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Symmetry indices based on accelerometric data in trotting horses
Journal of Biomechanics 43 (2010) 2608–2612
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Symmetry indices based on accelerometric data in trotting horses Maj Halling Thomsen a,n, Anders Tolver Jensen b, Helle Sørensen c, Casper Lindegaard a, Pia Haubro Andersen a a
Department of Large Animal Sciences, Faculty of Life Sciences, University of Copenhagen, Denmark Department of Basic Sciences and Environment, Faculty of Life Sciences, University of Copenhagen, Denmark c Department of Mathematical Sciences, Faculty of Science, University of Copenhagen, Denmark b
a r t i c l e in f o
a b s t r a c t
Article history: Accepted 7 May 2010
Detection and quantification of lameness in horses consists primarily of a subjective assessment, whereby both intra- and inter-observer disagreements exist, especially with low grade lameness. Therefore, clinically applicable methods are needed for reliable, objective assessments. The aim of this study was to describe three symmetry indices derived from a simple accelerometric method and investigate these in sound trotting horses. The indices describe the overall symmetry of the gait, the symmetry of loads placed on the limbs and the symmetry in timing between left and right steps. These symmetry indices were able to quantify the high degree of symmetry of the trot in sound horses that has been described in earlier studies using other gait analysis methods. Also, we have analysed the variances and have found high repeatability for all three indices. This provides a basis for future investigations of the symmetry indices and their potential for objective detection and quantification of lameness in horses. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Horse Locomotion Symmetry indices Accelerometry Fourier analysis
1. Introduction The main objective of lameness examinations in horses is to detect the lame limb or limbs and secondly to quantify the degree of lameness (Stashak, 2002). Lameness is a common problem in sports horses, resulting in lost training days or even an ended career (Jeffcott et al., 1982; Rossdale et al., 1985). Timely treatment is dependent on early correct diagnosis, that is crucial to prevent a progression into chronic lameness. The three most common gaits are: walk, trot and canter. Walk and trot are symmetric gaits, 4-beated and 2-beated respectively, while canter is an asymmetric gait. Lameness is a clinical sign displayed during locomotion, resulting in decreased symmetry of the movement (Buchner et al., 1996). In clinical lameness examinations, the detection and quantification of lameness consists primarily of visual inspection while the horse is moving in the symmetric gaits. For moderate to severe lameness, the asymmetry of movement at the trot is perceived easily because the horse will display obvious clinical symptoms (e.g. head nodding or hip hike) (Stashak, 2002). However, with low grade lameness these clinical characteristics are subtle and/or inter-
n Correspondence to: University of Copenhagen, Faculty of Life Sciences, Department of Clinical Sciences, Hoejbakkegaard Alle´ 5, 8.68 DK-2630 Taastrup, Denmark. Tel.: + 45 35332871; fax: +45 35333924. E-mail address: [email protected] (M. Halling Thomsen).
0021-9290/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2010.05.004
mittent, resulting in poor inter- and intra-observer agreement for visual assessments (Keegan et al., 1998, 2010). Attempts to avoid these obvious disadvantages have lead to the development of a number of instrumented methods for equine gait analysis during the last decades. This has lead to detailed knowledge of the kinetics and kinematics of the gaits as well as the influence of lameness. For example, force plate analysis have shown that lame horses display asymmetrically loading forces with decreased load on the lame limb (Weishaupt et al., 2004; Merkens and Schamhardt, 1988). To achieve this, the body centre of mass (BCM) moves away from the lame limb resulting in asymmetric movement of the BCM and trunk during the stride (Buchner et al., 1996, 2001). This, in turn, also causes asymmetry of the accelerations and decelerations of the trunk that occurs within each stride (Barrey and Desbrosse, 1996; Buchner et al., 1996). Trunk accelerations in one or more axes (i.e. dorsoventral, laterolateral and craniocaudal) can be measured by accelerometers (Moe-Nilssen, 1998b; Barrey et al., 1994; Keegan et al., 2004; Pfau et al., 2005). Advantages of accelerometers include low costs, simple instrumentation and no need for a gait laboratory since all equipment is mounted on the horse. Trunk accelerometric gait analysis in humans with sensors located close to the BCM has shown a good test–retest reliability (Henriksen et al., 2004) as well as ability to detect even small gait disturbances (Moe-Nilssen, 1998b). In horses, the surface location closest to the BCM is the lowest point of the back above approximately the 13th
M. Halling Thomsen et al. / Journal of Biomechanics 43 (2010) 2608–2612
thoracic vertebra (T13) (Buchner et al., 2000). To our knowledge, this location has never been used for measurements of trunk accelerations in horses. The aim of this study was to derive and describe three new symmetry indices that could be used for lameness detection and quantification. These symmetry indices were calculated from trunk accelerations measured at the lowest point in the midline of the back in sound horses. Finally, the intra- and inter-individual variability of these indices was investigated. 2. Material and methods
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acceleration signals with markers from the photoelectric sensors. Positive accelerations for the three axes were represented by dorsal, right and cranial directions, respectively. Based on no adverse movements like turning the head or changing direction observed in the video-recordings, the middle sequence of at least 24 m (defined by markers from photoelectric sensors) of a trotting run was selected. Stance of the right diagonal (i.e. right forelimb and left hindlimb), based on the video-recording, was marked in the sequence before transferring data to Matlabs (version 7.7) for further analysis. Measurements from eight strides were used for the final analysis, starting with the right diagonal. Data was filtered using a Butterworth filter of 2nd order at 50 Hz in a backward–forward filtering process. The data was corrected for the gravity component. The true horizontal (craniocaudal and laterolateral) and vertical (dorsoventral) accelerations were estimated (Moe-Nilssen, 1998a). These standardised data were used for all calculations of symmetry indices.
