Subject information
Seventeen individuals from the University of South Florida’s Tampa campus were invited to participate in the gait study. Four participants did not meet the eligibility criteria, and two participants decided to withdraw from the experiment after their first visit. This resulted in 11 eligible subjects that completed all six trials of the study. The baseline gait characteristics of these individuals are shown in Table 4.
Table 4
Demographics and baseline gait characteristics of eleven eligible subjects that completed the six trials.
Subject | Gender | Dominant leg | Gait velocity (m/s) | Stride time (s) | Step length asymmetry (%) | Step time asymmetry (%) |
S-2 | Male | Left | 1.15 | 1.10 | 2.4 | 5.2 |
S-3 | Male | Right | 1.15 | 1.08 | 2.5 | 2.1 |
S-4 | Male | Right | 1.10 | 1.15 | -0.5 | -2.9 |
S-5 | Female | Right | 1.00 | 1.07 | -1.1 | 4.7 |
S-6 | Female | Right | 1.00 | 1.06 | -2.3 | -1.8 |
S-7 | Male | Right | 1.17 | 1.08 | -1.4 | 2.0 |
S-8* | Female | Right | 1.10 | 1.05 | 3.3 | -3.8 |
S-9 | Male | Right | 1.20 | 1.06 | -5.0 | -2.0 |
S-10 | Female | Left | 1.15 | 1.12 | 1.2 | 2.6 |
S-11 | Female | Left | 1.00 | 1.11 | 1.1 | -1.6 |
S-12 | Male | Right | 1.10 | 1.14 | 1.1 | 0.9 |
Population average (± std) | 1.10 ± 0.074 | 1.09 ± 0.036 | -0.11 ± 2.46 | 0.02 ± 2.80 |
*Subject was removed from analysis |
S-8 returned on her fifth session with a high baseline step length asymmetry (approximately − 30%). The asymmetry exceeded the spatiotemporal asymmetry threshold that was specified for the subjects’ eligibility criteria, necessitating additional tests to investigate the effect of this change on the overall study. Pearson’s correlation test between the baseline and adaptation stages of average step length asymmetry for \({T}_{C}\)revealed that the outcomes of the overall subject population were likely to be significantly affected by this subject’s change: r = 0.672, p = 0.024. A second correlation test without S-8 showed that the baseline conditions of the resulting subject population (n = 10) no longer had a significant effect on step length asymmetry: r = 0.583, p = 0.768. Therefore, S-8 was dropped from all subsequent analysis. The remaining subject population consisted of two individuals that may have affected the overall gait outcomes:
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S-4’s spatiotemporal asymmetry appeared to increase during post-adaptation of \({T}_{C}\).
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S-10 had a misaligned femur-patella. This caused her left leg length to be greater than that of the right, a condition known as leg length discrepancy (LLD).
Effects of interference on acquired and retained gait (a)symmetry
Gait asymmetries were found to be non-normal using the Shapiro-Wilk test. Friedman’s test of the gait parameters for the six trials between the seven experimental stages showed statistical significance for asymmetries in step length (SLA) and step time (STA) at the 0.05 significance level. Differences in vertical reaction force asymmetry (GRF) between experimental stages were found to be statistically significant (p < 0.05) for all experiments except \({T}_{C}\). Statistical outcomes of the between-stages for the six trials are shown in Tables 5 (Step Length), 6 (Step Time), and 7 (Vertical Reaction Forces). Friedman’s test was performed between all the experimental stages (BL, EA-1, LA-1, EA-2, LA-2, EPA, LPA), and Wilcoxon signed-rank tests demonstrate the statistical significance of the difference in asymmetry at all experimental stages compared to baseline (BL) conditions (Tables 5–7).
Step length
Exaggeration of step length asymmetry was statistically significant during two or more adaptation stages in all six trials. SLA was retained during EPA for both control trials, i.e., \({T}_{S}\) and \({T}_{C}\), and sequential combination trials in which ARAC was followed by SBT, i.e., \({T}_{CS}\) and \({T}_{cS}\). The changes in SLA were retained until LPA for both control trials, i.e., \({T}_{S}\) and \({T}_{C}\), as well as \({T}_{cS}\), compared to baseline conditions (Table 5).
