of 5 mm in

our conditions. (3) Because the vertical displacements of

the trunk are not strictly periodic over one stride

duration, calculation of Fourier coefficients over one

stride duration introduced inaccuracies. To take into

account one frame error in selection of start and end of

stride cycle, the stride period (T) used to calculate

Fig. 2. Harmonic analysis over one stride duration of the vertical

displacement of a trunk marker at trot. Typical example of a sound

horse and a lame one. (): experimental vertical displacement; ( ):

A0 (mean value of the displacement); (): first harmonic; (- - - - -):

second harmonic; (n): displacement obtained with A0; the firstharmonic and the second one.

Fig. 1. Position of the markers: T6: sixth thoracic vertebra; T13:

thirteenth thoracic vertebra; L1: first lumbar vertebra; LS: lumbosacral

junction.

F. Audigi!e et al. / Journal of Biomechanics 35 (2002) 11731182 1175


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Fourier coefficients was defined in this study as the

stride duration eventually corrected by 71 sampling

interval (20 ms). In this way, the maximal errors in the

integration period were reduced to 70.5 sampling

interval. The effects of these three types of errors on

the amplitude and phase values of the harmonics were

quantified as previously described (Cappozzo, 1981;Cappozzo and Gazzani, 1983) using a general sensitivity

analysis. Because these effects depend on the values of

the harmonic parameters, they were evaluated for the

sound horses and for the 3 degrees of lameness. For

both sound and lame horses, this sensitivity analysis was

performed using simulated errors in the movement data

of one trial per horse.

2.4. Quantification of the lameness degree

In trotting horses, the vertical displacement of trunk

markers showed two oscillations per stride, one oscilla-tion per diagonal stance phase (Fig. 2). Therefore, the

second harmonic which makes equal contributions to

each vertical oscillation reflects the symmetric part of

the movement and is known as intrinsic harmonic

(Cappozzo, 1981; Crowe et al., 1995). The first harmonic

which makes unequal contributions to the two vertical

oscillations reflects the asymmetric part of the move-

ment and is known as extrinsic harmonic. For each trial,

the locomotion symmetry was quantified by calculating

for each marker the energy ratio (ERz)

ERz

A22

A21 A22 100:

The values of this ratio range from 0% to +100%,

100% standing for perfect symmetry. For each marker,

the 5 ERz obtained for each horse were used to calculate

the mean7sd ERz: The sd calculated over 5 trialsquantified the intra-individual variability of the ERz:The means calculated for 13 sound horses were averaged

to obtain the mean ERz of the sound horses. The sd of

the mean of these 13 mean ERz quantified the inter-

individual variability of the ERz in the sound horses.

Assuming the mean ERz values of the sound horses

were normally distributed, the mean ERz

of the 13

sound horses 72 times the value of the inter-individual

variability represented the 95% confidence interval.

Thus, for a lame horse, a mean ERz value outside this

confidence interval was considered statistically different

(po0:05).Similar calculations were performed for the difference

between the ERz values of T6 and LS. This parameter

(T6-LS) was used to compare the level of symmetry of

the cranial part of the trunk with respect to its caudal

part. As was the case for the mean ERz values, the mean

T6-LS value of a lame horse was compared to those of

the sound horses to identify statistical differences.

2.5. Identification of fore- and hindlimb lamenesses

To distinguish fore- and hindlimb lamenesses, it could

be hypothesised that the symmetry of trunk displace-

ments is more altered in the cranial part of the trunk in

forelimb lamenesses and in the caudal part of the trunk

in hindlimb lamenesses. Thus, the following binarydecision was tested using our 25 clinical cases: a lame

horse with a mean T6-LS value lower than the mean T6-

LS value of the sound horses presented a forelimb

lameness and a lame horse with a mean T6-LS value

higher than the mean T6-LS value of the sound horses

presented a hindlimb lameness.