2.1. Horses 2.4. Symmetry indices The study included 12 adult riding horses (five females and seven males), mean age of 7.2 years (range 3–10), mean height of 158 cm (range 145–171) and mean weight of 524 kg (range 372–671). The criteria for inclusion were no observed lameness and no reaction to flexion tests during a clinical lameness examination. All experimental procedures were pre-approved by the Danish Animal Experimentation Board and the study was performed according to the Danish Animal Testing Act. 2.2. Data acquisition A 3-axis 10 G piezo-resistant accelerometer (Mega Electronics Ltd., Finland) was held firmly in place by an elastic girth at the lowest point of the dorsal back region in the midline (approximately above T13) and connected to a datalogger (Mega Electronics Ltd., Finland) mounted on another girth (Fig. 1). Vertical, transversal and longitudinal accelerations were measured at 240 Hz, while the horse was trotted by hand in a straight line on an evenly surfaced asphalt track of approximately 60 m. The central 24 m delimited by photoelectric sensors were used as the test distance. Horses were trotted back and forth on the track at their own comfortable speed (3.4–4.4 m/s) until at least three trotting runs at a constant speed were obtained. Mean coefficient of variance of stride duration in the measurements were 3.2% (range 0.7–6.6). All trotting sequences were recorded on videotape (Panasonic NV-GS400-EN camcorder). The procedure was repeated for seven of the horses over four consecutive days. Five horses were measured one time. 2.3. Initial data analysis Data and video-recordings were imported and synchronised in Megawin software (Megawin 3.2.1, Mega Electronics Ltd., Finland). Data consisted of three
The dorsoventral acceleration signal was cyclic with a periodicity corresponding to each step. Therefore, the eight-stride data signal consisted of 16 oscillations. The time axis was scaled such that the interval [0,1] corresponded to eight gait cycles and the original signal was smoothed using Fourier basis functions: 1, sinðwtÞ, cosðwtÞ, sinð2wtÞ, cosð2wtÞ
ð1Þ
The value of w¼2p/(1/8) was chosen to extract the repetitious part of the signal and the first 21 basis functions (i.e. 10 harmonics) were used. Although trunk accelerations can attain higher frequencies preliminary robustness studies showed, that the symmetry indices change up to 8–10 harmonics, whereafter they stabilize. Increasing the number of basis functions does not affect the symmetry indices substantially. The smoothed signal xðtÞ ¼ a0 þ
K X
ðai cosðiwtÞÞþ bi sinðiwtÞÞ,
t A ½0,1
ð2Þ
i¼1
with K¼ 10 consisted of eight identical periods reflecting an average signal over a complete gait cycle with all non-repeatable features removed. Three symmetry indices were calculated from one of the (identical) eight periods of the Fourier smoothed dorsoventral signal: (1) S, describing the overall symmetry of the acceleration; (2) A, describing the symmetry of loading of the left and right diagonals and (3) W, describing the difference in phase of the two diagonals. (1) Overall symmetry, index S: A sound trotting horse will have a high degree of symmetry of the dorsoventral trunk accelerations. If the gait was completely symmetric, then the two half cycles of the Fourier smoothed dorsoventral signal would be identical, and thus, the complete signal could be described by the evennumbered harmonics. If the gait was asymmetric then the odd-numbered harmonics would contribute to the signal as well (Fig. 2). Based on this, the symmetry index S was defined as the natural logarithmic quotient of the squared odd-numbered and even-numbered Fourier coefficients, ! a2 þ b2 þ a2 þ b2 þ þ a2k1 þ b2K1 S ¼ log 1 2 1 2 3 2 3 2 ð3Þ 2 2 a2 þ b2 þ a4 þ b4 þ þ ak þ bK where a and b are the Fourier coefficients related to the harmonics. In other words, smaller values of S describe a more symmetric gait. Conversely, a lame horse would have a more asymmetric gait pattern compared to a sound horse, and thus a higher contribution of the odd-numbered harmonics to the signal, resulting in higher values of S. (2) Symmetry of loading of the left and right diagonal, index A: One period of the Fourier smoothed dorsoventral acceleration signal would contain two positive parts reflecting the vertical ground reaction forces (GRF) acting on the right and left diagonals, respectively. A lame horse would decrease the forces acting on the lame diagonal (Weishaupt et al., 2004, 2006), thus, the area under the positive part of the vertical acceleration curve during stance of the lame diagonal would decrease. As a measure of the symmetry of the loading in the two diagonals, the symmetry index A was defined as the natural logarithmic quotient of the area under the curve for the positive parts of a period AUC1 A ¼ log ð4Þ AUC2
Fig. 1. Equipment mounted on a horse: (A) datalogger and wireless receiver mounted on the front girth; (B) accelerometric sensor, firmly attached to the back of the horse by an elastic girth.
AUC1 was the area under the curve for the first positive part, reflecting the loading of the right diagonal and AUC2 was the area under the curve for the second positive part, reflecting the loading of the left diagonal (Fig. 3). In sound horses, the index A was expected to be dispersed around 0. Horses lame on a limb in the right diagonal would have a negative value, while horses lame on a limb in the left diagonal would have a positive value. Thus, the index A would provide information about the diagonal of the lameness. (3) Difference in the phase of left/right diagonal within a stride, W: The suspension phase after stance of the lame diagonal would be shorter than after stance of the sound diagonal (Buchner et al., 1995). Moreover, the contralateral advanced placement of lame to sound limb would decrease (Weishaupt et al., 2004, 2006). These phenomena would be most pronounced for forelimb lameness.
