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. 2026 Apr 27;16:19396. doi: 10.1038/s41598-026-49056-3

Spatial and temporal modulation of intra-limb coordination in kinematic synergies during hindlimb split-belt treadmill walking in rats

Soichiro Fujiki 1,#, Ryutaro Sakai 2,#, Tetsuro Funato 3, Dai Yanagihara 2,4,✉
PMCID: PMC13287708  PMID: 42045415

Abstract

Effective walking requires precise control of the spatiotemporal patterns of leg motions, involving both inter-limb and intra-limb coordination to maintain balance and generate propulsive force. Studies using a split-belt treadmill, which imposes asymmetrical walking conditions, have suggested that temporal modulation predominates over spatial modulation when evaluating locomotor parameters such as stance duration and stride length. However, since locomotion involves coordinated multi-joint motions, analyses based on these parameters, such as the duration and/or length, may not fully capture how modulations are implemented at the level of inter-segmental coordination within a limb. Therefore, it remains unclear whether locomotor adaptation at the multi-joint level is driven solely by temporal modulations of motor commands as inferred from the changes in a range of factors that can affect coordinated movement. Here, we examined intra-limb coordination during hindlimb bipedal locomotion in rats walking under tied and split-belt conditions. Using kinematic synergy analysis, multi-joint motions were decomposed into temporal and spatial components to determine whether locomotor adaptation is primarily governed by temporal modulations or also involves spatial reconfiguration. Our findings indicate that, in addition to temporal modulations, spatial modulations of intra-limb coordination are significantly reconfigured under asymmetrical walking conditions. These findings suggest that locomotor adaptation involves not only timing adjustments but also spatial reconfiguration of joint coordination, providing insight into the control strategies underlying stable locomotion.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-49056-3.

Keywords: Locomotion, Split-belt treadmill, Kinematic synergy, Rat, Bipedal walking

Subject terms: Anatomy, Engineering, Neuroscience, Physiology

Introduction

Walking requires precise control of the spatiotemporal patterns of leg motions to maintain balance, generate propulsive forces, and ensure appropriate limb protraction and foot placement. Because limb kinematics are closely linked to underlying force production, analyzing joint motion patterns provides insight into the control strategies that shape locomotor behavior. The spatiotemporal patterns of leg motions include inter-limb coordination, i.e., coordination between multiple legs, and intra-limb coordination, i.e., coordination between joints of one leg. The control of inter-limb and intra-limb coordination and the determination of their allocation ratio to generate proper gait movements still need to be resolved in order to better understand the mechanism of locomotion. Previous studies into these controls have made use of split-belt treadmills that allow the left and right belts to move at different speeds in order to investigate the effects of modulations in the spatiotemporal patterns of leg motions in an asymmetrical walking environment1–16. The locomotor coordination during split-belt treadmill walking is generally described in terms of four main locomotor parameters that characterize the spatial and temporal changes: duty factor, double support time, stride length, and step length1,4,13. These parameters successfully captured rapid and gradual locomotor coordination in response to changes in the walking environment. Previous studies, which focused on explicit motor adaptation whereas many others focused on implicit motor adaptation, have identified characteristic aspects of control strategies for split-belt treadmill walking. One study has shown that the visual feedback of steps, with the instruction to keep both step lengths equal, accelerated the reduction of spatial asymmetry, but not of temporal asymmetry8. Moreover, after explicit adjustments to step timing or stride length based on these locomotor parameters, temporal adjustments affect the other parameter, whereas the reverse effect is rarely observed17. These results suggest the predominance of temporal factors in gait control. Although these important findings have been reported, the coordination of individual joint motions that enable these movements has yet to be thoroughly analyzed18. Clarifying how individual joints are coordinated will also be important for understanding the essential mechanisms of adaptive gait generation.

