Abstract
readmill running simulates various conditions, including flat, uphill, and down- hill gradients, making it useful for training and rehabilitation. This study aimed to examine how incline and decline treadmill running affect local dynamic stability of individual running movement components that cooperatively contribute to achieving the running tasks. Principal component analysis (PCA) was used to decompose movement components, termed principal movements (PMs), from kinematic marker data collected from 19 healthy recreational runners (9 females and 10 males, 23.6±3.7 years) during treadmill running at 10 km/h across different gradients (−6,−3, 0, +3, +6 degrees). The largest Lyapunov exponent (LyE) of individual PM positions (higher LyE = greater instability) was analyzed using repeated-measures ANOVA to assess treadmill gradient effects across PMs. The results showed that the effects of treadmill gradient appear in PM3, which corresponds to the mid-stance phase of the gait cycle. Specifically, decline treadmill running signif- icantly decreased local dynamic stability (greater LyE) compared to equivalent incline conditions (p≤0.005). These findings suggest that decline treadmill running should be used cautiously in rehabilitation settings due to its potential to reduce an ability to control and respond to small perturbations, thereby increasing the risk of instability during the weight-bearing support phase of gait. Keywords:movement component; neuromuscular control; running biomechanics; dynamic stability; treadmill running; principal component analysis (PCA) 1. Introduction Running is a fundamental human motor task that plays a
be used cautiously in rehabilitation settings due to its potential to reduce an ability to control and respond to small perturbations, thereby increasing the risk of instability during the weight-bearing support phase of gait. Keywords:movement component; neuromuscular control; running biomechanics; dynamic stability; treadmill running; principal component analysis (PCA) 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 con- ditions 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, specifi- cally 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]. Signals2025,6, 2 https://doi.org/10.3390/signals6010002
Signals2025,6, 2 2 of 12 Regarding the effects of treadmill gradients, this type of running effectively simulates various conditions, including flat, inclined, and declined surfaces, making it ideal for tar- geted 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]. Ad- ditionally, 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 lit- erature 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 seg- ments, 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
relevant synergistic muscle activations [10]. This is particularly evident in running, where the complexity of movements necessitates the coordinated efforts of multiple body seg- ments, 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 reduc- tion techniques, such as principal component analysis (PCA), have gained prominence in analyzing complex three-dimensional (3D) kinematic data. PCA reduces the number of variables while retaining essential information about the motor behavior of individual movement components, referred to as “principal movements” (PM k), where k denotes the order of the movement components [12,13]. In locomotion analysis, each principal movement (PM) can be visualized as a distinct movement synergy representing phases of a gait cycle, such as swing or stance, which work in tandem to accomplish the task [1,2,14]. This PCA-based approach also offers valuable insights into each PM’s position and acceler- ation, reflecting the neuromuscular control associated with different movement strategies, including the forces exerted by the system [11,12] and related myoelectric activities [7]. Previous research has demonstrated the utility of PCA in identifying principal movement patterns [1,15,16] and assessing the effects of perturbations on running stability [14]. In motor control, variability refers to variations in the amplitude of a time series, quantified using measures like standard deviation [15]. Understanding the impact of treadmill gradi- ents on neuromuscular control at the level of individual running movement components could inform the development of training programs and rehabilitation protocols tailored to specific goals. Temporal variations in gait are analyzed using non-linear methods, such as the largest Lyapunov exponent (LyE), which measures how quickly trajectories diverge [17–20]. LyE reflects the “predictability” of a time series and is commonly interpreted as a measure of
