## 2 Methods
### Data Analysis  
We extracted the data using Balance Clinic software (ver. 2.02.01; AMTI, Watertown, MA, USA), while a forceplate (Accusway Plus; AMTI, Watertown, MA, USA) was used to record center of pressure (COP) data at a sampling rate of 50 Hz. The data were filtered with a fourth-order zero lag, low-pass filter with a cut-off frequency of 5 Hz [35]. COP data files were processed with a custom MATLAB program (MathWorks Inc., Natic, MA, USA) to calculate the mean and standard deviations of TTB minima in AP and ML directions [36; 37; 38]. For each ML COP data point, TTB in the TTBML was computed using COP ML and velocity (Formula (1)). When the COP MLi indicated a medial movement, we calculated the distance between COP MLi and the medial border of the foot, and then divided it by the COP MLi velocity to determine the time required for COP MLi to reach the medial border, assuming constant movement without acceleration or deceleration. Conversely, if COP MLi showed lateral movement, we computed the distance from COP MLi to the lateral border of the foot and divided it by the corresponding COP MLi velocity. Additionally, we generated a time series of TTB measures in the AP direction in a similar manner, determining the time it would take for COP API to reach either the anterior or the posterior foot boundary.  
\[VCOPMLi=dCOPMLi/0.02 sTTBMLi=dMLboundi//VCOPMLi \tag{1}\]  
Formula (1) shows how TTB was calculated based on center of pressure (COP) excursions in the mediolateral direction.  
TTB, which incorporates both spatial and temporal aspects within the context of the base of support size, has been demonstrated to be particularly sensitive in CAI patients. It represents a distinct pattern characterized by peaks and valleys, with each valley corresponding to a change in the COP direction. These valley points within the data can be interpreted as potential instances of postural instability, whereas the peaks signify moments of postural stability [39]. Essentially, these valleys mark the transition points when the COP is closest, in terms of time, to one edge of the base of support just before changing its course to move towards the opposite edge, which is further away. Lower TTB values indicate less stability due to a more rapid rate of change in the COP or proximity to the boundary. In our study, TTB measures served as dependent variables, representing the mean of minimum samples and the standard deviation (SD) of minimum samples in both ML and AP directions. The mean of minimum samples signifies the temporal margin to the boundary of support, indicating how much time is available before the boundary is reached. Meanwhile, the SD of minimum samples represents the variability among all of the identified valley minima observed throughout the entire trial. These values were then utilized to generate \"%modulation\" scores for each outcome, representing the extent of impairment of postural control when visual input is eliminated. The %modulation scores were calculated using the following formula: [(eyes open \(-\) eyes closed)/eyes open] \(\times\) 100 [40]. A lower %modulation score suggests decreased reliance on visual information and a greater emphasis on somatosensory information to maintain postural control.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Variables** & **Value** \\ \hline Rep. time (s) & 44.30 \(\pm\) 7.05 \\ HR & 184.80 \(\pm\) 6.34 \\ RPE & 17.73 \(\pm\) 1.35 \\ MVJH (cm) & 39.00 \(\pm\) 16.46 \\ \hline \hline \end{tabular} Abbreviations: HR, heart rate; RPE, rated perceived exertion; MVJH, maximum vertical jump height; Rep. time, repetition time.  
\end{table}
Table 2: The average completion time, heart rate, perceived exertion, and vertical jump height at the endpoint of the functional fatigue protocol (mean \(\pm\) SD).