2.6. Identification of the lame side and characterisation of

trunk displacements

In lame horses, one of the roles of the asymmetric

movements of the trunk is to reduce the loading of thelame limb during its stance phase (Buchner et al., 1996).

Therefore, once fore- and hindlimb lamenesses were

distinguished, it could be hypothesised that the analysis

of the pattern of trunk movement would allow to

identify the lame side.

The shape of the vertical displacement of trunk

markers could be characterised by the different harmo-

nic phase values. Thus, the following parameter was

calculated for each trial of a lame horse

Df f2

2

f1:

The Df parameter was calculated using the displace-

ments of T6 for the forelimb lamenesses and the

displacements of LS for the hindlimb ones. To test the

efficiency of this parameter as a lame side indicator, the

time origin, with respect to which harmonic phases were

calculated, coincided with the landing of the lame

diagonal. In this case, the relationship between Df

values and the shape of the vertical displacement of a

trunk marker is shown in Fig. 3. For each stance phase,

two ranges of vertical displacement could be calculated:

the restraint range (difference between the maximal

height reached just before the beginning of the stance

phase and the minimal height reached near midstance)

and the propulsion range (difference between the

maximal height reached just after the end of the stance

phase and the minimal height reached near midstance).

The propulsion range of the lame diagonal is smaller

than that of the sound one for Df values ranging from

451 to +1351, whereas the restraint range of the lame

diagonal is smaller than that of the sound one for Df

values ranging from +451 to 1351. Previous studies

(Buchner et al., 1996; Peloso et al., 1993) have shown for

induced lamenesses that the propulsion range of the

lame diagonal was smaller than that of the sound



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diagonal. Therefore, we have tested the hypothesis that

mean Df values of the 25 clinical cases ranged from

451 to +1351.

3. Results

3.1. Harmonic analysis of vertical displacements of trunk

markers

The high values of the percentage of reconstruction

(Table 2) showed that the vertical displacement of trunk

markers could be represented with accuracy using only

the first and second harmonics. These harmonics

allowed to reconstruct at least 95% of the trials with

an accuracy X99% (Table 2).

For one trial, the maximal errors in the ERz and

Df which could be caused by random errors,

lens distortions and incorrect integration period

are presented in Table 3. Alterations of the ERzvalues were o73%. In contrast, Df values of

the sound horses could be greatly affected by

experimental errors. Thus, Df was not studied in

sound horses.

Fig. 3. Relationship between Df values of a lame horse and the pattern of trunk displacements (vertical displacements plotted were obtained with

A1 25 mm and A2 30 mm).



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3.2. Quantification of the lameness degree

The mean ERz values of the sound horses ranged

from 93% to 97% (Table 4). The mean value of T6

-

LS=3.5% which showed that the locomotion symmetry

was greater in the cranial part of the trunk than in the

caudal one. The inter-individual variability of all

parameters was smaller than the intra-individual one.

In moderate and severe forelimb lamenesses, the ER zofT6 and T13 markers were significantly decreased in all

horses. In contrast, ERz were significantly altered in

only 2 of the 5 mild forelimb lamenesses. Moreover, one

horse (horse 3) presented only a significant alteration in

the T6-LS value.

In moderate and severe hindlimb lamenesses, sig-

nificant decreases of the ERz were observed for most

trunk markers. However, the ERz presented a cranio-

caudal decrease along the trunk which showed that the

lameness proceeded from the hindlimbs. As in mild

forelimb lamenesses, significant alterations in ERzvalues were observed in only 2 of the 5 mild hindlimb

lamenesses.