In general, hindlimb coordination is evaluated by observing the joint movements of the thigh, shank, and foot. It is known that the movement trajectory in three-dimensional space during walking can be accurately represented in a two-dimensional plane, and that the fundamental two-dimensional structure is preserved even when walking speed is altered or other actions such as kicking are performed19,20. Furthermore, this fundamental structure has been observed in a range of animal species21. These common basic structures and condition-dependent differences are thought to reflect an aspect of the neural control strategy in the generation of locomotion. One concern with this approach is that it attempts to capture phenomena in terms of subspace changes, which makes it difficult to understand changes in the spatiotemporal pattern intuitively. An alternative approach is to use kinematic synergy analysis which allows decomposition of multiple joint motions into temporal and spatial components and ranks the contributions of those components22,23. This method is expected to facilitate interpretation, especially in the analysis of gait, since it extracts the primary temporal patterns composing the movement and clarifies the magnitude of change in each joint (spatial coordination structure). By identifying where changes occur within the simplified structures that compose complex systems, an aspect of the neural control strategy could be revealed. Based on previous studies using split-belt treadmill walking4,17, locomotor adaptation at the level of inter-segmental coordination has been inferred to be predominantly driven by modulation of temporal motor commands. However, this has not been clearly confirmed; thus, by decomposing hindlimb joint motions into temporal and spatial components through kinematic synergy analysis, we should be able to determine whether temporal component changes alone, spatial component changes alone, or both temporal and spatial component changes are involved.

In this study, hindlimb bipedal locomotion on a split-belt treadmill in intact rats was analyzed using a motion-capture system (Fig. 1a). Tied and split-belt conditions were used as the walking environments (Fig. 1b), and the four locomotor parameters were calculated to compare qualitative differences in the coordinated movements with those reported previously1,4,13,24. In addition, kinematic synergy analysis was applied to the measured joint motions in this study (Figs. 1c and d), decomposing the motion into temporal components, contribution rates, and spatial components; statistical analyses were performed on each parameter. The clarification of the changes in intersegmental coordinated movements during split-belt treadmill walking is expected to provide a better understanding of the motor control strategies of each joint to generate a stable gait.

Fig. 1.

Fig. 1

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(a) Experimental system for measuring the kinematics of split-belt walking in rats using their hind limbs. To enable walking on the two hind limbs, the upper body was gently supported by a harness and both forepaws were rested on to the handrail. Gray circles indicate measurement markers, which were attached to both sides. (b) Experimental paradigm for split-belt walking (consisting of tied, split-belt and wash-out blocks), with red lines indicating fast belt speeds and blue lines indicating slow belt speeds. (c) The elevation angle on the sagittal plane was calculated from the location information obtained from the markers. (d) Kinematic synergy analysis decomposed the joint angles of each gait cycle into temporal and spatial components. Φ is phase of locomotor cycle. Abbreviations: iliac crest (IC), greater trochanter (GT), knee (KN), external ankle (EA), fourth metatarsal head (MH), pelvis (PE), thigh (TH), shank (SH), and foot (FO).

Results

Locomotor parameters

In the split-belt treadmill walking experiments, we measured locomotor parameters under three conditions: the tied condition in which the speeds of the left and right belts are the same; the split-belt condition in which the left and right belts have different speeds; and the wash-out phase condition in which the belt speeds were returned to those of the tied condition to determine the effect of this switch. Some sessions for each speed condition were grouped into blocks and conducted in the order of tied, split-belt, and wash-out blocks (Fig. 1b).