Signals2025,6, 2 3 of 12 dynamic or local stability, indicating the stability of the system across step cycles [17–20]. LyE has been used to evaluate the ability to compensate for small internal or external per- turbations and maintain functional locomotion [17–20]. In this context, stability refers to a system’s (e.g., the movement system) capacity to preserve its original state when confronted with internal (e.g., neuromuscular) or external (e.g., environmental) disturbances [19]. Stability parameters provide insight into the variability in motor task performance and quantify the system’s ability to correct dynamic errors [21]. LyE, when applied to the positions of individual principal movements (PMs), reflects the neuromuscular system’s ability to control and adapt to minor disruptions in movement patterns [1,14]. In running, local dynamic stability indicates the neuromuscular system’s capability to handle these small perturbations [17–20]. Reduced stability has been linked to an increased risk of overuse injuries, such as bone stress injuries, which occur when repetitive loads exceed the bone’s capacity for recovery [22,23]. The current study builds on these methodologies to investigate gradient-specific neuromuscular adaptations during running. In summary, this study aimed to explore how variations in treadmill gradient—both incline and decline—affect the local dynamic stability of individual running movement components/synergies, reflecting neuromuscular control during locomotion. It was hy- pothesized that changes in gradients would modulate the neuromuscular control of running movement components, as incline and decline treadmill gradients introduce altered biome- chanical aspects to running [6]. It was also expected that the gradient effects on running stability would particularly influence the weight-bearing support phase, which is crucial for balance and stability [14]. The findings provide valuable insights into how treadmill gradi- ents affect movement stability, with implications for optimizing training and rehabilitation, especially for patients recovering from lower-limb injuries. 2. Materials and Methods 2.1. Participants and Experimental Procedure The kinematic marker data of 19 healthy recreational runners (9 females and 10 males) during treadmill running at different gradients were retrieved from the C3D files of a peer- reviewed open access dataset [24]. The study was approved by the local ethics committee (nr. 2019-1138) and was conducted in accordance
injuries. 2. Materials and Methods 2.1. Participants and Experimental Procedure The kinematic marker data of 19 healthy recreational runners (9 females and 10 males) during treadmill running at different gradients were retrieved from the C3D files of a peer- reviewed open access dataset [24]. The study was approved by the local ethics committee (nr. 2019-1138) and was conducted in accordance with the Declaration of Helsinki [24]. All participants provided informed consent prior to the measurements. The experimental procedure was fully described by Van Hooren et al. [24,25]. In brief, all participants completed a single test session and were instructed to avoid strenuous activity for 36 h, alcohol for 24 h, caffeine for 6 h, and a heavy meal 1 h before the session. Prior to data collection, participants were instructed to run for 8 min at a fixed-paced speed of 2.78 m/s to familiarize themselves with treadmill running. Each participant randomly performed a single session of treadmill running on a CAREN system (Motek, The Netherlands) at various gradients (−6,−3, 0, +3, +6 degrees), wearing their own shoes. Rest periods were allowed between trials. For each running condition, the treadmill speed gradually increased from zero to a constant speed of 2.78 m/s (approximately equivalent to 10.008 km/h) within 30 s, remained constant for 30 s, and then gradually decreased to a stop. However, there was no explicit justification provided for the choice of these particular speeds [24]. Twenty-six retroreflective markers were attached to anatomical landmarks on the trunk (C7, T10, xiphoid process, sternum), pelvis (ASIS and PSIS), and lower extremities (thigh, knee, lateral malleolus, heel, 2nd and 5th metatarsal bones). Running movements were recorded using a 12-camera three-dimensional motion capture system (Vicon Nexus v2.1, Oxford Metrics Group, Oxford, UK) with a sampling frequency of 100 Hz. Participant characteristics are detailed in Table.
Signals2025,6, 2 4 of 12 Table 1.Characteristics of participants (mean±SD; *p< 0.001). Total Female ( n= 9) Male ( n= 10) Age (yrs.) 23.6 ±3.7 23.3 ±3.9 23.8 ±3.7 Weight (kg) 67.2 ±10.4 61.5 ±9.1 72.2 ±9.0 * Height (cm) 174.9 ±9.2 168.2 ±7.4 180.9 ±5.9 * Body mass index (kg/m 2 ) 21.9±2.0 21.6 ±1.9 22.0 ±2.1 2.2. Signal Processing and Movement Component Analysis All data processing was conducted in MATLAB version 2024a (MathWorks Inc., Nat- ick, MA, USA). The 30 s constant running of each trial of each participant was selected for analysis. An example of original running movement is represented in Supplementary Video S1. Twenty-six markers from each dataset, contributing 78 spatial coordinates (x, y, z), were interpreted as 78-dimensional posture vectors. Each dataset was preprocessed by sub- tracting the mean posture vector and then normalized to the mean Euclidean distance [13]. The data from all volunteers were concatenated to form an input matrix (100 [sampling rate]×5 [number of trials]×30 [trial duration]×19 [number of participants]×78 [marker coordinates]) for further PCA. PCA was calculated using a singular-value decomposition of the covariance matrix through the PManalyzer software [13] to decompose all kinematic marker data retrieved from five running conditions of all participants into a set of orthogonal eigenvectors, i.e., principal components (PCs), wherekdenotes the order of movement components. Animated stick figures can be created to characterize each eigenvector’s