Balance perturbations as a measurement tool for trunk impairment in cross-country sit skiing

1 In cross-country sit-skiing, the trunk plays a crucial role in propulsion generation and balance 2 maintenance. Trunk stability is evaluated by automatic responses to unpredictable 3 perturbations; however electromyography is challenging. The aim of this study is to identify a 4 measure to group sit-skiers according to their ability to control the trunk. Seated in their 5 competitive sit-ski, ten male and five female Paralympic sit-skiers received six forward and 6 six backward unpredictable perturbations in random order. k-means clustered trunk position 7 at rest, delay to invert the trunk motion, and trunk range of motion significantly into two 8 groups. In conclusion, unpredictable perturbations might quantify trunk impairment and may 9 become an important tool in the development of an evidence-based classification system for 10 cross-country sit-skiers. 11


Introduction
Paralympic cross-country (XC) sit skiing is a Paralympic discipline in which athletes are skiing seated because they have an impairment in function or structure of the lower 23 extremities, pelvis and/or trunk. XC sit-skiers ski using a sledge mounted on a pair of XC 24 skis, named sit-ski, and a couple of poles to generate propulsion. To guarantee a fair 25 competition, in Paralympic events, seated athletes are divided into five different classes (LW 26 [locomotor winter] 10, 10.5, 11, 11.5, 12) reflecting a lower impact of the athlete's 27 impairment on XC-skiing performance (International Paralympic Committee, 2014). 28 In order to achieve maximal performance, an athlete needs to effectively generate 29 propulsion force by means of a symmetrical double poling action and to maintain the balance 30 on the sit-ski during pushing, in downhills and various curves. A common factor that impacts 31 on both propulsion generation and balance maintenance is the athlete's ability to control the 32 trunk. The complex role of the trunk in generating propulsion can be subdivided in three main and maintain the stability as much as possible during the perturbation. Time was given to 121 athletes to recover the initial position on the sit-ski before the following perturbation was 122 initiated. 123 A motion analysis system composed of 8 Vicon cameras and the Vicon Nexus software 124 (Vicon Motion Systems Ltd., Oxford, UK) was used to register trunk movements. A passive 125 reflective marker was fixed on the posterior right corner of the plate. In addition, five markers 126 were placed on the right side of each athlete; on the shoulder (acromion), the elbow (lateral 127 epicondyle), the wrist (ulnar styloid process), on the hip (great trochanter), and on the knee 128 (lateral epicondyle). When the sit-ski seat did not allow fixing the marker directly on the hip, 129 the marker was fixed on the sit-ski in correspondence to the great trochanter. In this study, 130 only the acromion and hip markers were used to evaluate trunk angle with respect to a 131 vertical line (trunk angle). The trunk movement onset was identified as an increase in the 132 acceleration of the acromion marker along the anteroposterior direction.

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Temporal variables 134 To assess the temporal response to unpredictable balance perturbations, two different 135 delays were calculated for each stimulus: the delay between the onset of the sledge 136 acceleration and the onset of the shoulder acceleration (DLY1) and the delay between the 137 onset of the shoulder acceleration and the time when the trunk inverted the motion (DLY2).

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To evaluate the kinematic response, the trunk ROM was assessed. The trunk angle was 140 calculated at three specific times: at rest before the first stimulus (REST), 150 ms after the 141 onset of the shoulder acceleration, and when the trunk inverted the motion. The time span of 142 150 ms was chosen since it represents the interval of possible reflex contribution before 143 voluntary activation (Enoka, 2008), considering the electromechanical delay (Cavanagh & Komi, 1979;Howatson, Glaister, Brouner, & van Someren, 2009;Szpala, Rutkowska-Kucharska, & Drapala, 2014). Trunk flexions and extensions are reported positive and 146 negative, respectively. For each perturbation two trunk ROMs were calculated: ROM150 147 between REST and 150 ms, and ROMinv between REST and when the trunk inverted the 148 motion.

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For each athlete, temporal and kinematic results for the six forward stimuli were averaged; 150 the same was done for the backward stimuli.