Table 5
Between-stages statistical test outcomes for step length asymmetry (SLA).
Step length | \({T}_{S}\) | \({T}_{C}\) | \({T}_{SC}\) | \({T}_{CS}\) | \({T}_{Sc}\) | \({T}_{cS}\) |
Friedman’s test outcomes | \({\chi }^{2}\left(6\right)=53.271, p<0.001\)* | \({\chi }^{2}\left(6\right)=19.586, p=0.003\)* | \({\chi }^{2}\left(6\right)=41.657, p<0.001\)* | \({\chi }^{2}\left(6\right)=43.157, p<0.001\)* | \({\chi }^{2}\left(6\right)=41.571, p<0.001\)* | \({\chi }^{2}\left(6\right)=46.329, p<0.001\)* |
Statistical difference in asymmetry against BL | EA-1 | Z = -2.803, p = 0.005* | Z = -1.580, p > 0.05 | Z = -2.803, p = 0.005* | Z = -1.070, p > 0.05 | Z = -2.803, p = 0.005* | Z = 0.153, p p > 0.05 |
LA-1 | Z = -2.803, p = 0.005* | Z = -2.497, p = 0.013* | Z = -1.274, p > 0.05 | Z = -1.988, p = 0.047* | Z = -1.784, p > 0.05 | Z = -1.988, p = 0.047* |
EA-2 | Z = -2.803, p = 0.005* | Z = -2.090, p = 0.037* | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* |
LA-2 | Z = -2.090, p = 0.037* | Z = -2.191, p = 0.028* | Z = -0.663, p > 0.05 | Z = -1.988, p = 0.047* | Z = -1.070, p > 0.05 | Z = -2.293, p = 0.022* |
EPA | Z = -2.803, p = 0.005* | Z = -2.395, p = 0.017* | Z = -0.968, p > 0.05 | Z = -2.803, p = 0.005* | Z = -1.478, p > 0.05 | Z = -2.803, p = 0.005* |
LPA | Z = -2.497, p = 0.013* | Z = -2.293, p = 0.022* | Z = -1.376, p > 0.05 | Z = -0.561, p > 0.05 | Z = -1.070, p > 0.05 | Z = -2.191, p = 0.028* |
Statistically significant outcomes (p < 0.05) are indicated in bold and with a single asterisk (*). |
Friedman’s test revealed that there were statistically significant (p < 0.05) differences during EA between (i) the control trials and their corresponding sequential combinations: \({}^{2}\left(5\right)=42.57, p<0.001\), and (ii) between adaptation-1 and adaptation-2 of the sequential combination trials: \({}^{2}\left(7\right)=58.8, p<0.001\). Similar outcomes were found for LA between (i) the control trials and sequential combination trials: \({}^{2}\left(5\right)=22.51, p<0.001\) and (ii) between adaptation-1 and adaptation-2 of the sequential combination trials: \({}^{2}\left(7\right)=17.83, p=0.0127\).
Between-trial pairwise comparisons using Wilcoxon signed-rank tests showed that acquired and retained SLA were significantly greater for \({T}_{S}\) compared to \({T}_{C}\) at the following experimental stages: EA (Z = -2.80, p = 0.005), EPA (Z = 3.74, p = 0.0002), and LPA (Z = 2.80, p = 0.005).
Wilcoxon signed-rank tests also showed that the differences in SLA between \({T}_{S}\) and the sequential combination trials in which ARAC was followed by SBT (\({T}_{CS}\) and \({T}_{cS}\)) were not statistically significant (p > 0.05) during EPA or LPA. Changes in SLA during early and late adaptation (EA and LA) to SBT between adaptation-1 and adaptation-2 of the sequential combination trials (\({T}_{CS}\) vs \({T}_{SC}\), and \({T}_{cS}\) vs \({T}_{Sc}\)) were also statistically insignificant (p > 0.05).