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10 Acceleration (m/s2)
Acceleration (m/s2)
10
0
-10
0
-10 Fourier smoothed signal Symmetric part of the signal Asymmetric part of the signal
0
0.1
0.2
0.3 0.4 Time (s)
0.5
Part1 of the signal Part2 of the signal Warped part2 of the signal Index W
0.6
Fig. 2. One stride of the Fourier smoothed signal shown with its two components, the symmetric part and the asymmetric part, used for calculation of index S. The signal is from a non-lame horse, why the symmetric part (sum of the even harmonics) describes the majority of the signal and the asymmetric part (sum of the odd harmonics) only contributes a little to the signal. The index S is based on the ratio of the Fourier coefficients (defining the amplitude of the harmonics) of the odd and even harmonics.
0
0.05
0.1
0.15 t
0.2
0.25
0.3
Fig. 4. The two parts of the Fourier smoothed dorsoventral acceleration signal of one stride plotted together with the warped (time deformated) second part. The warped second part is the second part dragged towards the first part. The maximal drag, describing the maximal time delay (positive or negative) in the second part, is showed as the index W, the maximal time distance between the second part and the warped second part.
horses. Also, forelimb lameness was expected to result in a larger change of W than hindlimb lameness.
Acceleration (m/s2)
10
2.5. Statistics
AUC1
In order to quantify the between-horses and the within-horse variability an analysis of variance model with random effect of horse was used. The effect of velocity was tested in the analysis. Results are presented as mean, SEM, betweenhorses variance and within-horse variance. The repeatability of the symmetry indices was also evaluated by plotting the deviation from the mean vs. the mean for each horse measured more than once in comparison with 7 two standard deviations for all horses. Difference from 0 of the two symmetry indices A and W were tested using a t-test. A p-value r0.05 was considered significant.
AUC2
0
-10
3. Results
0
0.1
0.2
0.3 0.4 Time (s)
0.5
0.6
Fig. 3. One stride of the Fourier smoothed signal from a non-lame horse. AUC1 is the area under the curve of the positive part of the Fourier smoothed acceleration signal during stance of the right diagonal, while AUC2 is the area under the curve of the positive part of the signal during stance of the left diagonal. The AUC’s are the time integrated positive accelerations and according to Newton’s second law reflects the impulses (time integrated forces) acting on the diagonals. Index A is based on the ratio of AUC1 and AUC2. The AUC1 and AUC2 are of approximately the same size in this figure, as a non-lame horse loads the diagonals equally.
Two of the seven horses were included only on three out of the four days, one due to technical problems and one due to illness. All the symmetry indices (S, A and W) showed a high degree of symmetry, with no dependency on velocity (Table 1). For all the indices S, A and W the within-horse variance was lower than the between-horses variance, 24%, 41% and 31%, respectively, indicating a high repeatability. Furthermore, the deviation of the measurements from the mean within each horse measured more than once were lower than 2 standard deviations of the means of all horses, for all indices (Fig. 5). There were no significant difference from 0 of the indices A and W (Table 1).
In order to measure this aspect of temporal asymmetry, the signal was split into two parts, of equal length, and a warping, or time deformation, function h was applied to one part such that
4. Discussion
X1 ðtÞ ¼ X2 ðhðtÞÞ
4.1. Symmetry indices
ð5Þ
Then the function h(t) t describes the delay (positive or negative) of the second part of the signal. Index W (Fig. 4) was defined as the largest delay, still measured with a sign, that was as h(t0) t0,where t0 was the time point where 9h(t) t9 was the largest. W was expected to be dispersed around 0 in sound
This study proposes three symmetry indices that describe different biological features of the trotting horse. The symmetry indices are based on Fourier analysis. Fourier analysis has been
M. Halling Thomsen et al. / Journal of Biomechanics 43 (2010) 2608–2612
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Table 1 Results for the analysis of variance. Mean, SEM and within-horse and between-horses variances for the three symmetry indices, S, A and W. p-Values for the tests of effect of velocity for all indices, and of mean ¼0 for indices A and W are also shown in the table. Symmetry indices
Mean
SEM
Between-horses variances
Within-horses variances
Test for velocity
Test for mean ¼ 0
S A W
5.82 0.0282 0.322 10 3
0.16 0.0155 3.936 10 3
0.219 0.0022 0.137 10 3
0.167 0.0013 0.094 10 3
p ¼ 0.620 p ¼ 0.403 p ¼ 0.115
– p ¼0.096 p ¼0.936
Deviation of measurement from mean of horses
1 0 -1 -6
-5.5 Mean of index S
-5
0.1 0 -0.1 -0.15
-0.1
-0.05 0 0.05 Mean of index A
0.1
0.15
0.02 0 -0.02 -0.02
-0.01
0 0.01 Mean of index W
0.02
Fig. 5. The deviations from the mean plotted against the mean of each horse for the symmetry indices S (a), A (b) and W (c). The dotted lines represent 7 two standard deviations of the mean of all horses. All the symmetry indices showed a high repeatability as deviations from the mean within each horse are lower than two standard deviations of the mean of the horses.