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The first step dealt with data preprocessing and variables selection. The data was checked for 153 outliers using the method of the mean plus or minus three standard deviations. The 154 coefficients of variability for temporal and kinematic variables were calculated to select those 155 variables to be considered for the subsequent cluster analysis.

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In a second step, a k-means cluster analysis was performed in order to empirically group 157 athletes according to their ability to control the trunk, ensuring minimal difference within a 158 cluster and maximum difference between clusters (Altmann, Groen,Hart,Vanlandewijck,& 159 Keijsers, 2017). k-means was performed defining distances by means of the squared 160 Euclidean and defining the initial seed by means of the k-means++ algorithm. Since the 161 variables were measured in different scales, they were normalized using the z-score. k-means 162 method requires a defined number of clusters (k) a priori or it can be estimated from data.

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The third step was the cluster analysis validation using both internal and external criteria.

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Model selection for choosing the optimal number of clusters was performed using an internal 165 validation criterion, Silhouette (Rousseeuw, 1987), which is a data-based index that measures 166 both cluster tightness and separation. The number of clusters was a priori hypothesized to be 167 between 2 and 4) and the mean silhouette for each model was calculated. The number of 170 clusters k used for the analysis was identified as the peak in the mean silhouette. The current 171 classes of the athletes were used as external criterion to compare clustering results to a priori 172 information (Xu & Wunsch, 2008). However, it should be remembered that the current 173 classification is not evidence based and thus it does not represent a gold standard.

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In the fourth step, Mann-Whitney test was applied to the clustering input variables in order to 175 assess how strongly they contribute to the discrimination between the clusters and, thereby,  Statistical significance was set at p<0.05 for all analyses.

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The analyses and the statistics were performed using custom-made code prepared in MatLab

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During the perturbation stimuli, the plate movements ranged between 15 cm to 30 cm and in 184 all cases the athletes were able to invert the trunk motion before the sledge stopped moving.

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For all athletes, forward perturbations induced a backward trunk motion, while backward 186 perturbation moved the trunk forward.

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The results for REST, DLY1, DLY2, ROM150, and ROMinv are reported as mean ± standard 188 deviation in Table 1   Results for the external validation criterion were reported in the confusion matrix (Table 2).

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An agreement equal to 80% was found between the two identified clusters (cluster 1 with 212 high impact of impairment and cluster 2 with low impact of impairment) and the real 213 athletes' classes (group 1: LW10 -LW10.5 -LW11 and group 2: LW11.5 -LW12). In 214 addition, sensitivity equal to 67% and 89% was found for group 1 and group 2 respectively 215 and precision equal to 80% for both clusters. Three of the selected variables were of most importance in determining the clusters (Table 3).

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Concerning the temporal variables, DLY2 was higher for cluster 1 in both forward (p=0.003,  At rest, the effect size was equal to 71% (Table 3) (Table 3). The second question regarded coherence between the clusters outcome from the 293 perturbation test and the actual classification of the athletes. Analyses were done for k equal 294 to 2 because of the highest mean silhouette; however the mean silhouette for k equal to 3 was 295 high too. The possibility to consider three clusters would also be interesting as it would 296 divide athletes among total, partial, and no trunk control; nevertheless, considering only two 297 clusters allowed dividing athletes in significant clusters according to their trunk control.

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Lower number of clusters compared to what expected could be due to the small sample size, 299 which should be increased in future studies maybe including athletes with comparable 300 impairment who practice similar sports. Actual results showed accuracy between clusters and 301 the current classes of 80%, very high precision in defining clusters (80%) and high to very 302 high sensitivity for both groups (67% and 89% for group 1 and group 2, respectively). These 303 results were very good considering that the current classification system is not evidence-  Despite some limitations, the unpredictable balance perturbations test together with cluster 348 analysis appears to be a promising addition for the evidence-based classification process in 349 the future because it seems to group the athletes in a valid way due to their impairment level.  grouped four out of six elements coherently with the actual classification; whereas for 506 athletes belong to classed from LW11.5 to LW12 (low level of impairment) athletes 507 coherently grouped are eight out of nine. Therefore, the accuracy is equal to 0.8, which 508 means that a total of 80% of athletes are grouped coherently with the actual classification.       perturbation direction showed higher trunk ROM than forward direction.