movement pattern, which has been called “principal movement” (PM k), visually representing movement synergies that contributed to achieve the running task [13,26]. Moreover, the actual time evolution (t, time series) of individual PM kis quantified by the PC scores called principal positions (PP k(t)), representing positions in posture space, i.e., the vector space spanned by the PC eigenvectors [13]. Additionally, the acceleration of each PM called principal acceleration (PA k(t)) can also be determined through the second-time differentiations, reflecting the neuromuscular control of each PM, as it is associated with myoelectric activity [7]. The term “principal” in the variable names denotes that these variables were obtained through a PCA, and (t) indicates that these variables are functions of timet[13]. In this
acceleration of each PM called principal acceleration (PA k(t)) can also be determined through the second-time differentiations, reflecting the neuromuscular control of each PM, as it is associated with myoelectric activity [7]. The term “principal” in the variable names denotes that these variables were obtained through a PCA, and (t) indicates that these variables are functions of timet[13]. In this study, the PM time series were filtered with a third-order zero-phase 6 Hz low-pass Butterworth filter to avoid noise amplification in the differentiation processes. The leave-one-out cross-validation was then used to evaluate the vulnerability of the PM kand the dependent variables to changes in the input data matrix to address validity considerations [13]. The first five PCs, which proved robust and explained 97.7% of the total variance, were selected to test the hypotheses. Each participant-specific relative explained variance (rVAR) of PP k(PP k_rVAR) and PA k(PA k_rVAR) calculated from the PP k(t) and PA k(t) represent the coordinative structure or composition of running movements and running acceleration, respectively [14]. The PP k_rVAR and PA k_rVAR quantify how much (in percent) each PM contributed to the total variance in postural positions and postural accelerations, respectively [14]. It has been suggested in the literature that movement components with limited positional amplitudes, when performed rapidly, significantly affect accelerations and, in turn, the forces acting in the system [27]. 2.3. Computing PCA-Based Variables The local dynamic stability of individual PMs for each participant was computed using the largest Lyapunov exponent (LyE) of PP k(t), denoted as PP k_LyE, which has been applied in previous studies [1,14,27–30]. LyE is a non-linear analysis method that quantifies the rate of divergence of nearby trajectories in state space, representing the motor system’s
Signals2025,6, 2 5 of 12 ability to attenuate small perturbations [31]. Specifically, a greater LyE value indicates reduced motor system efficiency in controlling perturbations, resulting in higher divergence of state space trajectories and thus lower running stability [32,33]. LyE was calculated using Wolf’s algorithm [34], where the time delay (τ= 10) and embedding dimension (m= 4) were determined through average mutual information (AMI) [1,29] and the false nearest neighbor method [35], respectively. Embedding dimension and time delay were chosen based on previous studies [32] to optimize the sensitivity of LyE in detecting subtle stability changes during running. A greater LyE value reflects the inability of the motor system to diminish the perturbations, resulting in a higher divergence of the state space trajectories that reflects the lower running stability of the individual [14,18]. Additionally, the root mean square (RMS) of PA k(t), denoted as PA k_RMS, was com- puted for each participant’s individual principal movements (PMs) [14,36] as a measure of the magnitude or intensity of the acceleration signals [37]. This additional measure aids in better understanding neuromuscular control, as higher principal postural acceleration is correlated with increased myoelectric activity [7]. 2.4. Statistical Analysis With the alpha level set atα= 0.05, all statistical analyses were conducted using IBM SPSS Statistics software version 26.0 (SPSS Inc., Chicago, IL, USA). The Shapiro–Wilk test was used to assess the normality of the data distribution. For each PCA-based variable (PP k_LyE and PA k_RMS), repeated-measures ANOVA was performed to evaluate the main effects of treadmill gradient (−6,−3, 0, +3, +6 degrees). The effect size (partial eta squared, ηp 2) and observed power (1−β) were reported. Post hoc tests for pairwise comparisons across the five treadmill gradients were conducted, with the alpha level adjusted toα= 0.01. Cohen’s d for each pairwise comparison was calculated to provide more context about the magnitude of differences. 3. Results 3.1. Movement Components of Treadmill Running Visualizations of the first five PMs (PM1–5) and their compositions of principal position (PP k_rVAR) and acceleration (PA k_rVAR) are depicted in Figure teristics are described in Table. The first principal movement (PM 1), which