During EA, acquisition of SLA in adaptation to ARAC was greater in \({T}_{SC}\) compared to \({T}_{C}\). This was shown by the statistically significant difference in SLA between (i) \({T}_{S\varvec{C}}\) and \({T}_{C}\) (Z = -2.8, p = 0.005), as well as (ii) \({T}_{S\varvec{c}}\) and \({T}_{c}\) (Z = -2.70, p = 0.007). Changes in SLA during late-stage adaptation (LA) to ARAC were not statistically significant (p > 0.05) between (i) \({T}_{C}\) and \({T}_{SC}\), or (ii) \({T}_{c}\) and \({T}_{Sc}\). However, comparisons between adaptation-1 and adaptation-2 stages within the sequential combination trials showed contrasting trends in adaptation to ARAC during EA and LA:
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\({T}_{\varvec{c}S}\) (adaptation-1) and \({T}_{S\varvec{c}}\) (adaptation-2). EA: Z = -2.80, p = 0.005; LA: Z = -2.50, p = 0.013
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\({T}_{\varvec{C}S}\) (adaptation-1) and \({T}_{S\varvec{C}}\) (adaptation-2). EA: Z = -2.80, p = 0.005; LA: Z = -2.19, p = 0.028
Pairwise comparisons were performed between sequential combination trials with the same order to determine the effect of congruence on adaptability to the intervention during adaptation-2. Wilcoxon signed-rank tests showed that SLA was significantly greater during EA-2 of \({T}_{S\varvec{C}}\) compared to \({T}_{S\varvec{c}}\): Z = -2.80, p = 0.005. However, the difference in SLA between \({T}_{CS}\) and \({T}_{cS}\) (Z = 0.56, p > 0.05) was not statistically significant (p > 0.05) during EA-2 (Fig. 2).
Friedman’s test performed between the six trials revealed that there were statistically significant differences in retained SLA between the six trials during (i) EPA: \({}^{2}\left(5\right)=33.94, p<0.001\), and (ii) LPA: \({}^{2}\left(5\right)=19.37, p =0.0016\). Between-trial pairwise comparisons using Wilcoxon signed-rank test showed that \({T}_{S}\) retained a higher magnitude of SLA than \({T}_{C}\) during the post-adaptation stages: (i) EPA: Z = 3.742, p = < 0.001 (ii) LPA: Z = 2.803, p = 0.0051. Additionally, retained SLA during EPA and LPA was greater for \({T}_{S}\) compared to sequential combinations in which SBT was followed by ARAC: (i) \({T}_{S}\) and \({T}_{SC}\) (EPA: Z = 3.363, p < 0.001, LPA: Z = 2.599, p = 0.009) and (ii) \({T}_{S}\) and \({T}_{Sc}\) (EPA: Z = 3.213, p = 0.001, LPA: Z = 1.988, p = 0.047). The differences in retained SLA at EPA between \({T}_{S}\) and sequential combinations in which ARAC was followed by SBT, i.e., \({T}_{CS}\) and \({T}_{cS}\), were not statistically significant (p > 0.05).
Wilcoxon signed-rank test showed that the differences in retained SLA during EPA were not statistically significant (p > 0.05) between \({T}_{C}\) and sequential combination trials in which SBT was followed by ARAC, i.e., \({T}_{SC}\) and \({T}_{Sc}\). Changes in SLA were greater for sequential combination trials in which ARAC was followed by SBT compared to \({T}_{C}\), as shown by the following outcomes: \({T}_{CS} vs. {T}_{C} (Z= -3.742, p<0.001) and {T}_{cS}\) vs. \({T}_{C}\) (Z = -3.515, p < 0.001) during EPA. During LPA, the differences in SLA were statistically significant between \({T}_{C}\) and the congruent sequential combination trials: \({T}_{SC}\) (Z = -1.988, p = 0.047) and \({T}_{CS}\) (Z = -2.599, p = 0.009). The difference between \({T}_{C}\) and the incongruent sequential combination trials were not statistically significant (p > 0.05) during LPA.