used in the analysis of trunk displacement data to calculate indices for detection of lameness in horses (Peham et al., 1999; Audigie et al., 2002; Keegan et al., 2001). To our knowledge, Fourier analysis has not been applied directly to trunk acceleration data in horses. The symmetry index, S, describes the high degree of symmetry of healthy trotting horses, which corresponds well with other studies of trotting horses. Kinematic data showed a high degree of symmetry for both vertical displacement and acceleration amplitudes at the withers in sound horses and decreasing degrees of symmetry with increasing degrees of lameness (Buchner et al., 1996). Fourier analysis of vertical displacement data showed a high degree of symmetry at T13 in sound horses (Audigie et al., 2002). Barrey et al. (2002) found a high degree of symmetry of vertical trunk accelerations in sound horses using an autocorrelation function. This symmetry was shown to decrease with forelimb lameness (Barrey and Desbrosse, 1996). The index S used in this study concurs with the findings of Barrey and Desbrosse (1996) using a different method of calculation. With Fourier smoothing, random noise is removed from the signal. This results in lower variances, which might increase the sensitivity and specificity of the index S to detect low grade lameness. The symmetry index A describes the symmetry of loading on the diagonals and reflects the vertical impulses acting on the diagonals during stance. In this study, index A in sound horses was on average 0.0282 and not significantly different from 0,
which corresponds to complete symmetry. Weishaupt et al. (2004, 2006) measured GRF in sound and lame trotting horses on an instrumented treadmill. They found a high degree of symmetry of impulses in the diagonals in normal horses that decreased in lame horses as a result of a decrease in impulse of the lame diagonal and an increase in impulse of the sound diagonal. Therefore, a change of the index A towards a lower degree of symmetry would be expected in lame horses. The index W showed a high degree of symmetry between the phases of the acceleration signal for the two diagonals. The index W was on average 0.322 10 3 and not significantly different from 0, which corresponds to complete symmetry. Since W measures the symmetry of the temporal stride pattern, then it might further distinguish between forelimb and hindlimb lameness. In a study of temporal stride patterns, Buchner et al. (1995) found larger decrease of the symmetry in the suspension phases for forelimb lameness compared to hindlimb lameness, and a decrease in symmetry of the contralateral advanced placements (i.e. timelag from landing of one limb to landing of the contralateral limb). 4.2. Variances For all the indices (S, A and W) we found that the within-horse variances were lower than the between-horses variances. A high repeatability was reflected by the deviations of the measurements from the mean within each horse being lower than two standard deviations of the means of horses for all the indices (Fig. 5). The magnitude of the between-horses variances should be compared to expected changes due to lameness. Data from an experimental lameness model are under investigation in our group, and will be reported later. However, an unpublished clinical case showed symmetry indices (S¼ 2.61, A¼ 0.275 and W¼ 0.089) deviating more from normal horses, than what could be explained by the between-horses variances of Table 1. 4.3. Measurement error Using the algorithms proposed by Moe-Nilssen (1998a), the measured accelerations were corrected for the average tilt (mean angular location (MAL)) of the accelerometer in the horizontal plane. This correction is feasible when the velocity is constant, and accelerations are measured in three orthogonal axes. However, rotations of the spine during movement would cause measurement errors due to deviations from MAL and rotations of the sensor itself. The maximal deviation from the MAL would be approximately half the size of the range of angular motion, which at T13 is 4.21 for flexion–extension and 3.11 for axial rotation (Faber et al., 2001). An estimation of the error was (1 (cos(4.21/2) cos(3.11/2))) 100%¼0.1%. However, some accelerations from the horizontal axes would also be in the dorsoventral signal when there is a deviation from the MAL. In this study the amplitude of the longitudinal acceleration was up to four times bigger and the amplitude of the lateral acceleration was the same size or smaller than that of the dorsoventral. Taking these maximal deviations into account a maximum error of 2.4%
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was estimated. The rotations of the sensor itself caused an error due to centrifugal forces. The rotational speeds were low and this error was estimated to a maximum of 0.04 m/s2. However, in sound horses these errors could be expected to be symmetric between the two diagonals, therefore affecting the symmetry indices minimally. 4.4. Clinical applicability A method for use in clinical practice should ideally have a high repeatability, the instrumentation should be simple and interfere with the horse only to a minimal extent. The symmetry indices used in this study were able to describe the high degree of symmetry in the movement of sound trotting horses, and the repeatability was high for the indices. The instrumentation needed for the method described here is simple compared to other gait analysis methods. The location of all equipment in the saddle area causes minimal disturbance to the horse, since most horses are trained to accept a saddle or girth. Furthermore, there was no need for clipping the coat or gluing sensors to the skin in order to achieve a firm connection of the sensor. This study was based on data obtained from 12 horses, including repeated data from 7 horses. Estimation of a valid interval of the three indices for sound horses requires investigation of a larger number of sound and lame horses.
5. Conclusion The method presented in this study seems promising as the symmetry indices can quantify important biological features of the gait of sound horses. These biological features change with lameness as shown by other authors. Hence the presented symmetry indices merit further investigation regarding the ability to detect asymmetric movements associated with lameness and regarding further validation.
Conflict of interest statement The authors have no financial or personal relationships with organisations or people that could have inappropriately influenced our work.
Acknowledgements Funding: The study was supported by grants from Intervet Denmark A/S and Foreningen KUSTOS of 1881. References Audigie, F., Pourcelot, P., Degueurce, C., Geiger, D., Denoix, J.M., 2002. Fourier analysis of trunk displacements: a method to identify the lame limb in trotting horses. Journal of Biomechanics 35, 1173–1182.