Cohen’s d for each pairwise comparison was calculated to provide more context about the magnitude of differences. 3. Results 3.1. Movement Components of Treadmill Running Visualizations of the first five PMs (PM1–5) and their compositions of principal position (PP k_rVAR) and acceleration (PA k_rVAR) are depicted in Figure teristics are described in Table. The first principal movement (PM 1), which resembles the swing-phase movement coupled with trunk rotation, shows the highest contribution to the total variance in postural positions and in postural accelerations. Animated stick figures of PM2–5corresponding to phases of the gait cycle are represented in Supplementary Video S2. Table 2.Characteristics of the first five principal movements (PM 1–5). PM k Movement Characteristics PP k_rVAR (%) PA k_rVAR (%) k = 1 Swing-phase movement coupled with trunk rotation: One leg moves forward while the trunk rotates to balance the body’s momentum. 72.5±7.3 49.0 ±4.2 2 Double-leg support coupled with anteroposterior sliding: Both feet are on the ground (double-leg support) and involve anteroposterior (forward–backward) movement. 12.8±6.6 2.8 ±0.8 3 Single-leg support coupled with trunk rotation: One leg supports the body while the other swings forward. Trunk rotation is also involved here, assisting in the balance during the single-leg support. 7.3±3.2 5.3 ±2.1 4 Double-leg support coupled with hip and knee flexion/extension: Hip and knee movements during double-leg support, capturing the flexion and extension of these joints as both feet are in contact with the ground. 2.9±0.5 27.0 ±2.4 5 Single-leg support coupled with mediolateral sliding: The mediolateral (side-to-side) movements during the single-leg support phase. 2.2±1.8 0.2 ±0.1
Signals2025,6, 2 6 of 12Signals 2025, 6, x FOR PEER REVIEW 6 of 13 movements during this phase contribute more to accelerations. Finally, PM 5, correspond- ing to single-leg support with mediolateral sliding, exhibited the least variance, with PP 5_rVAR at 2.2 ± 1.8% and PA 5_rVAR at 0.2 ± 0.1%, suggesting that this phase has mini- mal impact on postural positions and accelerations. These results highlight that different components of the running gait cycle contribute to the complete execution of treadmill running. Figure 1.Visualizations of the first five principal movements (PM 1–5; left column), shown in sagittal and frontal views, examples of principal position (PP k) and principal acceleration (PA k) over time (middle column), and the space–time representation of the calculated Lyapunov exponent (LyE) for PP 1–5(right column). The dashed line represents the right limb. Example data were derived from a single male participant. PM 1reflects swing-phase movement with trunk rotation to balance momentum. PM 2represents double-leg support with forward–backward sliding. PM 3illustrates single-leg support with trunk rotation aiding balance. PM 4captures hip and knee flexion/extension during double-leg support, while PM 5highlights side-to-side movements during single-leg support.
Signals2025,6, 2 7 of 12 As shown in Figure, the analysis of movement characteris- tics revealed distinct patterns in the variance of principal movements (PM k) during running. PM1, which involves the swing-phase movement coupled with trunk rotation, exhibited the highest variance in both PP1_rVAR (72.5±7.3%) and PA1_rVAR (49.0±4.2% ), indicating that this phase significantly contributes to both postural positions and accelerations. The swing phase plays a critical role in balancing the body’s momentum, contributing to high forces acting on the system. In contrast, PM2, during double-leg support with antero- posterior sliding, showed lower variance, with PP2_rVAR at 12.8±6.6% and PA2_rVAR at2.8±0.8% , suggesting that this phase contributes less to both postural positions and accelerations. PM3, the single-leg support phase coupled with trunk rotation, showed values of7.3±3.2% for PP3_rVAR and 5.3±2.1% for PA3_rVAR, suggesting lower forces and greater stability compared to the swing phase. PM4, which involves double-leg sup- port coupled with hip and knee flexion/extension, showed higher variance in PA4_rVAR (27.0±2.4% ) compared to PP4_rVAR (2.9±0.5%), indicating that joint movements during this phase contribute more to accelerations. Finally, PM5, corresponding to single-leg sup- port with mediolateral sliding, exhibited the least variance, with PP5_rVAR at2.2±1.8% and PA5_rVAR at0.2±0.1% , suggesting that this phase has minimal impact on postu- ral positions and accelerations. These results highlight that different components of the running gait cycle contribute to the complete execution of treadmill running. 3.2. Treadmill Gradient Effects on Local Dynamic Stability and Acceleration Magnitude The results indicate that the main effects of treadmill gradients on running stability, as assessed by the LyE of individual PMs (PP k_LyE), are predominantly observed in PM3, corresponding to the mid-stance phase of the gait cycle (PP3_LyE: F (4,72)= 10.877,p< 0.001, ηp 2= 0.377, 1−β= 1). Post hoc tests (FigureA) reveal that decline treadmill running results in higher instability compared to incline treadmill running. Specifically, running with a 6-degree decline exhibited a higher LyE value, indicating lower stability than running with both a 3-degree incline (p< 0.001, Cohen’s d = 1.162) and a 6-degree incline (p= 0.005, Cohen’s d = 1.176). Furthermore, running with a 3-degree decline
Description
The study investigates the effects of treadmill gradients on running stability and movement synergies.