The same four locomotor parameters were investigated as in previous evaluations of the adaptive locomotor changes on a split-belt treadmill1,4,13,24. In Fig. 2, we show the results for Rat A under a split-belt condition experiment in which the right belt was moving twice as fast as the left. The averages of the first five steps of each session for the fast and slow limbs for the four parameters are shown in Figs. 2a (duty factor), 2c (double support time), 2e (stride length), and 2g (step length). Data on the differences between fast and slow locomotor parameters were obtained for each block of all individual rats at each speed ratio and are shown in Figs. 2b (duty factor), 2d (double support time), 2f (stride length) and 2h (step length). A linear mixed model (LMM), which is shown in Eq. (5), was fitted to the data with belt condition and speed ratio as fixed effects and subject as a random effect. Analyses of variances (ANOVAs) of the model revealed significant interaction between belt condition and speed ratio in the duty factor (Supplementary Table S4), the double support time (Supplementary Table S10), the stride length (Supplementary Table S16), and the step length (Supplementary Table S22). Furthermore, in post hoc pairwise comparisons, significant differences were identified between the tied and split-belt blocks and the split-belt and wash-out blocks; no significant differences were found between the tied and wash-out blocks in the duty factor (Supplementary Table S6), the double support time (Supplementary Table S12), and the step length (Supplementary Table S24). These results suggest that these parameters showed adaptive changes when switching from the tied to split-belt blocks, and then returned to their original values in the wash-out block. The trend of these changes is consistent with the results of our previous work in rats4 and the reports in humans with cerebellar damage24. With regard to stride length (Fig. 2f), a post-hoc pairwise comparison showed significant differences between the tied and split-belt blocks and between the split-belt and wash-out blocks at a speed ratio of 2.0x, but no significant differences were found in the other cases (Supplementary Table S18). This indicates that the fast side had a larger stride length relative to the slow side in the split-belt block, at least at the largest speed ratio; this is consistent with previous reports in humans13,24. On the other hand, no significant differences were found at other speed ratios; this trend is consistent with our previous study in rats4. These results suggest that the properties of the locomotor parameters in the present experiments are consistent with the results of previous studies.

Fig. 2.

Fig. 2

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(a) An example of duty factors in a measurement experiment. The red and blue circles represent the mean duty factors of the fast and slow sides, respectively, among the first five steps of each session and the shaded areas show their standard deviations. T(n) represents the nth tied session, S(n) represents the nth split-belt session, W(n) represents the nth wash-out session. (b) Statistical analyses of duty factor in the five animals are shown in the swarm plot. Each point represents the average of the five steps. The s in T(s), S(s) and W(s) represents the belt speed ratio. The averages of T, S and W blocks respectively for the same speed conditions are connected by straight lines. * indicates a significant difference at the 5% level. (c) An example of double support time in a measurement experiment. Notation is the same as in (a). (d) Statistical analyses of double support time in the five animals. Notation is the same as in (b). (e) An example of stride length in a measurement experiment. Notation is the same as in (a). (f) Statistical analyses of stride length in the five animals. Notation is the same as in (b). (g) An example of step length in a measurement experiment. Notation is the same as in (a). (h) Statistical analyses of step length in the five animals. Notation is the same as in (b).

Kinematic synergy

A kinematic synergy analysis was applied to each gait cycle to extract the spatial component, temporal component, and contribution rate (Fig. 1d). Since the cumulative contribution rate for each gait cycle exceeded 90% up to the second component in all cases, the analysis was performed up to the second component thereafter.

Figure 3a shows the temporal components of the first and second synergies of the fast and slow limbs in each block. In each of the first and second synergies, the shapes of the components were similar between blocks, but the positions of the peaks were different. Significant interactions between the peaks of the fast and slow limbs were found using ANOVAs for the fitted LMMs (Supplementary Tables S28 and S34). Post-hoc pairwise comparisons showed significant differences between tied and split-belt blocks and between split-belt and wash-out blocks, but not between tied and wash-out blocks (Supplementary Tables S30 and S36). These results indicate that the split-belt condition resulted in adaptive changes in the temporal components of the kinematic synergies between the left and right limbs.

Fig. 3.

Fig. 3

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(a) Examples of temporal components of the fast and slow limbs for synergies 1 and 2 during the tied, split-belt, and wash-out blocks in a measurement. The lines are the means and the shaded areas are the standard deviations. (b) Results of statistical analysis of the differences between peak positions of the fast and slow limbs at each speed ratio. Each point represents the average of five steps. The averages of the data in each condition are connected by black lines for a series of the experimental blocks. * p < 0.05.