Pairwise comparisons between the sequential combination trials revealed that order is a noteworthy factor for SLA during the initial stage of post-adaptation. Sequential combination trials in which ARAC was followed by SBT (\({T}_{CS}\) and \({T}_{cS}\)) retained a higher magnitude of SLA than the corresponding trials with the opposite sequence (\({T}_{SC}\) and \({T}_{Sc}\)) during EPA: (i) \({T}_{SC}\) and \({T}_{CS}\) (Z = -3.213, p = 0.001), and (ii) \({T}_{Sc}\) and \({T}_{cS}\) (Z = -2.759, p = 0.006). The same pairwise comparisons performed during LPA showed a lack of statistical significance (p > 0.05). The difference in retained SLA was statistically significant between \({T}_{Sc}\) and \({T}_{SC}\): Z = -2.079, p = 0.037 Conversely, congruence was not a significant factor in retained SLA (EPA and LPA), as shown by the lack of statistically significant difference (p > 0.05) between sequential combinations in which ARAC was followed by SBT, i.e., \({T}_{CS}\) and \({T}_{cS}\).
Step time
Friedman’s test showed that step time asymmetry (STA) was significantly different (p < 0.05) between baseline (BL) conditions and other experimental stages (Table 6). Pairwise comparisons using Wilcoxon signed-rank tests showed that STA was retained until EPA for \({T}_{C}\) and the two congruent sequential combination trials: \({T}_{SC}\) and \({T}_{CS}\). Five out of the six trials showed that STA had returned to baseline conditions during LPA, except \({T}_{CS}\) which exhibited retained STA during LPA that was significantly greater than BL conditions (Table 6).
For the between-trial evaluation, Friedman’s test revealed that there were statistically significant differences between the control trials and sequential combinations: \({}^{2}\left(5\right)=27.37, p<0.001\), as well as between adaptation-1 and adaptation-2 stages of the sequential combination trials: \({}^{2}\left(7\right)=45.73, p <0.001\) during early adaptation (EA). Similar outcomes were found for the late adaptation (LA) stage between control trials and sequential combinations: \({}^{2}\left(5\right)=26.69, p<0.001\), and between adaptation-1 and adaptation-2 of the sequential combination trials: \({}^{2}\left(7\right)=39.37, p<0.001\) (Fig. 3). The differences in retained STA were statistically significant during EPA: \({}^{2}\left(5\right)=22.91, p<0.001\), but not during LPA: \({}^{2}\left(5\right)=8.63, p>0.05\).
Table 6
Between-stages statistical test outcomes for step time asymmetry (STA).
Step time | \({T}_{S}\) | \({T}_{C}\) | \({T}_{SC}\) | \({T}_{CS}\) | \({T}_{Sc}\) | \({T}_{cS}\) |
Friedman’s test outcomes | \({\chi }^{2}\left(6\right)=46.071, p<0.001\)* | \({\chi }^{2}\left(6\right)=30.257, p<0.001\)* | \({\chi }^{2}\left(6\right)=32.486, p<0.001\)* | \({\chi }^{2}\left(6\right)=48.686, p<0.001\)* | \({\chi }^{2}\left(6\right)=39.686, p<0.001\)* | \({\chi }^{2}\left(6\right)=32.100, p<0.001\)* |
Statistical difference in asymmetry against BL | EA-1 | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -0.357, p > 0.05 |
LA-1 | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -1.478, p > 0.05 |
EA-2 | Z = -2.803, p = 0.005* | Z = -2.803, p = 0.005* | Z = -1.784, p > 0.05 | Z = -2.803, p = 0.005* | Z = -0.051, p > 0 .05 | Z = -2.803, p = 0.005* |
LA-2 | Z = -2.701, p = 0.007* | Z = -2.803, p = 0.005* | Z = -2.497, p = 0.013* | Z = -2.803, p = 0.005* | Z = -2.191, p = 0.028* | Z = -2.701, p = 0.007* |
EPA | Z = -0.561, p > 0.05 | Z = -2.701, p = 0.007* | Z = -2.701, p = 0.007* | Z = -2.191, p = 0.028* | Z = -1.274, p > 0.05 | Z = -0.968, p > 0.05 |