3.3. Identification of fore- and hindlimb lamenesses

The mean value of T6-LS of all forelimb lamenesses

was lower than the mean value of the sound horses

which showed that the lameness proceeded from the

Table 2

Percentage of reconstruction of the experimental vertical displace-

ments of the trunk markers obtained with A0 and the first and second

harmonics

Horses T6 T13 L1 LS

Mean %

reconstruction(sd)

Sound horses 99.6 (0.3) 99.7 (0.2) 99.6 (0.2) 99.5 (0.3)

Lame horses 99.4 (0.4) 99.7 (0.2) 99.7 (0.2) 99.6 (0.2)

Percentage of

trials with a

reconstruction

%X99%

Sound horses 98 100 100 95

Lame horses 96 100 99 96

Table 3

Maximal errors in the ERz and Df values caused by experimental

errors

Horses Random

errors

Lens

distortions

Incorrect

integration

period

ERz (%)

Sound horse 70.1 70.3 70.1

Mild lameness 70.4 71.1 70.1

Moderate

lameness

70.6 71.6 70.1

Severe lameness 70.8 72.1 70.2

Df (1)

Sound horse 77 753 720

Mild lameness 71 710 73

Moderate

lameness

71 77 72

Severe lameness 71 77 72

Table 4

Mean ERz values and associated intra- (between brackets) and inter-

individual (between square brackets) variabilities of the sound and

lame horses. ERz values in bold differed significantly (po0:05) fromthose of sound horses

ERz (%) T6 T13 L1 LS T6-LS

Sound horses 96 (2) 97 (2) 96 (3) 93 (5) 3.5 (4.6)[2] [2] [2] [3] [2.8]

Forelimb lameness

Mild lameness

1 82 (5) 84 (3) 84 (3) 79 (5) 2.8 (2.8)

2 97 (2) 97 (3) 97 (2) 95 (3) 1.6 (2.7)

3 93 (2) 96 (2) 96 (2) 95 (4) 2.4 (4.9)

4 96 (3) 98 (2) 98 (2) 98 (3) 1.1 (2.0)

5 91 (3) 95 (1) 97 (1) 96 (3) 4.4 (6.1)

Moderate lameness

6 85 (7) 87 (7) 89 (7) 88 (9) 2.4 (4.0)

7 85 (9) 92 (7) 93 (5) 91 (8) 5.5 (8.4)

8 76 (9) 89 (4) 90 (3) 93 (4) 17.2 (9.8)

9 85 (4) 93 (3) 95 (2) 94 (5) 8.7 (5.9)

10 89 (2) 93 (3) 94 (3) 95 (5) 5.8 (3.0)

Severe lameness

11 75 (8) 78 (6) 78 (7) 76 (6) 0.8 (8.4)

12 85 (6) 91 (4) 93 (5) 93 (6) 7.9 (7.3)

Hindlimb lameness

Mild lameness

13 98 (1) 97 (1) 95 (2) 87 (3) 11.4 (3.8)

14 97 (2) 94 (4) 92 (5) 89 (7) 7.7 (7.1)

15 98 (2) 98 (2) 95 (4) 89 (11) 9.3 (11.4)

16 96 (4) 95 (5) 92 (8) 85 (11) 11.6 (7.6)

17 97 (3) 99 (1) 94 (4) 89 (7) 8.1 (6.4)

Moderate lameness

18 80 (7) 74 (6) 71 (5) 65 (5) 14.9 (3.2)19 82 (9) 78 (6) 72 (6) 56 (8) 25.8 (11.5)

20 91 (11) 88 (8) 80 (7) 61 (10) 30.7 (12.4)

21 95 (3) 92 (3) 83 (3) 65 (5) 29.1 (5.7)

22 95 (5) 92 (7) 87 (7) 69 (12) 25.8 (9.9)

Severe lameness

23 86 (7) 91 (5) 92 (7) 93 (9) 6.5 (10.5)

24 68 (8) 54 (7) 46 (5) 31 (4) 23.6 (6.8)

25 93 (4) 84 (5) 68 (9) 50 (12) 32.6 (9.2)



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forelimbs (Table 4). Except in one case (horse 23), the

mean value of T6-LS of all hindlimb lamenesses was

higher than the mean value of the sound horses which

showed that the lameness proceeded from the hindlimbs.