The changes in contribution rates are shown in Fig. 4. On the fast side, ANOVAs for the fitted LMMs did not show significant interactions (Supplementary Tables S40 and S52). On the slow side, ANOVAs for the fitted LMMs did not show significant interactions but showed significant main effects for belt condition (Supplementary Tables S46 and S58). Post-hoc pairwise comparisons showed significant differences in some combinations (Supplementary Tables S48 and S60). However, there were no clear associations with changes in speed ratios or belt conditions. In other words, there was no clear change as found in temporal components.

Fig. 4.

Fig. 4

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Results of statistical analysis of the contribution rates Inline graphic of the fast and slow limbs for synergies 1 and 2 at each speed ratio. Each point represents the average of five steps. The averages of the data in each condition are connected by black lines across the experimental blocks. * p < 0.05.

The results of the analyses of synergy 1 and 2 spatial components are shown in Figs. 5 and 6, respectively. Synergy 1 corresponds to axial flexion and extension motion in the hindlimb (Figs. 5a and 6a), whereas synergy 2 corresponds to rotational motion (see Supplementary Videos S2–S4). Figures 5b and 6b show scatter plots of the data for the fast limb at a speed ratio of 2.0x as an example. A multivariate linear mixed model (shown in Eq. (6)) was fitted separately to four datasets on spatial components: the first and second synergies in the fast and slow limbs. In the model, belt condition and speed ratio were used as fixed effects and subject was used as a random effect. ANOVAs of the model revealed significant main effects and/or interactions (Supplementary Tables S64, S70, S76 and S82). The results of the post-hoc pairwise comparisons are shown in Figs. 5c and 6c (Supplementary Tables S66, S72, S78 and S84). Notably, there were significant differences between tied and split-belt blocks and between split-belt and wash-out blocks in the shank and foot of the fast limb in both synergies, independent of the speed ratio. More specifically, there were differences in flexion and extension motions by the lower leg and foot (see Supplementary Video S5). With one exception—the shank of the fast limb of the synergy 2 at the 1.5x speed ratio—there were no significant differences between tied and wash-out blocks. This suggests that the spatial components of the synergies are modulated depending on the belt speed conditions.

Fig. 5.

Fig. 5

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(a) The averages of the spatial components (pelvis, thigh, shank, and foot) of the fast and slow limbs for synergy 1 during tied, split-belt, and wash-out blocks at the 2.0x speed ratio. Error bars show the standard deviations. (b) Distributions of the data points used in (a) are shown in two-dimensional space composed of two components, and histograms of their distributions are also shown. (c) Results of statistical analysis of the spatial components of the fast and slow limbs for synergy 1 at each speed ratio. Each point represents the average of five steps. The averages of the data in each condition are connected by black lines across the experimental blocks. * p < 0.05.

Fig. 6.

Fig. 6

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(a) The averages of the spatial components (pelvis, thigh, shank, and foot) of the fast and slow limbs of synergy 2 during tied, split-belt, and wash-out blocks at the 2.0x speed ratio. Error bars show the standard deviations. (b) Distributions of the data points used in (a) are shown in two-dimensional space composed of two components, and histograms of their distributions are also shown. (c) Results of statistical analysis of the spatial components of the fast and slow limbs for synergy 2 at each speed ratio. Each point represents the average of five steps. The averages of the data in each condition are connected by black lines across the experimental blocks. * p < 0.05.

Discussion

In this study, adaptive locomotion of the hindlimbs on a split-belt treadmill was investigated in intact rats. The locomotor parameters that were indexed to the adaptation of split-belt treadmill walking were identical to those used in previous studies4,13,24. The kinematic synergy analysis showed that both temporal and spatial components were modulated. In other words, not only was the timing of motion modulated, but also the coordination among joints (intra-limb coordination) was adaptively modulated.