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Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Symmetry indices based on accelerometric data in trotting horses Maj Halling Thomsen a,n, Anders Tolver Jensen b, Helle Sørensen c, Casper Lindegaard a, Pia Haubro Andersen a a
Department of Large Animal Sciences, Faculty of Life Sciences, University of Copenhagen, Denmark Department of Basic Sciences and Environment, Faculty of Life Sciences, University of Copenhagen, Denmark c Department of Mathematical Sciences, Faculty of Science, University of Copenhagen, Denmark b
a r t i c l e in f o
a b s t r a c t
Article history: Accepted 7 May 2010
Detection and quantification of lameness in horses consists primarily of a subjective assessment, whereby both intra- and inter-observer disagreements exist, especially with low grade lameness. Therefore, clinically applicable methods are needed for reliable, objective assessments. The aim of this study was to describe three symmetry indices derived from a simple accelerometric method and investigate these in sound trotting horses. The indices describe the overall symmetry of the gait, the symmetry of loads placed on the limbs and the symmetry in timing between left and right steps. These symmetry indices were able to quantify the high degree of symmetry of the trot in sound horses that has been described in earlier studies using other gait analysis methods. Also, we have analysed the variances and have found high repeatability for all three indices. This provides a basis for future investigations of the symmetry indices and their potential for objective detection and quantification of lameness in horses. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Horse Locomotion Symmetry indices Accelerometry Fourier analysis
1. Introduction The main objective of lameness examinations in horses is to detect the lame limb or limbs and secondly to quantify the degree of lameness (Stashak, 2002). Lameness is a common problem in sports horses, resulting in lost training days or even an ended career (Jeffcott et al., 1982; Rossdale et al., 1985). Timely treatment is dependent on early correct diagnosis, that is crucial to prevent a progression into chronic lameness. The three most common gaits are: walk, trot and canter. Walk and trot are symmetric gaits, 4-beated and 2-beated respectively, while canter is an asymmetric gait. Lameness is a clinical sign displayed during locomotion, resulting in decreased symmetry of the movement (Buchner et al., 1996). In clinical lameness examinations, the detection and quantification of lameness consists primarily of visual inspection while the horse is moving in the symmetric gaits. For moderate to severe lameness, the asymmetry of movement at the trot is perceived easily because the horse will display obvious clinical symptoms (e.g. head nodding or hip hike) (Stashak, 2002). However, with low grade lameness these clinical characteristics are subtle and/or inter-
n Correspondence to: University of Copenhagen, Faculty of Life Sciences, Department of Clinical Sciences, Hoejbakkegaard Alle´ 5, 8.68 DK-2630 Taastrup, Denmark. Tel.: + 45 35332871; fax: +45 35333924. E-mail address: [email protected] (M. Halling Thomsen).
0021-9290/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2010.05.004
mittent, resulting in poor inter- and intra-observer agreement for visual assessments (Keegan et al., 1998, 2010). Attempts to avoid these obvious disadvantages have lead to the development of a number of instrumented methods for equine gait analysis during the last decades. This has lead to detailed knowledge of the kinetics and kinematics of the gaits as well as the influence of lameness. For example, force plate analysis have shown that lame horses display asymmetrically loading forces with decreased load on the lame limb (Weishaupt et al., 2004; Merkens and Schamhardt, 1988). To achieve this, the body centre of mass (BCM) moves away from the lame limb resulting in asymmetric movement of the BCM and trunk during the stride (Buchner et al., 1996, 2001). This, in turn, also causes asymmetry of the accelerations and decelerations of the trunk that occurs within each stride (Barrey and Desbrosse, 1996; Buchner et al., 1996). Trunk accelerations in one or more axes (i.e. dorsoventral, laterolateral and craniocaudal) can be measured by accelerometers (Moe-Nilssen, 1998b; Barrey et al., 1994; Keegan et al., 2004; Pfau et al., 2005). Advantages of accelerometers include low costs, simple instrumentation and no need for a gait laboratory since all equipment is mounted on the horse. Trunk accelerometric gait analysis in humans with sensors located close to the BCM has shown a good test–retest reliability (Henriksen et al., 2004) as well as ability to detect even small gait disturbances (Moe-Nilssen, 1998b). In horses, the surface location closest to the BCM is the lowest point of the back above approximately the 13th
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thoracic vertebra (T13) (Buchner et al., 2000). To our knowledge, this location has never been used for measurements of trunk accelerations in horses. The aim of this study was to derive and describe three new symmetry indices that could be used for lameness detection and quantification. These symmetry indices were calculated from trunk accelerations measured at the lowest point in the midline of the back in sound horses. Finally, the intra- and inter-individual variability of these indices was investigated. 2. Material and methods
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acceleration signals with markers from the photoelectric sensors. Positive accelerations for the three axes were represented by dorsal, right and cranial directions, respectively. Based on no adverse movements like turning the head or changing direction observed in the video-recordings, the middle sequence of at least 24 m (defined by markers from photoelectric sensors) of a trotting run was selected. Stance of the right diagonal (i.e. right forelimb and left hindlimb), based on the video-recording, was marked in the sequence before transferring data to Matlabs (version 7.7) for further analysis. Measurements from eight strides were used for the final analysis, starting with the right diagonal. Data was filtered using a Butterworth filter of 2nd order at 50 Hz in a backward–forward filtering process. The data was corrected for the gravity component. The true horizontal (craniocaudal and laterolateral) and vertical (dorsoventral) accelerations were estimated (Moe-Nilssen, 1998a). These standardised data were used for all calculations of symmetry indices.
