Continuous versus discrete data analysis for gait evaluation of horses with induced bilateral hindlimb lameness

Abstract Background Gait kinematics measured during equine gait analysis are typically evaluated by analysing (asymmetry‐based) discrete variables (eg, peak values) obtained from continuous kinematic signals (eg, timeseries of datapoints). However, when used for the assessment of complex cases of lameness, such as bilateral lameness, discrete variable analysis might overlook relevant functional adaptations. Objectives The overall aim of this paper is to compare continuous and discrete data analysis techniques to evaluate kinematic gait adaptations to lameness. Study design Method comparison. Methods Sixteen healthy Shetland ponies, enrolled in a research programme in which osteochondral defects were created on the medial trochlear ridges of both femurs, were used in this study. Kinematic data were collected at trot on a treadmill before and at 3 and 6 months after surgical intervention. Statistical parametric mapping and linear mixed models were used to compare kinematic variables between and within timepoints. Results Both continuous and discrete data analyses identified changes in pelvis and forelimb kinematics. Discrete data analyses showed significant changes in hindlimb and back kinematics, where such differences were not found to be significant by continuous data analysis. In contrast, continuous data analysis provided additional information on the timing and duration of the differences found. Main limitations A limited number of ponies were included. Conclusions The use of continuous data provides additional information regarding gait adaptations to bilateral lameness that is complementary to the analysis of discrete variables. The main advantage lies in the additional information regarding time dependence and duration of adaptations, which offers the opportunity to identify functional adaptations during all phases of the stride cycle, not just the events related to peak values.


| INTRODUC TI ON
Currently, quantitative gait analysis systems for clinical lameness evaluations in horses rely on the detection of movement asymmetries between left and right. 1 Typically, 3-dimensional (3D) kinematic signals are recorded, separated into multiple continuous 2D angle-time or displacement-time signals and then further analysed by extracting single (peak) values. Using this approach, the horses' complex motion pattern is reduced to a manageable amount of scalar, time discrete variables.
Several kinematic and kinetic differences between the locomotion of healthy and unilaterally lame horses have already been identified. 1 These include decreased vertical displacement of the head, withers and/or pelvis during the stance phase of the lame limb, 2-4 increased upward movement of the tuber coxae before touchdown of the affected limb (hip hike) 5 and reduced peak vertical force (PVF) of the affected limb, 6,7 all resulting in movement asymmetry. However, these discrete variables represent only a small part of the horse's movement and when an asymmetric pattern is absent, such as in cases of bilateral lameness, 8 analyses based solely on such discrete variables may be insufficient to discriminate between healthy and lame horses.
The reliance on discrete variables to identify gait adaptations to lameness has three limitations. Firstly, adaptations may occur over phases of the stride that cannot be described by single discrete variables. Secondly, the timing of single values can differ between sides without changing in amplitude. And thirdly, discrete variables are not necessarily independent and analysing them as such may result in bias. 9 To overcome these limitations, continuous data analysis techniques, 10 such as statistical parametric mapping (SPM), 9 have been developed. To assess the value of continuous data analysis for identifying functional adaptations to lameness in general and more specifically to bilateral hindlimb lameness in equine locomotion analysis, a comparison of kinematic findings retrieved from continuous versus discrete analyses is warranted.
The purpose of the current study was to compare results from continuous and discrete data analysis techniques to evaluate kinematic adaptations to induced bilateral hindlimb lameness. We hypothesised that continuous data analysis techniques would provide more detailed information about functional kinematic adaptations compared to the analysis of discrete values.

| Animals
Sixteen sound Shetland ponies were used in this study. All ponies were enrolled in an articular cartilage repair study in which they underwent a surgical intervention to create osteochondral defect bilaterally on the medial trochlear ridges of both femurs and treated by the implantation of a bio-engineered scaffold. 11 All were mares, with an age distribution of 4-12 years and a mean ± SD body mass of 169 ± 29 kg.

| Data collection
Prior to the experiment, the ponies were accustomed to treadmill exercise. 12 Kinematic data were recorded using six infra-red threedimensional (3D) optical motion capture (OMC) cameras (Qualisys AB, Motion Capture Systems) that registered the positions of 28 skin mounted spherical reflective markers (19-24 mm) at 200 Hz. For detailed marker placement, see Figure S1. Data collection lasted 30 s for each trial at trot on a treadmill after a warm-up period at walk and trot.
Measurements were performed at the individually preferred trotting speed for each pony, based on visual assessment of locomotion regularity. 12 Subsequent measurements were speed matched, ensuring control over speed along all timepoints. The ponies were measured at three timepoints: prior to the surgical intervention at baseline (T0), and at 3 months (T1) and 6 months (T2) after surgical intervention.

| Data processing
The reconstruction of the 3D coordinates of each marker was automatically calculated by using motion capture software (QTM a , version 2.9). Each marker was identified and labelled using an au- Bone segments were formed based on marker locations and angles between these segments were calculated for each stride. See Table 1 for variable definitions. The data were exported as discrete variables (ie, minima, maxima, and range of motion (ROM)) for discrete data analysis and exported as a timeseries of 101 datapoints per stride for continuous data analysis.

