## 1 Introduction  
Running is a fundamental human motor task that plays a vital role in various physical activities and sports, serving not only as a primary mode of locomotion but also as a key element in competitive athletics. The complexity of running movements involves the coordinated contribution of multiple body segments, including the arms, legs, hips, and core, to achieve effective and efficient movement [1, 2]. Each stride requires synchronized muscle activation, joint movement, and balance, all of which must adapt to changing conditions such as terrain [3], speed [4], and incline [5]. Treadmill running, as a specific form of running, is an effective exercise and training modality, offering several advantages for fitness, performance enhancement, and rehabilitation. However, relatively few studies have investigated how these factors influence neuromuscular control during running, specifically focusing on the movement synergies involved. The central nervous system (CNS) coordinates complex muscle activations to maintain stability and optimize performance under varying conditions [6, 7]. Regarding the effects of treadmill gradients, this type of running effectively simulates various conditions, including flat, inclined, and declined surfaces, making it ideal for targeted training and rehabilitation. Incline treadmill running has been shown to increase step frequency and internal mechanical work, demanding higher levels of muscular activation, especially in the hip and lower-limb muscles required to lift the body against gravity [8]. Additionally, incline running places significant demands on the glutes, hamstrings, and calves, necessitating enhanced joint stabilization, particularly at the hip. This increased workload translates into a higher metabolic cost, as the cardiovascular system must work harder to supply oxygen to the muscles [9]. Moreover, uphill running increases energy expenditure, further amplifying the body's metabolic demands [6]. In contrast, declined treadmill running maintains similar contact times to level running but tends to decrease step frequency, potentially increasing forward momentum and elevating the risk of falls [8]. It induces greater peripheral fatigue in the knee extensors compared to incline or level running and is often perceived as less pleasant, more effortful, and more painful [5]. Additionally, declined running increases knee joint moment contributions, raising concerns about joint health and the potential for cartilage degeneration, particularly in individuals who have undergone anterior cruciate ligament (ACL) reconstruction [9]. This form of running also heightens tibial shock and impact forces, often linked to overuse injuries [6]. While both incline and decline treadmill gradients present altered biomechanical challenges critical for training and rehabilitation, their specific effects on motor behavior--particularly running movement components or synergies--remain less explored. This gap in the literature highlights the need for further investigation into how these gradients influence movement strategies. The CNS employs near-optimal strategies to govern movements by utilizing task-relevant synergistic muscle activations [10]. This is particularly evident in running, where the complexity of movements necessitates the coordinated efforts of multiple body segments, including the arms, legs, hips, and core [1,2]. Observations of motor behaviors reveal various task-dependent movement synergies--patterns of muscle coordination that work together to achieve specific motor goals [7]. These synergies flexibly adapt to both internal conditions and external demands, such as changes in terrain [11]. Dimensionality reduction techniques, such as principal component analysis (PCA), have gained prominence in analyzing complex three-dimensional (3D) kinematic data.