2.1. Horses 2.4. Symmetry indices The study included 12 adult riding horses (five females and seven males), mean age of 7.2 years (range 3–10), mean height of 158 cm (range 145–171) and mean weight of 524 kg (range 372–671). The criteria for inclusion were no observed lameness and no reaction to flexion tests during a clinical lameness examination. All experimental procedures were pre-approved by the Danish Animal Experimentation Board and the study was performed according to the Danish Animal Testing Act. 2.2. Data acquisition A 3-axis 10 G piezo-resistant accelerometer (Mega Electronics Ltd., Finland) was held firmly in place by an elastic girth at the lowest point of the dorsal back region in the midline (approximately above T13) and connected to a datalogger (Mega Electronics Ltd., Finland) mounted on another girth (Fig. 1). Vertical, transversal and longitudinal accelerations were measured at 240 Hz, while the horse was trotted by hand in a straight line on an evenly surfaced asphalt track of approximately 60 m. The central 24 m delimited by photoelectric sensors were used as the test distance. Horses were trotted back and forth on the track at their own comfortable speed (3.4–4.4 m/s) until at least three trotting runs at a constant speed were obtained. Mean coefficient of variance of stride duration in the measurements were 3.2% (range 0.7–6.6). All trotting sequences were recorded on videotape (Panasonic NV-GS400-EN camcorder). The procedure was repeated for seven of the horses over four consecutive days. Five horses were measured one time. 2.3. Initial data analysis Data and video-recordings were imported and synchronised in Megawin software (Megawin 3.2.1, Mega Electronics Ltd., Finland). Data consisted of three
The dorsoventral acceleration signal was cyclic with a periodicity corresponding to each step. Therefore, the eight-stride data signal consisted of 16 oscillations. The time axis was scaled such that the interval [0,1] corresponded to eight gait cycles and the original signal was smoothed using Fourier basis functions: 1, sinðwtÞ, cosðwtÞ, sinð2wtÞ, cosð2wtÞ
ð1Þ
The value of w¼2p/(1/8) was chosen to extract the repetitious part of the signal and the first 21 basis functions (i.e. 10 harmonics) were used. Although trunk accelerations can attain higher frequencies preliminary robustness studies showed, that the symmetry indices change up to 8–10 harmonics, whereafter they stabilize. Increasing the number of basis functions does not affect the symmetry indices substantially. The smoothed signal xðtÞ ¼ a0 þ
K X
ðai cosðiwtÞÞþ bi sinðiwtÞÞ,
t A ½0,1
ð2Þ
i¼1
with K¼ 10 consisted of eight identical periods reflecting an average signal over a complete gait cycle with all non-repeatable features removed. Three symmetry indices were calculated from one of the (identical) eight periods of the Fourier smoothed dorsoventral signal: (1) S, describing the overall symmetry of the acceleration; (2) A, describing the symmetry of loading of the left and right diagonals and (3) W, describing the difference in phase of the two diagonals. (1) Overall symmetry, index S: A sound trotting horse will have a high degree of symmetry of the dorsoventral trunk accelerations. If the gait was completely symmetric, then the two half cycles of the Fourier smoothed dorsoventral signal would be identical, and thus, the complete signal could be described by the evennumbered harmonics. If the gait was asymmetric then the odd-numbered harmonics would contribute to the signal as well (Fig. 2). Based on this, the symmetry index S was defined as the natural logarithmic quotient of the squared odd-numbered and even-numbered Fourier coefficients, ! a2 þ b2 þ a2 þ b2 þ þ a2k1 þ b2K1 S ¼ log 1 2 1 2 3 2 3 2 ð3Þ 2 2 a2 þ b2 þ a4 þ b4 þ þ ak þ bK where a and b are the Fourier coefficients related to the harmonics. In other words, smaller values of S describe a more symmetric gait. Conversely, a lame horse would have a more asymmetric gait pattern compared to a sound horse, and thus a higher contribution of the odd-numbered harmonics to the signal, resulting in higher values of S. (2) Symmetry of loading of the left and right diagonal, index A: One period of the Fourier smoothed dorsoventral acceleration signal would contain two positive parts reflecting the vertical ground reaction forces (GRF) acting on the right and left diagonals, respectively. A lame horse would decrease the forces acting on the lame diagonal (Weishaupt et al., 2004, 2006), thus, the area under the positive part of the vertical acceleration curve during stance of the lame diagonal would decrease. As a measure of the symmetry of the loading in the two diagonals, the symmetry index A was defined as the natural logarithmic quotient of the area under the curve for the positive parts of a period AUC1 A ¼ log ð4Þ AUC2
Fig. 1. Equipment mounted on a horse: (A) datalogger and wireless receiver mounted on the front girth; (B) accelerometric sensor, firmly attached to the back of the horse by an elastic girth.
AUC1 was the area under the curve for the first positive part, reflecting the loading of the right diagonal and AUC2 was the area under the curve for the second positive part, reflecting the loading of the left diagonal (Fig. 3). In sound horses, the index A was expected to be dispersed around 0. Horses lame on a limb in the right diagonal would have a negative value, while horses lame on a limb in the left diagonal would have a positive value. Thus, the index A would provide information about the diagonal of the lameness. (3) Difference in the phase of left/right diagonal within a stride, W: The suspension phase after stance of the lame diagonal would be shorter than after stance of the sound diagonal (Buchner et al., 1995). Moreover, the contralateral advanced placement of lame to sound limb would decrease (Weishaupt et al., 2004, 2006). These phenomena would be most pronounced for forelimb lameness.