3.4. Identification of the lame side and characterisation of

trunk displacements

The mean phase values expressed with respect to the

landing of the lame diagonal are presented in Table 5.

The Df values of T6 for the forelimb lamenesses ranged

from 131 to 1281, whereas the Df values of LS for the

hindlimb lamenesses ranged from 491 to 781 (Fig. 4).

Except in one case (horse 17), mean Df values of the

lame horses ranged from 451 to +1351 which means

that the lame propulsion range was always smaller than

the sound one whereas the lame restraint range was

either smaller or greater than the sound one.

4. Discussion

Several methods have been used to determine thenumber of harmonics which adequately represent a

particular waveform (Cappozzo et al., 1975; Hottinger

et al., 1996; Jackson, 1979; Schneider and Chao, 1983;

Winter et al., 1974). The method used by Hottinger et al.

(1996) is close to that of Cappozzo et al. (1975) but has

the advantage to relate the differences between the

experimental and recomputed waveforms to the ampli-

tude of the experimental waveform. With this method,

the essential number of harmonics could be chosen as

the number of harmonics which reconstructed X95% of

the trials with a percentage of reconstruction X99%.

Such accuracy was achieved in our study with the first

and second harmonics (Table 2).

At each trial, the experimental errors described

previously caused alterations in the ERz and Df values

which magnitude differed greatly between sound and

lame horses (Table 3). Moreover, these alterations could

be considered as random over 5 trials. Therefore, the

mean value of the ERz and Df calculated for a lame

horse will probably be unaltered, whereas their sd could

be increased. In contrast, the alterations of the Df

values could not be neglected in sound horses because of

their magnitude. Thus, to determine the phase values of

sound subjects, the experimental errors should be

Table 5

Mean phase values and associated intra-individual variabilities

(between brackets) of the lame horses

Phase (1) f1 f2 Df

Forelimb lameness (T6)

Mild lameness

1 21 (7) 95 (10) 68 (8)

2 1 (74) 96 (14) 49 (73)

3 14 (25) 61 (10) 44 (28)

4 6 (53) 79 (10) 34 (55)

5 35 (28) 96 (15) 13 (21)

Moderate lameness

6 21 (18) 77 (16) 60 (17)7 80 (11) 97 (7) 128 (11)

8 53 (27) 80 (10) 93 (28)

9 2 (20) 84 (11) 43 (21)

10 23 (32) 92 (9) 69 (29)

Severe lameness

11 30 (15) 86 (5) 73 (15)

12 66 (10) 62 (7) 98 (13)

Hindlimb lameness (LS)

Mild lameness

13 96 (19) 102 (4) 45 (18)

14 10 (21) 79 (8) 50 (18)

15 21 (53) 70 (10) 56 (50)

16 12 (13) 43 (14) 9 (11)

17 96 (14) 93 (13) 49 (9)

Moderate lameness

18 42 (10) 72 (13) 78 (7)

19 1 (12) 69 (10) 35 (10)

20 4 (16) 69 (20) 31 (11)

21 8 (17) 92 (12) 38 (18)

22 23 (14) 73 (15) 13 (15)

Severe lameness

23 48 (87) 87 (19) 5 (84)

24 23 (14) 37 (22) 41 (5)

25 15 (22) 43 (37) 37 (6)

Fig. 4. MeanDf values of the 25 lame horses: forelimb lamenesses are

plotted on the small circle and hindlimb ones are plotted on the large

circle.



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corrected. Procedures were not used to correct for these

errors because Df values of sound horses were not

needed for any part of this study. The effects of random

errors and incorrect integration periods can be reduced

by using spline functions before the calculation of

Fourier coefficients (Cappozzo and Gazzani, 1983;

Soudan and Dierckx, 1979). The errors resulting fromlens distortions can be reduced by using the lens

distortion model proposed by Marzan and Karara

(1975) or by applying correction functions to the 3-D

data (Chen et al., 1994). These techniques were not used

in this study because one of our objectives was to

develop a method for identifying the lame limb which

can be easily implemented in a computer.