LPA | Z = -1.172, p > 0.05 | Z = -1.682, p > 0.05 | Z = -0.561, p > 0.05 | Z = -2.191, p = 0.028* | Z = -0.663, p > 0.05 | Z = -0.051, p > 0.05 |
Statistically significant outcomes (p < 0.05) are indicated in bold and with a single asterisk (*). |
Pairwise comparisons performed using Wilcoxon signed-rank test showed that acquired STA was significantly greater for \({T}_{S}\) than \({T}_{C}\) during EA: Z = 2.49, p = 0.013. The difference in STA between \({T}_{S}\) and \({T}_{C}\) was not statistically significant (p > 0.05) during other experimental stages, i.e., LA, EPA, and LPA. The effect of congruence was evaluated by comparisons between (i) \({T}_{SC}\) and \({T}_{Sc}\), and (ii) \({T}_{CS}\) and \({T}_{cS}\). It was found that acquired STA was significantly higher during EA-2 of \({T}_{CS}\) compared to \({T}_{cS}\): Z = 2.293, p = 0.022. This difference in STA between \({T}_{CS}\) and \({T}_{cS}\) was not statistically significant during other experimental stages: LA, EPA, and LPA. Additionally, acquired and retained STA was significantly higher for \({T}_{SC}\) compared to \({T}_{Sc}\) during LA-2 and EPA, as shown by the statistically significant difference between them: (i) LA-2 (Z = -2.39, p = 0.017) and (ii) EPA (Z = -2.079, p = 0.038). Order was not a statistically significant factor during EPA or LPA, demonstrated by the lack of statistical significance between sequential combination trials of opposite order(s).
Vertical reaction force
Friedman’s test showed that there were statistically significant differences between the different experimental stages for all trials except \({T}_{C}\). Pairwise comparisons using Wilcoxon signed-rank test showed that changes in GRF were not retained until LPA for any of the six trials (Table 7).
The differences in GRF between the six trials were found to be statistically significant between the control trials and their sequential combinations using Friedman’s test during the following stages: (i) EA: \({}^{2}\left(5\right)=31.26, p<0.001\) and (ii) LA: \({}^{2}\left(5\right)=12.63, p=0.027\). Friedman’s test comparing GRF between adaptation-1 and adaptation-2 of the sequential combination trials showed significant differences in GRF during EA: \({}^{2}\left(7\right)=45.37, p<0.001\). However, the differences in GRF between adaptation-1 and adaptation-2 within the sequential combination trials were not statistically significant during LA: \({}^{2}\left(7\right)=9.47, p>0.05\).
Table 7
Between-stages statistical test outcomes for vertical reaction force asymmetry (GRF).
Vertical reaction force | \({T}_{S}\) | \({T}_{C}\) | \({T}_{SC}\) | \({T}_{CS}\) | \({T}_{Sc}\) | \({T}_{cS}\) |
Friedman’s test outcomes | \({\chi }^{2}\left(6\right)=32.529, p<0.001\)* | \({\chi }^{2}\left(6\right)=9.943, p>0.05\) | \({\chi }^{2}\left(6\right)=32.143, p<0.001\)* | \({\chi }^{2}\left(6\right)=23.571, p<0.001\)* | \({\chi }^{2}\left(6\right)=24.943, p<0.001\)* | \({\chi }^{2}\left(6\right)=29.314, p<0.001\)* |
Statistical difference in asymmetry against BL | EA-1 | Z = -2.701, p = 0.007* | N/A | Z = -2.701, p = 0.007* | Z = -2.701, p = 0.007* | Z = -2.599, p = 0.009* | Z = -1.58, p > 0.05 |
LA-1 | Z = -1.58, p > 0.05 | N/A | Z = -0.357, p > 0.05 | Z = -1.07, p > 0.05 | Z = -0.255, p > 0.05 | Z = -1.682, p > 0.05 |
EA-2 | Z = -1.478, p > 0.05 | N/A | Z = -2.701, p = 0.007* | Z = -1.682, p = 0.093 | Z = -2.497, p = 0.013* | Z = -2.701, p = 0.007* |
LA-2 | Z = -1.07, p > 0.05 | N/A | Z = -2.497, p = 0.013* | Z = -0.357, p > 0.05 | Z = -0.663, p > 0.05 | Z = -1.07, p > 0.07 |