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10 Acceleration (m/s2)
Acceleration (m/s2)
10
0
-10
0
-10 Fourier smoothed signal Symmetric part of the signal Asymmetric part of the signal
0
0.1
0.2
0.3 0.4 Time (s)
0.5
Part1 of the signal Part2 of the signal Warped part2 of the signal Index W
0.6
Fig. 2. One stride of the Fourier smoothed signal shown with its two components, the symmetric part and the asymmetric part, used for calculation of index S. The signal is from a non-lame horse, why the symmetric part (sum of the even harmonics) describes the majority of the signal and the asymmetric part (sum of the odd harmonics) only contributes a little to the signal. The index S is based on the ratio of the Fourier coefficients (defining the amplitude of the harmonics) of the odd and even harmonics.
0
0.05
0.1
0.15 t
0.2
0.25
0.3
Fig. 4. The two parts of the Fourier smoothed dorsoventral acceleration signal of one stride plotted together with the warped (time deformated) second part. The warped second part is the second part dragged towards the first part. The maximal drag, describing the maximal time delay (positive or negative) in the second part, is showed as the index W, the maximal time distance between the second part and the warped second part.
horses. Also, forelimb lameness was expected to result in a larger change of W than hindlimb lameness.
Acceleration (m/s2)
10
2.5. Statistics
AUC1
In order to quantify the between-horses and the within-horse variability an analysis of variance model with random effect of horse was used. The effect of velocity was tested in the analysis. Results are presented as mean, SEM, betweenhorses variance and within-horse variance. The repeatability of the symmetry indices was also evaluated by plotting the deviation from the mean vs. the mean for each horse measured more than once in comparison with 7 two standard deviations for all horses. Difference from 0 of the two symmetry indices A and W were tested using a t-test. A p-value r0.05 was considered significant.
AUC2
0
-10
3. Results
0
0.1
0.2
0.3 0.4 Time (s)
0.5
0.6
Fig. 3. One stride of the Fourier smoothed signal from a non-lame horse. AUC1 is the area under the curve of the positive part of the Fourier smoothed acceleration signal during stance of the right diagonal, while AUC2 is the area under the curve of the positive part of the signal during stance of the left diagonal. The AUC’s are the time integrated positive accelerations and according to Newton’s second law reflects the impulses (time integrated forces) acting on the diagonals. Index A is based on the ratio of AUC1 and AUC2. The AUC1 and AUC2 are of approximately the same size in this figure, as a non-lame horse loads the diagonals equally.
Two of the seven horses were included only on three out of the four days, one due to technical problems and one due to illness. All the symmetry indices (S, A and W) showed a high degree of symmetry, with no dependency on velocity (Table 1). For all the indices S, A and W the within-horse variance was lower than the between-horses variance, 24%, 41% and 31%, respectively, indicating a high repeatability. Furthermore, the deviation of the measurements from the mean within each horse measured more than once were lower than 2 standard deviations of the means of all horses, for all indices (Fig. 5). There were no significant difference from 0 of the indices A and W (Table 1).
In order to measure this aspect of temporal asymmetry, the signal was split into two parts, of equal length, and a warping, or time deformation, function h was applied to one part such that
4. Discussion
X1 ðtÞ ¼ X2 ðhðtÞÞ
4.1. Symmetry indices
ð5Þ
Then the function h(t) t describes the delay (positive or negative) of the second part of the signal. Index W (Fig. 4) was defined as the largest delay, still measured with a sign, that was as h(t0) t0,where t0 was the time point where 9h(t) t9 was the largest. W was expected to be dispersed around 0 in sound
This study proposes three symmetry indices that describe different biological features of the trotting horse. The symmetry indices are based on Fourier analysis. Fourier analysis has been
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Table 1 Results for the analysis of variance. Mean, SEM and within-horse and between-horses variances for the three symmetry indices, S, A and W. p-Values for the tests of effect of velocity for all indices, and of mean ¼0 for indices A and W are also shown in the table. Symmetry indices
Mean
SEM
Between-horses variances
Within-horses variances
Test for velocity
Test for mean ¼ 0
S A W
5.82 0.0282 0.322 10 3
0.16 0.0155 3.936 10 3
0.219 0.0022 0.137 10 3
0.167 0.0013 0.094 10 3
p ¼ 0.620 p ¼ 0.403 p ¼ 0.115
– p ¼0.096 p ¼0.936
Deviation of measurement from mean of horses
1 0 -1 -6
-5.5 Mean of index S
-5
0.1 0 -0.1 -0.15
-0.1
-0.05 0 0.05 Mean of index A
0.1
0.15
0.02 0 -0.02 -0.02
-0.01
0 0.01 Mean of index W
0.02
Fig. 5. The deviations from the mean plotted against the mean of each horse for the symmetry indices S (a), A (b) and W (c). The dotted lines represent 7 two standard deviations of the mean of all horses. All the symmetry indices showed a high repeatability as deviations from the mean within each horse are lower than two standard deviations of the mean of the horses.