Differences in the placement of the hoof marker from

one horse to the next (Audigi!e et al., 1998) could

introduce a systematic error in the identification of

the hoof landing of71 sampling interval (20 ms at

50 Hz). At a slow trot, the stride duration is about

760 ms. Consequently, such an error shifts the value

off1 by 79.51 and the value off2 by 7191. Because

of its magnitude and its systematic nature, this error

could not be neglected when using low frequency

kinematic analysis system. The calculation of Df

allowed us to suppress this error. Nevertheless, care

should be taken when using such parameter because the

division of f2 could introduce discontinuities in Df

values if f2 values range from 1801 to +1801. For

example, f2 values of 1781 and 1781 are close in terms

of harmonic analysis whereas f2=2 values of 891 and891 are different.

With only three markers (T6; LS and a marker placedon one hoof), the method presented in Fig. 5 allowed us

to reach 3 objectives: (1) the quantification of the

lameness degree, (2) the identification of the lame limb

and (3) the characterisation of trunk displacements. The

quantification of the lameness degree was performed by

calculating a ratio similar to that proposed by Peham

et al. (1996), but our ratio compared the energy of the

harmonics instead of their amplitudes which were found

less discriminating. Nevertheless, significant alterations

of ERz and T6-LS values were not always found in lame

horses of degree 1. To increase the sensitivity of these

lameness indicators and to consider errors in the

evaluation of the sd of the normal group, the threshold

for lameness detection may be set at 1 sd (Merkens and

Schamhardt, 1988).

The identification of the lame limb was performed

using ERz and Df values. By convention, if the

harmonic phases are calculated with respect to the

landing of the left diagonal, sectors in Df values

indicating the lame limb could be defined (Fig. 5). These

grey sectors were determined using both the Df values

of the 25 clinical cases (Fig. 4) and the relationship

between Df values and the pattern of trunk displace-

ment (propulsion range of the lame diagonal smaller

than that of the sound one). These sectors included all

clinical cases except the horse 17 which lay just beyond

the limit of one sector. For such a boundary case, it can

be assumed that the lame limb is that corresponding to

this sector. With this assumption, the algorithm

described in Fig. 5 is in agreement with the judgement

of the experienced veterinarian in 24/25 clinical cases. Inother words, this algorithm allowed to identify the lame

limb in 24/25 clinical cases, which represents a reliability

>95%. This method has the advantage to combine the

analysis of the symmetry of movements of the cranial

and caudal parts of the trunk, whereas previous studies

have focused their analysis on the symmetry of move-

ments of the head (Peham et al., 1996, 1999) or only one

part of the trunk (Barrey and Desbrosse, 1996; Barrey

et al., 1994, 1995; Peham et al., 2001). Results obtained

for the cranial and caudal parts of the trunk allowed the

identification of the lame limb in two steps: (1)

identification of fore- or hindlimb lameness and (2)

identification of the lame side.

The identification of the lame limb was successfully

performed even for mild lame horses which presented no

statistically significant alteration of their locomotion

symmetry. In Fig. 5, the white sectors represented Df

values which were not observed in our clinical cases.

These sectors may represent either patterns of trunk

displacement caused by other locomotor injuries or

patterns never used by horses to minimise the pain

causing the lameness.

The identification of the lame limb has failed only

for horse 23. This horse presented a non-painful

lameness due to a neurological disorder in which trunkdisplacements remained relatively symmetrical. These

characteristics may explain the error made in the

distinction between fore- and hindlimb lameness. This

horse presenting large asymmetries in hindlimb move-

ments due to the neurological disorder, the distinction

between fore- and hindlimb lameness could be achieved

by quantifying the symmetry of limb movements

(Pourcelot et al., 1997b) which requires, nevertheless,

to place markers on the limbs. Because the method

described in this study is based on the analysis of

the symmetry of movements, this method is unable to

detect lamenesses in which both sides are equally

affected.

