## 4 Discussion  
The primary aim of this study was to investigate the impact of different perturbation possibilities, including their timing (Initial Contact, Mid-Stance, and Pre-Swing) and direction (acceleration or deceleration of the one treadmill belt), on gait regularity. Gait regularity was assessed based on the displacement of the center of mass (CoM) in the anterior-posterior (AP), medial-lateral (ML), and vertical (vert) directions. As the regularity of the CoM time series was quantified using sample entropy (SampEn), an additional aim of this study was closely associated with understanding the behavior of this parameter. Consequently, the subsequent aim was to analyze SampEn values in the above-mentioned directions, considering the comparison of the vector length (\(m\)). This study implemented a perturbation protocol via the GRAIL system (Motek Medical BV, Amsterdam, The Netherlands), enabling precise timing and intensity control of perturbations. This accuracy facilitated the manipulation of the time-series duration for analysis. Although the SampEn value is independent of the time series length, Richman and Moorman [22] recommended that the analyzed data consist of at least 200 points. In this study, each dataset comprised 3189 points. However, the SampEn value depends on the choice of \(m\) and \(r\) parameters, and determining suitable parameters for gait analysis is not straightforward [34]. Studies focusing on postural control during quiet standing commonly use an \(m\) value of 2, while \(r\) equals 0.2 times the standard deviation of the data (SD) [12]. However, when considering gait analysis, the selection of parameters becomes less clear, particularly due to the authors' focus on various parameters, such as joint angle and torque waveforms, as well as stride characteristics [35; 36]. According to Tochigi et al. [37], employing a longer \(m\) template (higher \(m\) value) theoretically augments specificity in identifying matched templates, but may lead to a potential decrease in discriminatory power. Many researchers [34; 37] have opted for a minimum template length (\(m=2\)) for gait-related data to maximize discriminatory power. Additionally, previous authors [15; 18; 20] exploredhigher \(m\) values (\(m\) = 4, 6, 8, 10), resulting in consistently lower SampEn values, a trend also observed in this study, mainly for SampEn calculated in ML and vert direction. For the AP direction, the trend differed--SampEn values were the lowest for \(m\) = 2 across all perturbations, except for treadmill deceleration during the Pre-Swing phase. In this case, as \(m\) values increased, SampEn values decreased. To date, no studies have been found that describe the regularity of the human body movement or its segments in reaction to gait perturbations using nonlinear measures, particularly sample entropy. This paper presented results regarding the SampEn values computed for the CoM time series separately in the anterior-posterior (AP), medial-lateral (ML), and vertical directions. This approach enabled the identification of perturbations causing the most irregular gait. It is important to note that the analysis was conducted for \(m\) equal to 2, 4, 6, 8, and 10. The study revealed clear patterns in the center of mass (CoM) displacement, particularly in the vertical and anterior-posterior directions. The most coherent CoM displacement, indicated by low SampEn values indicating regularity, occurred during treadmill deceleration in the Pre-Swing phase. This consistency was reproducible across all \(m\) in both AP and vertical directions. This coherence suggests that the body anticipated and skillfully adapted to this perturbation, recovering quickly to the baseline displacement of CoM, resulting in a regular gait. However, higher SampEn values, reflecting increased irregularity, were recorded at other times, depending on the direction. In the AP direction, irregular CoM behavior was noticeable during treadmill deceleration in the Mid-Stance phase, indicated by the highest SampEn values across all \(m\)-values.