## 1 Introduction  
When individuals experience perturbations, such as unexpected obstacles or environmental changes, their gait patterns temporarily change to accommodate these disruptions. The body's natural response is to adjust the gait to maintain balance and avoid falling [1]. Some common examples of perturbations that can affect gait patterns include the following: encountering obstacles (when individuals encounter an obstacle in their path, they may modify their gait to step over or around it, leading to changes in their step length, height, or cadence) [2]; changes in the walking surface (walking on an uneven or slippery surface can cause alterations in gait to ensure stability, such as taking smaller steps or walking slower to maintain balance) [3]; and unexpected balance challenges (any disturbance to a person's postural control, whether external (e.g., a push or pull) or internal (e.g., dizziness), can lead to immediate changes in gait to regain equilibrium) [4; 5; 6; 7]. In a laboratory setting, it is possible to induce postural disturbances during gait and observe the body's reactions under controlled and safe conditions. According to a review written by [PERSON], et al. [8], the most common method of balance perturbation during gait was treadmill translation. The authors also employed other perturbation methods, including the following: participant perturbation devices (waist- or hip-worn attachments connected to external structures that pulled or pushed participants [9; 10; 11; 12]); vibration devices for muscles [13]; an oscillating pendulum system worn on participants' backs [14]; a mechanized foot block [15]; and a narrow treadmill-based step task while participants performed a cognitive task [16]. When choosing a perturbation method for gait, such as a treadmill, there are opportunities to vary several parameters, including the direction of the perturbation application (forward corresponds to tripping, backward corresponds to slipping) [17], the magnitude [18], the duration of the perturbation [19], and the phase of the gait cycle at which it is applied [20]. Of course, all these alterations can occur at different gait speeds. The possibilities are indeed many. Both in laboratory conditions and in reality, to avoid falling, individuals perform rapid, often involuntary, reflex-like compensatory motions [3; 5]. The described reactions are part of the dynamic balance control system. It is a continuous process that involves a complex interplay of sensory information from the vestibular system (inner ear--provides information related to the position, balance, and spatial orientation), visual input (helps identify obstacles or changes in terrain), and proprioceptive feedback (sensory information from muscles and joints) to make real-time adjustments to counteract any disturbances or perturbations encountered during walking or other activities [21]. Based on central processing, the brain sends motor commands to muscles, directing them to adjust the gait pattern and posture to counteract the perturbation. These adjustments may include changes in step length, foot placement, joint angles, and muscle activations. These adaptive changes are generally temporary and help prevent falls. However, if the changes in gait patterns are severe, they can lead to micro-injuries. In the aforementioned review [8], only two papers analyzed the reactions to perturbations applied during the toe-off phase [11; 22]. In both papers, perturbations were applied in the mediolateral direction. [PERSON], et al. [22] investigated gait kinematics and gluteus medius muscle activity during the first recovery step in ten chronic-stage stroke survivors. [PERSON], et al. [11] explored perturbed human walking, focusing on the relationship between the horizontal velocity of the center of mass (CoM) at heel strike and toe-off with variables such as foot placement relative to the CoM, the upcoming center of pressure relative to the CoM, and the ground reaction forces.