The pattern of trunk displacement could be char-

acterised quantitatively and independently of the lame-

ness degree by Df: Such parameter would make itpossible to determine whether or not a particular injury

of the locomotor apparatus generates a particular

pattern of trunk displacement. Nevertheless, the analysis

of a great number of lame horses is required to answer

to such a question and to complete and refine the

method described in this study. In the same way, it

would be of interest to perform these analyses more than

once in the same lame horses.



9/10

Fig. 5. Algorithm used to quantify the lameness degree, to identify the lame limb and to characterise the pattern of trunk displacements.



10/10

Acknowledgements

This study was supported by the Institut National de

la Recherche Agronomique and the Service des Haras et

de LEquitation.

References

Abdel-Aziz, Y.I., Karara, H.M., 1971. Direct linear transformation

from comparator coordinates into object-space coordinates in

close-range photogrammetry. In: Proceedings of the ASP/UI

Symposium on Close-Range Photogrammetry. American Society

of Photogrammetry, Falls Church, VA, pp. 118.

Audigi!e, F., Pourcelot, P., Degueurce, C., Denoix, J-M., Geiger, D.,

1998. Asymmetry in placement of bilateral skin markers on

horses and effects of asymmetric skin marker placement on

kinematic variables. American Journal of Veterinary Research

59, 938944.

Barrey, E., Desbrosse, F., 1996. Lameness detection using an

accelerometric device. Pferdeheilkunde 12, 617622.Barrey, E., Hermelin, M., Vaudelin, J.L., Poirel, D., Valette, J.P.,

1994. Utilisation of an accelerometric device in equine gait analysis.

Equine Veterinary Journal Supplement 17, 712.

Barrey, E., Auvinet, B., Courouc!e, A., 1995. Gait evaluation of race

trotters using an accelerometric device. Equine Veterinary Journal

Supplement 18, 156160.

Buchner, F., Kastner, J., Girtler, D., Knezevic, P.F., 1993. Quantifica-

tion of hind limb lameness in the horse. Acta Anatomica 146,

196199.

Buchner, H.H.F., Savelberg, H.H.C.M., Schamhardt, H.C., Barne-

veld, A., 1996. Head and trunk movement adaptations in horses

with experimentally induced fore- or hindlimb lameness. Equine

Veterinary Journal 28, 7176.

Cappozzo, A., 1981. Analysis of the linear displacement of the head

and trunk during walking at different speeds. Journal ofBiomechanics 14, 411425.

Cappozzo, A., 1984. Gait analysis methodology. Human Movement

Science 3, 2750.

Cappozzo, A., Gazzani, F., 1983. Comparative evaluation of

techniques for the harmonic analysis of human motion data.

Journal of Biomechanics 16, 767776.

Cappozzo, A., Leo, T., Pedotti, A., 1975. A general computing method

for the analysis of human locomotion. Journal of Biomechanics 8,

307320.

Cappozzo, A., Figura, F., Gazzani, F., Leo, T., Marchetti, M.,

1982. Angular displacements in the upper body of AK amputees

during level walking. Prosthetics and Orthotics International 6,

131138.

Chen, L., Armstrong, C.W., Raftopoulos, D.D., 1994. An investiga-

tion on the accuracy of three-dimensional space reconstructionusing the direct linear transformation technique. Journal of

Biomechanics 27, 493500.

Crowe, A., Schiereck, P., de Boer, R.W., Keesen, W., 1995.

Characterization of human gaits by means of body center of mass

oscillations derived from ground reaction forces. IEEE Transac-

tions on Biomedical Engineering 42, 293303.

Drevemo, S., Dalin, G., Fredricson, I., Hjert!en, G., 1980.

Equine locomotion: 1. The analysis of linear temporal stride

characteristics of trotting Standardbreds. Equine Veterinary

Journal 12, 6065.