EPA | Z = -2.803, p = 0.005* | N/A | Z = -2.293, p = 0.022* | Z = -2.803, p = 0.005* | Z = -0.357, p > 0.05 | Z = -2.497, p = 0.013* |
LPA | Z = -1.172, p > 0.05 | N/A | Z = -1.274, p > 0.05 | Z = -0.968, p > 0.05 | Z = -0.764, p > 0.05 | Z = -1.886, p > 0.05 |
Statistically significant outcomes (p < 0.05) are indicated in bold and with a single asterisk (*). |
Pairwise comparisons using Wilcoxon signed-rank test showed that acquired and retained GRF were significantly greater for \({T}_{S}\) than \({T}_{C}\) during the following experimental stages: EA (Z = -2.70, p = 0.007), LA (Z = -2.19, p = 0.028), and EPA (Z = 2.684, p = 0.0073). ARAC proved to be ineffective as an intervention technique for GRF on its own, as shown by the lack of statistically significant differences between BL and the other experimental stages of \({T}_{C}\) (Table 7). However, GRF exhibited a reduction in acquired asymmetry during LA when ARAC was applied before SBT. This was revealed by the statistically significant difference between \({T}_{S}\) and \({T}_{CS}\) during LA: Z = -1.99, p = 0.047.
On the other hand, applying SBT before ARAC resulted in increased GRF during early stages of adaptation (EA-2) to ARAC for both congruent and incongruent trials. This was demonstrated by the statistically significant differences between \({T}_{C}\) and the sequential combination trials in which SBT was followed by ARAC: (i) \({T}_{C}\) and \({T}_{S\varvec{C}}\) (Z = -2.60, p = 0.009), and (ii) \({T}_{c}\) and \({T}_{S\varvec{c}}\) (Z = -2.80, p = 0.005). Additionally, results of pairwise comparisons between EA-1 and EA-2 of (i) \({T}_{S\varvec{C}}\) vs \({T}_{\varvec{C}S}\) (Z = -1.988, p = 0.047), and (ii) \({T}_{S\varvec{c}} vs {T}_{cS}\) (Z = -2.40, p = 0.017) confirm this outcome. GRF was also significantly higher for the congruent combination (i.e.,\({T}_{SC})\) compared to the incongruent combination (i.e., \({T}_{Sc})\) during EA: Z = -2.80, p = 0.005. Conversely, GRF did not exhibit statistically significant changes from the after-effects of ARAC during the early stages of adaptation (EA) to SBT (Fig. 4).
Friedman’s test showed that the difference in GRF between the six trials was statistically significant during EPA: \({}^{2}\left(5\right)=19.6, p=0.0015\), but not LPA: \({}^{2}\left(5\right)=4.69, p>0.05\). Pairwise comparisons showed that the difference in retained GRF between \({T}_{S}\) and sequential combination trials in which ARAC was followed by SBT, i.e., \({T}_{CS}\) and \({T}_{cS}\), were not statistically significant (p > 0.05). Retained GRF during EPA was significantly greater for \({T}_{S}\) compared to sequential combination trials in which SBT was followed by ARAC, as shown by the following pairwise comparisons: (i) \({T}_{S}\) vs \({T}_{SC}\): Z = 3.137, p = 0.0017, (ii) \({T}_{S}\) vs \({T}_{Sc}\): Z = -2.608, p = 0.009. Similarly, retained GRF during EPA was greater for sequential combination trials in which ARAC was followed by SBT compared to \({T}_{C}\): (i) \({T}_{C}\) vs \({T}_{CS}\): Z = -3.137, p = 0.0017, and (ii) \({T}_{C}\) vs \({T}_{cS}\): Z = -3.14, p = 0.0017. In addition, order was found to be a substantial factor in retained GRF during EPA, as shown by the statistically significant difference between (i) \({T}_{SC}\) and \({T}_{CS}\) (Z = -2.99, p = 0.003), and (ii) \({T}_{Sc}\) and \({T}_{cS}\) (Z = -2.61, p = 0.009). The differences between the congruent and incongruent trials were not statistically significant (p > 0.05) for either sequence: (i) SBT followed by ARAC, and (ii) ARAC followed by SBT.
