## 2 Materials and Methods
### Statistical Analysis  
We investigated the muscle activation patterns of the lower limb during walking overground with the Ekso. We verify two main hypotheses:  
**Hypothesis 1**. : _While walking with the exoskeleton, the muscle activations changed depending on two factors: (a) the walking aids, i.e., walker or crutches normally used in combination with the exoskeleton; and (b) the assistance provided by the device._  
**Hypothesis 2**. : _The muscle activations changed between walking with and without the exoskeleton, depending on the mechanical structure of the device and the assistance provided by the device._  
To verify these hypotheses, we used the statistical parametric mapping (SPM) approach [29; 41], which allows analyzing statistical differences among continuous curves, without extracting specific scalar variables. We used the repeated measure Anova approach (rANOVA) (spm1d.org), and we ran this analysis for all the eight bilateral muscles we recorded, as well as for all the activation profiles of the muscle synergies. Specifically, for answering the first hypothesis, we performed a rANOVA with three within subject factors: 'assistance' (five levels: B-FA, B-AA, U-AA, U-NA, B-NA), leg (two levels: right versus left leg), and aids (two levels: walker versus crutches). A main significant effect of the latter factor would support the hypothesis that aids influence the lower limb muscle activations while walking with the exoskeleton. A main effect of the first factor would support the hypothesis that different assistance modalities determine different muscle patterns. We expected this difference to be significant, and we planned (pre-planned comparisons) to further verify (a) the effects of adaptive assistance by investigating changes in the muscle activation patterns with respect to imposed maximal assistance, i.e., by comparing B-AA versus B-FA; (b) the effect of unilateral assistance with respect to bilateral assistance by comparing U-AA and B-AA, as well as U-NA and B-NA; (c) the difference between assistance and no assistance by comparing the assistive modalities (-A: B-FA, B-AA, and U-AA) with the non-assistive modalities (-NA: B-NA, U-NA). For our population of healthy controls, we did not expect any significant difference in the leg factor. For each condition, in the Ekso-based modalities, 120 strides for each subject were included in the SPM analysis (= six strides \(\times\) five modalities \(\times\) two legs \(\times\) two aids). Specifically, the comparison among the different assistive modalities was based on 24 strides (= six strides \(\times\) two legs \(\times\) two aids) per condition per subject. The comparison between legs as well as between aids was based on 60 trials (= six strides \(\times\) five modalities \(\times\) two aids/legs)  
As for the second hypothesis, we investigated differences in the muscle activations between normal walking and Ekso-assisted walking, considering separately two modalities: full bilateral assistance or no assistance (rANOVA, two factors: gait with and without exoskeleton and left versus right leg). Since we had five strides starting with each leg for the normal walking, we considered the first five strides for each condition, i.e., we considered 20 strides for each subject in both comparisons (five strides \(\times\) two legs \(\times\) two walking modalities). To exclude that eventual differences while walking with the exoskeleton were due to the aids instead of the Ekso mechanical structure, we asked three subjects (S2, S7, S8) to walk also without the exoskeleton with the two aids, and we compared, performing an rANOVA, the three conditions, i.e., walking without the Ekso (a) with no aids, (b) with a walker, and (c) with crutches. As for the muscle synergies activations profile, we performed an rANOVA with one main factor: walking conditions (with six levels: B-FA, B-AA, U-AA, U-NA, B-NA, and NW).