ISL(n) and ISU(n) were calculated for both lower and upper limits of the ExFSR and presented as an average among all steps in a walking trial (ISL,avg and ISU,avg). BCL and BCU were also calculated for each walking trial. We compared ISL,avg, ISU,avg, BCL and BCU in the non-disabled group between the high-perturbation and low-perturbation conditions using Wilcoxon signed-rank test. In addition, for each step in each gait trial, we calculated the following stability measures to investigate potential correlations between those and our proposed measures. The definition and symbol used for each stability measure are given in Table Table11.

Hof et al.25,26 used an inverted pendulum model of the human body and suggested that, for dynamic stability of walking and standing, the body XCOM should remain within the BOS limits:

where PCOM and VCOM are the body’s COM position and velocity, g is the gravitational acceleration and l is the equivalent trochanteric length of each participant. They defined the margin of stability (b) as the shortest distance between the XCOM and the BOS boundaries, and calculated it for every instant. The most unstable moment is when the value of b is minimum (bmin) within a step. We chose bmin because it is the most widely used biomechanical stability measure in the literature7,25,37. We calculated bmin for each step and considered the average of bmin among all steps (bmin,avg) as a measure of stability during a walking trial.

The variability of gait parameters such as GCT and SPP (defined in Table Table1)1) has been introduced as an indicator of gait stability and risk of falling38,39. To characterize the inter-stride variability of GCT and SPP, we calculated robust measures, i.e., MAD 24 and nMAD% (Table (Table1),1), among all gait cycles of each walking trial.

To investigate if our proposed measures of stability show, in general, a similar trend of gait stability with variability measures and margin of stability (bmin,avg), despite their different mathematical definitions, we calculated (i) all of the above measures for the two perturbed walking trials of each participant; and (ii) the Spearman’s correlation coefficient between these measures among participants.

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