Dyson, S.J., 1991. Desmitis of the accessory ligament of the deep

digital flexor tendon: 27 cases (19861990). Equine Veterinary

Journal 23, 438444.

Hottinger, H.A., DeCamp, C.E., Olivier, N.B., Hauptman, J.G.,

Soutas-Little, R.W., 1996. Noninvasive kinematic analysis of the

walk in healthy large-breed dogs. American Journal of Veterinary

Research 57, 381388.

Jackson, K.M., 1979. Fitting of mathematical functions to biomecha-nical data. IEEE Transactions on Biomedical Engineering 26,

122124.

Keegan, K.G., Pai, P.F., Wilson, D.A., Smith, B.K., 2001. Signal

decomposition method of evaluating head movement to measure

induced forelimb lameness in horses trotting on a treadmill. Equine

Veterinary Journal 33, 446451.

Marzan, G.T., Karara, H.M., 1975. A computer program for direct

linear transformation solution of colinearity condition, and some

applications of it. In: Proceedings of the Symposium on Close-

Range Photogrammetric Systems, Champaign. American Society

of Photogrammetry, Falls Church, VA, pp. 420476.

May, S.A., Wyn-Jones, G., 1987. Identification of hindleg lameness.

Equine Veterinary Journal 19, 185188.

Merkens, H.W., Schamhardt, H.C., 1988. Evaluation of equine

locomotion during different degrees of experimentally inducedlameness: I: lameness model and quantification of ground reaction

force patterns of the limbs. Equine Veterinary Journal Supplement

6, 9699.

Peham, C., Scheidl, M., Licka, T., 1996. A method of signal processing

in motion analysis of the trotting horse. Journal of Biomechanics

29, 11111114.

Peham, C., Licka, T., Girtler, D., Scheidl, M., 1999. Supporting

forelimb lameness: clinical judgement vs. computerised symmetry

measurement. Equine Veterinary Journal 31, 417421.

Peham, C., Licka, T., Girtler, D., Scheidl, M., 2001. Hindlimb

lameness: clinical judgement versus computerised symmetry

measurement. Veterinary Record 148, 750752.

Peloso, J.G., Stick, J.A., Soutas-Little, R.W., Caron, J.C., DeCamp,

C.E., Leach, D.H., 1993. Computer-assisted three-dimensional gait

analysis of amphotericin-induced carpal lameness in horses.American Journal of Veterinary Research 54, 15351543.

Pourcelot, P., Degueurce, C., Audigi!e, F., Denoix, J-M., Geiger, G.,

1997a. Kinematic analysis of the locomotion symmetry of sound

horses at a slow trot. Equine Veterinary Journal Supplement 23,

9396.

Pourcelot, P., Audigi!e, F., Degueurce, C., Denoix, J-M., Geiger, G.,

1997b. Kinematic Symmetry Index: a method for quantifying the

horse locomotion symmetry using kinematic data. Veterinary

Research 28, 525538.

Schneider, E., Chao, E., 1983. Fourier analysis of ground reaction

forces in normals and patients with knee joint disease. Journal of


Soudan, K., Dierckx, P., 1979. Calculation of derivates and Fourier

coefficients of human motion data, while using spline functions.

Journal of Biomechanics 12, 2126.Uhlir, C., Licka, T., K.ubber, P., Peham, C., Scheidl, M., Girtler, D.,

1997. Compensatory movements of horses with a stance phase

lameness. Equine Veterinary Journal Supplement 23, 102105.

Vorstenbosch, M.A.T.M., Buchner, H.H.F., Savelberg, H.H.C.M.,

Schamhardt, H.C., Barneveld, A., 1997. Modeling study of

compensatory head movements in lame horses. American Journal

of Veterinary Research 58, 713718.

Winter, D.A., Sidwall, H.G., Hobson, D.A., 1974. Measurement and

reduction of noise in kinematics of locomotion. Journal of



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