used in the analysis of trunk displacement data to calculate indices for detection of lameness in horses (Peham et al., 1999; Audigie et al., 2002; Keegan et al., 2001). To our knowledge, Fourier analysis has not been applied directly to trunk acceleration data in horses. The symmetry index, S, describes the high degree of symmetry of healthy trotting horses, which corresponds well with other studies of trotting horses. Kinematic data showed a high degree of symmetry for both vertical displacement and acceleration amplitudes at the withers in sound horses and decreasing degrees of symmetry with increasing degrees of lameness (Buchner et al., 1996). Fourier analysis of vertical displacement data showed a high degree of symmetry at T13 in sound horses (Audigie et al., 2002). Barrey et al. (2002) found a high degree of symmetry of vertical trunk accelerations in sound horses using an autocorrelation function. This symmetry was shown to decrease with forelimb lameness (Barrey and Desbrosse, 1996). The index S used in this study concurs with the findings of Barrey and Desbrosse (1996) using a different method of calculation. With Fourier smoothing, random noise is removed from the signal. This results in lower variances, which might increase the sensitivity and specificity of the index S to detect low grade lameness. The symmetry index A describes the symmetry of loading on the diagonals and reflects the vertical impulses acting on the diagonals during stance. In this study, index A in sound horses was on average 0.0282 and not significantly different from 0,
which corresponds to complete symmetry. Weishaupt et al. (2004, 2006) measured GRF in sound and lame trotting horses on an instrumented treadmill. They found a high degree of symmetry of impulses in the diagonals in normal horses that decreased in lame horses as a result of a decrease in impulse of the lame diagonal and an increase in impulse of the sound diagonal. Therefore, a change of the index A towards a lower degree of symmetry would be expected in lame horses. The index W showed a high degree of symmetry between the phases of the acceleration signal for the two diagonals. The index W was on average 0.322 10 3 and not significantly different from 0, which corresponds to complete symmetry. Since W measures the symmetry of the temporal stride pattern, then it might further distinguish between forelimb and hindlimb lameness. In a study of temporal stride patterns, Buchner et al. (1995) found larger decrease of the symmetry in the suspension phases for forelimb lameness compared to hindlimb lameness, and a decrease in symmetry of the contralateral advanced placements (i.e. timelag from landing of one limb to landing of the contralateral limb). 4.2. Variances For all the indices (S, A and W) we found that the within-horse variances were lower than the between-horses variances. A high repeatability was reflected by the deviations of the measurements from the mean within each horse being lower than two standard deviations of the means of horses for all the indices (Fig. 5). The magnitude of the between-horses variances should be compared to expected changes due to lameness. Data from an experimental lameness model are under investigation in our group, and will be reported later. However, an unpublished clinical case showed symmetry indices (S¼ 2.61, A¼ 0.275 and W¼ 0.089) deviating more from normal horses, than what could be explained by the between-horses variances of Table 1. 4.3. Measurement error Using the algorithms proposed by Moe-Nilssen (1998a), the measured accelerations were corrected for the average tilt (mean angular location (MAL)) of the accelerometer in the horizontal plane. This correction is feasible when the velocity is constant, and accelerations are measured in three orthogonal axes. However, rotations of the spine during movement would cause measurement errors due to deviations from MAL and rotations of the sensor itself. The maximal deviation from the MAL would be approximately half the size of the range of angular motion, which at T13 is 4.21 for flexion–extension and 3.11 for axial rotation (Faber et al., 2001). An estimation of the error was (1 (cos(4.21/2) cos(3.11/2))) 100%¼0.1%. However, some accelerations from the horizontal axes would also be in the dorsoventral signal when there is a deviation from the MAL. In this study the amplitude of the longitudinal acceleration was up to four times bigger and the amplitude of the lateral acceleration was the same size or smaller than that of the dorsoventral. Taking these maximal deviations into account a maximum error of 2.4%
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was estimated. The rotations of the sensor itself caused an error due to centrifugal forces. The rotational speeds were low and this error was estimated to a maximum of 0.04 m/s2. However, in sound horses these errors could be expected to be symmetric between the two diagonals, therefore affecting the symmetry indices minimally. 4.4. Clinical applicability A method for use in clinical practice should ideally have a high repeatability, the instrumentation should be simple and interfere with the horse only to a minimal extent. The symmetry indices used in this study were able to describe the high degree of symmetry in the movement of sound trotting horses, and the repeatability was high for the indices. The instrumentation needed for the method described here is simple compared to other gait analysis methods. The location of all equipment in the saddle area causes minimal disturbance to the horse, since most horses are trained to accept a saddle or girth. Furthermore, there was no need for clipping the coat or gluing sensors to the skin in order to achieve a firm connection of the sensor. This study was based on data obtained from 12 horses, including repeated data from 7 horses. Estimation of a valid interval of the three indices for sound horses requires investigation of a larger number of sound and lame horses.
5. Conclusion The method presented in this study seems promising as the symmetry indices can quantify important biological features of the gait of sound horses. These biological features change with lameness as shown by other authors. Hence the presented symmetry indices merit further investigation regarding the ability to detect asymmetric movements associated with lameness and regarding further validation.
Conflict of interest statement The authors have no financial or personal relationships with organisations or people that could have inappropriately influenced our work.
Acknowledgements Funding: The study was supported by grants from Intervet Denmark A/S and Foreningen KUSTOS of 1881. References Audigie, F., Pourcelot, P., Degueurce, C., Geiger, D., Denoix, J.M., 2002. Fourier analysis of trunk displacements: a method to identify the lame limb in trotting horses. Journal of Biomechanics 35, 1173–1182.
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