| Data analysis
For the analysis of discrete variables, stride-level data were analysed in Open software R (version 3.3.1) (R-studio, Boston, Massachusetts, USA), using package lme4 (version 1.1-15) for mixed modelling. In each linear mixed model (LMM), random effect was "pony" and "timepoint" was used as the fixed effect. The dependent variables were investigated for a transformation close to normality using probability plotting and examining for skewness and kurtosis. When nonnormally distributed variables were found, these variables were transformed using the Box-Cox method. The model estimates were represented as least squares means and confidence intervals. to compare kinematics between the three timepoints. If there were significant results, post hoc paired t tests were done to determine which timepoints were different. For both the SPM and discrete value analyses, significance was set at P value < .05, and P values were adjusted for multiple comparisons using the Benjamin-Hochberg procedure. 14

| RE SULTS
Two ponies were lost from the study: one due to severe lameness, another because no baseline measurement was recorded. Also, due to a misplaced marker, trials for forelimb kinematics were removed for one pony. The mean ± SD trotting speed was 2.18 ± 0.16, 2.21 ± 0.15 and 2.21 ± 0.16 m/s for T0, T1 and T2, respectively. At all timepoints the mean stride duration was 0.54 ± 0.01 s.
The differences in pelvis pitch and forelimb fetlock extension significantly increased over time. In contrast, the differences in pelvis yaw and forelimb protraction peaked at T1 and decreased again at T2 in relation to T0.

| D ISCUSS I ON
The purpose of the current study was to compare continuous and discrete data analysis techniques to evaluate gait adaptations in cases of induced bilateral hindlimb lameness. With the use of the discrete variable analysis, more variables were found to change significantly compared to continuous data analysis. However, changes outside the peak value areas and the duration of the changes are not taken into account using discrete variables alone, whereas the continuous data analysis considered both.
Analysis of trunk kinematics indicated there was no change in upper body vertical movement, except for the maxDiff of the withers, which was, however, of minor magnitude that is deemed not clinically relevant. 15 Both types of analysis identified comparable adaptations in pelvis pitch and back flexion-extension kinematics.
The change in back flexion-extension was only significant for the discrete variable analysis but a trend was present in the continuous data. The curves for these movements are all sinusoidal and the adaptations are largest at the peaks ( Figure 2B). Discrete variable analysis indicated considerable increases in pelvis yaw and back lateral bending, which were not identified using continuous data analysis.
For pelvis roll kinematics, both types of analyses indicated an increase in pelvis roll angles. The continuous data analysis showed that time wise the difference was largest from mid-to late stance of each hindlimb (Figure 2A), the discrete analysis only identified the significant difference in ROM. The analysis of continuous data hence provides additional information about the moment and duration of the differences during the stride, which can help us better understand and explain the dynamics of gait adaptations to lameness.
In hindlimb fetlock extension angles, small but significant differences were identified using discrete variable analysis, which were not detected by continuous data analysis. Both methods suggested a decrease in protraction ROM and an increase in fetlock extension ROM for both forelimbs. The SPM results additionally showed the presence of significant delays in the timing of the sagittal plane movement of the forelimbs with regard to stride segmentation ( Figure 2C).
In this study the stride segmentation is based on maximal vertical displacement of the sacrum, which is tightly related to the timing of hindlimb kinematics. 16 Therefore, it is possible that forelimb kinematics are not delayed, but that the hindlimb placement is advanced, resulting in earlier support of the trunk during the stride cycle, which is consistent with findings of studies on unilateral lameness. 2 There are several explanations for the differences in findings between continuous and discrete data analysis. Firstly, fewer parameters were found to be significant using SPM compared to LMM. This is concordance with earlier studies comparing discrete to continuous data analysis of under hoof ground reaction forces. 17  p<0.001,p<0.001 *** *** *** *** *** *** p<0.001,p<0.001 *** *** *** *** *** *** *** *** *** *** p<0.001,p<0.001 *** *** *** *** *** *** *** *** *** to which extent continuous data analysis techniques agree with clinical assessments of movement patterns during lameness evaluations.
In conclusion, this study has shown that the use of continuous data provides additional information regarding gait adaptations to bilateral lameness that is complementary to the analysis of discrete variables. The main asset lies in the additional information regarding time dependence and duration of adaptations. This offers opportunities to identify functional adaptations during all phases of the stride cycle, instead of only during events related to peak values.

ACK N OWLED G EM ENTS
The authors sincerely thank the students and caretakers, who helped with the data collection and WMAC Groen for help during the planning of this study.

CO N FLI C T O F I NTE R E S T S
No competing interests have been declared.

AUTH O R CO NTR I B UTI O N S
I. Smit and F. Serra Bragança contributed to data collection, data processing and statistics. E. Hernlund contributed to the statistics.
F. Serra Bragança, H. Brommer and R. van Weeren contributed to planning the experiment. All authors contributed to the preparation of the manuscript and approved the final version.

E TH I C A L A N I M A L R E S E A RCH
The study was approved by the Ethical Committee of Utrecht University (Approval number AVD108002015307 WP23).

PEER R E V I E W
The peer review history for this article is available at https:// publo ns.com/publo n/10.1111/evj.13451.

DATA ACC E S S I B I L I T Y S TAT E M E N T
The complete data set used in this study including raw optical motion capture (OMC) data and processed OMC data can be accessed