## 4 Discussion  
The current study investigated the impacts of treadmill gradients on running stability (LyE) and the acceleration magnitude (RMS) of individual phases of motion (PMs). As expected, the results indicate that these effects emerge in specific phases of the gait cycle. Running on a decline treadmill significantly decreases local dynamic stability (indicated by greater LyE) compared to running on an incline, with the effect particularly pronounced in the mid-stance phase of the gait cycle (PM\({}_{3}\)). Additionally, the effects of treadmill gradients were also tested on the acceleration magnitude (RMS) of individual phases of motion (PMs), showing that incline running produces higher acceleration magnitudes (RMS) than decline running, particularly in the mid-stance phase (PM\({}_{3}\)). Regarding running stability, running on a 3-degree and 6-degree decline resulted in higher LyE values, indicating greater instability compared to equivalent incline conditions, particularly in the mid-stance phase (PM\({}_{3}\)) of the gait cycle. These findings might be attributed to several key biomechanical and neuromuscular factors. First, the increased forward momentum generated during downhill running propels the runner forward with possibly less control, unlike uphill running, where gravity slows the runner's pace and offers more stability [6,8]. Unlike outdoor terrain running, which presents irregular perturbations, treadmill gradients provide a controlled perturbation environment. The findings align with [PERSON] et al. study [38], where decline running exhibited heightened instability due to increased eccentric loading. Second, declined gradient treadmill running has been reported to lead to reduced foot-ground contact time, making it harder to maintain balance and stability as the body spends more time in the air and less time in controlled contact with the ground [8]. Third, decline running also places a significant demand on eccentric muscle contractions, especially in the quadriceps, to absorb shock and control descent that might lead to muscle fatigue, impaired motor control, and reduced stability [5]. The rear-foot strike pattern typical in decline running results in higher joint impact forces, particularly on the knees, disrupting movement control and further increasing instability [6,9]. Moreover, progressive incline running produces higher acceleration magnitudes (RMS) than decline running, particularly during the mid-stance phase (PM\({}_{3}\)). This difference can be attributed to several biomechanical factors. Running uphill significantly increases the workload on key muscle groups, including the glutes, hamstrings, and calves, which require greater joint stabilization, especially at the hips [8]. This heightened effort translates into increased metabolic costs as the cardiovascular system works harder to deliver oxygen to these active muscles [6,8]. Biomechanically, incline running tends to increase step frequency while shortening the swing phase, promoting greater strength and endurance, which aids in injury prevention [8]. The reduced foot-ground contact time associated with increased forward momentum makes it more challenging to maintain stability, potentially raising the risk of falls and overuse injuries [8]. Although decline running provides specific training benefits, such as enhancing downhill endurance and strengthening muscles engaged in braking, it also imposes unique challenges, including greater joint impact forces due to a rear-foot strike pattern [6,8]. From a practical perspective, the current findings suggest that decline treadmill running, while beneficial for certain training purposes, should be approached cautiously due to its destabilizing effects. Running is often likened to bouncing; when the foot strikes the ground, kinetic and gravitational potential energy are stored as elastic strain energy in muscles, tendons, and ligaments, which is subsequently recovered during the propulsive phase of the stance [39].