Contribution of SBT and ARAC in acquisition and retention of gait asymmetry
Acquisition and retention of gait asymmetry were modeled over the adaptation and post-adaptation stages, respectively. The control trials (\({T}_{S}, {T}_{C}\)) were used to generate the linear regression models using the superposition principle. Gait asymmetries acquired during the first intervention in the sequential combination trials (\({T}_{SC}, {T}_{CS},{T}_{Sc}, and {T}_{cS}\)), i.e., during adaptation-1 (Fig. 1), were not used to conceive the four linear regression models; gait asymmetries during these experimental stages, i.e., EA-1 and LA-1, are shown over a grey background in Fig. 5. Acquisition (during adaptation-2) and retention (during post-adaptation) of gait asymmetries were modeled individually to enable accurate comparisons of characteristics between SBT and ARAC.
Acquisition of gait asymmetry
The coefficients of the linear model, i.e., “S” and “A” (indicated in Equations 4 − 1 and 4 − 2), and the goodness-of-fit corresponding to the four sequential combination trials are shown in Table 8. The relative effect of the second intervention (ongoing during adaptation-2) was greater compared to the previous intervention in magnitude during adaptation-2. The extent to which after-effects from SBT impacted the ability to adapt to ARAC (\({S}_{1}\) = 0.11) was notably higher compared to the extent to which after-effects from ARAC affected adaptation to SBT (\({A}_{1}\) = 0.03). It was also found that goodness-of-fit of the linear models for trials in which SBT was followed by ARAC, i.e., \({T}_{SC}\) and \({T}_{Sc}\), were substantially lower than those in which ARAC was followed by SBT, i.e., \({T}_{CS}\) and \({T}_{cS}\).
Table 8
Contribution of SBT and ARAC in acquired gait asymmetry and the sequential trials’ model fit.
Trial sequence | Contribution of SBT (S) | Contribution of ARAC (A) | Goodness of fit |
Congruent | Incongruent |
SBT → ARAC \({(T}_{SC}\), \({T}_{Sc}\)) | \({\text{S}}_{\text{1}}\text{ }\)= 0.11 | \({\text{A}}_{\text{2}}\)= 0.85 | \({R}^{2}\) = 0.2, p < 0.001 | \({R}^{2}\) = 0.08, p = 0.007 |
ARAC → SBT (\({T}_{CS}\), \({T}_{cS}\)) | \({\text{S}}_{\text{2}}\) = 0.9 | \({\text{A}}_{\text{1}}\) = 0.03 | \({R}^{2}\) = 0.64, p < 0.001 | \({R}^{2}\) = 0.65, p < 0.001 |
Retention of gait asymmetry
The proportion of after-effects from the second intervention was greater than those from the first in the sequential combination trials. Additionally, the after-effects of ARAC were relatively more impactful than SBT during post-adaptation stages – regardless of the order within the sequential combination, as shown in Table 9.
Table 9
Contribution of SBT and ARAC in retained gait asymmetry and the sequential trials’ model fit.
Trial sequence | Contribution of SBT (S) | Contribution of ARAC (A) | Goodness of fit |
Congruent | Incongruent |
SBT → ARAC \({(T}_{SC}\), \({T}_{Sc}\)) | \({\text{S}}_{\text{1}}\) = 0.1 | \({\text{A}}_{\text{2}}\) = 0.76 | \({R}^{2}\) = 0.71, p < 0.001 | \({R}^{2}\) = 0.22, p < 0.001 |
ARAC → SBT (\({T}_{CS}\), \({T}_{cS}\)) | \({\text{S}}_{\text{2}}\) = 0.24 | \({\text{A}}_{\text{1}}\) = 0.14 | \({R}^{2}\) = 0.35, p < 0.001 | \({R}^{2}\) = 0.51, p < 0.001 |