Journal of NeuroEngineering and Rehabilitation

This is the first time that the SPS vs SNS regression is reported in the literature and that a quadratic relationship is described. The nonlinear fit is not surprising, because SPS is non-linearly related to the interplay of 1) the sounds and affected side stance durations and 2) the two double support durations. The quadratic fit stresses the importance of stance time symmetry, since it influences step asymmetry by a factor 2. Question Q3 Question Q3 asked if the study of gait symmetry can be limited to just stance temporal symmetry, leaving out loading symmetry. Results support a negative answer. When IMS vs SNS was examined considering the full set of subjects, a quadratic fit emerged: SNS explained as much as 79% of the variance in IMS. This is the first time this relationship is examined and reported. Since IMS is the integral of GRF over the stance phase, it is not surprising that IMS and SNS are related: a high stance time asymmetry is a leading factor for a high impulse asymmetry. However, GRF magnitude does not linearly increase with time, and has a shape which can differ between the sound and affected side. When all these elements become part of a ratio, it is not surprising that the relation between IMS and SNS can be non-linear. This conclusion is valid for TFM and TFC at group level too, given the R 2 > 0.64. However, this is just partially true for TT, because R 2 decreases to 0.37 and the RMSE is high (0.128): reporting SNS and not IMS can be misleading. This different evidence for TT can be ascribed to two factors only: The improvement in SNS asymmetry (1.03, IQR 0.06) compared to TFM (1.22, IQR 0.09) and TFC (1.11, IQR 0.09) (Table 3 ) ; A greater asymmetry in GRF magnitude between sides. This is supported by the evidences for P1S, as reported in Fig. 7 . Further discussions are postponed to Q6 below. An adequate regression for P1S vs SNS was not found for none of the groups and ALL: the two indexes must measure different construct and therefore they must be separately reported. Question Q4 Question Q4 asked if gait symmetry depends on the level of amputation. Results support a positive answer. With reference to SNS, all amputee groups had statisti- cally different median values. All TF spend more time on the sound side: TFM have the highest asymmetry (median asymmetry of 22%), which is twofold the TFC ’ s (11%). As can be seen in Fig. 4 , this is also true for 75% of TT, which means that ¼ of TT do spend more time on the affected side . This was never clearly reported in the literature. The TT asymmetry (3%) is 4 times less than TFC. Controls, in median, have a perfect symmetry, with a IQR of just 3%. Fig. 7 a Box plot for the first peak symmetry index (P1S) after grouping all transfemoral amputee together (TF); b Results of the Kruskal-Wallis test; c Pairwise comparisons: non-overlapping lines indicate a statistically significant difference. TF: transfemoral amputees, TT: transtibial amputees Cutti et al. Journal of NeuroEngineering and Rehabilitation 2018, 15 (Suppl 1):61 Page 37 of 72