Experiments with the split-belt treadmill suggested that the spatial and temporal components of limb movements were controlled individually25. A previous study reported that in adaptation to split-belt treadmill condition, instructions to adjust the timing of the motion affected the spatial and temporal factors of motion whereas adjustment of the position of motion affected the spatial factors but not the temporal factors17. From these studies, it is expected that the modulation of the temporal component may have the stronger effect, but that the ability to control the spatial component also has a meaningful effect. The results of the present study captured not only changes in the timing of motion (Fig. 3), but also changes in the coordination among joints (Figs. 5 and 6). The changes in intersegmental coordination are interpreted as being necessary to achieve proper locomotion in response to acute environmental changes; further work will be needed to clarify the functional role of these modulations.

Modulation of the spatial components in response to belt speed conditions was significant in the lower legs and feet (Figs. 5 and 6). The legs are used to balance and carry the center of mass during walking, whereas the lower legs and feet are used to balance the body rather than to generate propulsive force26. The role of the foot in controlling the body balance during walking has received increasing attention in recent years27–29. Our results suggest that the asymmetry in the left and right locomotor environment caused by the split-belt condition destabilized body balance, and that modulations were made by the lower legs and feet to correct this. If this interpretation is correct, then more specific strategies of balance control and the nervous system mobilized for it need to be investigated physiologically.

Previous experimental studies suggest a cerebellar contribution in the generation of adaptive locomotion and learning to split-belt conditions1,24,30. It has also been suggested that unlearned locomotor coordination that can respond immediately to changes in the environment may be modulated by the spinal nervous system2,3. Although contributions from the cerebral neocortex, basal ganglia, or other nervous systems are possible, to date, most research has focused on the spinal cord and cerebellum. The nervous system controls muscle activities to generate body movement. In recent years, many hypotheses have suggested the nervous system generates motor commands using a unit called muscle synergy in order to control the redundant and complex body in a simple manner31,32. If such a mechanism is inherent in the nervous system, it will be important to investigate which nervous system controls muscle synergy and how and by what means, especially as to how it changes the inter-segmental coordination as revealed by kinematic synergy analysis in this study. For this purpose, we believe it is necessary to clarify the relationship between muscle synergy and kinematic synergy, and to establish the groundwork for analyzing the relationship between movement and neuronal activities in the future.

The split-belt treadmill is not only of value for investigating locomotor coordination processes, but also for use in rehabilitation of gait disorders. There have been reports of improvement in asymmetric walking disability caused by cerebral stroke33–36. However, the physiological background of which part contributed to functional compensation is still unclear, and further physiological studies on the adaptation process will help to resolve these questions. It is hoped that clarification of this mechanism will lead to the development of more efficient treatment methods in the future.

In this study, kinematic data were separated into temporal and spatial components, showing that both were adaptively modulated. However, the present analysis does not reveal what kind of control commands are generated in realizing those spatiotemporal modulations in response to changes in the walking environment, nor where in the brain the responsible region is located. Simulations and validation of control systems using robots have suggested potentially responsible brain regions and their role in adaptation4,37. Further physiological verification is needed to elucidate the neural mechanisms of intra- and inter-limb coordination in the realization of adaptive walking in the future.

Methods

Animals

Five healthy male Wistar rats (CLEA Japan, Inc.), aged 17–25 weeks and weighing 438.8 ± 31.6 g (mean ± SD), were used in the experiments. This study was approved by the Ethical Committee for Animal Experiments at the University of Tokyo and conducted in accordance with the Guidelines for Research with Experimental Animals of the University of Tokyo.

Locomotor task

A custom-made split-belt treadmill was used. The length and width of each belt were 20 and 10 cm, respectively. The rats rested their forepaws on a handrail in front of them and wore a harness connected to a flexible beam fixed on the treadmill. The harness supported their upper body so that more than half of their body weight was supported by their hindlimbs and the hindlimb motions were not encumbered (Fig. 1a). Prior to the experimental measurements, the rats were first trained to walk bipedally using their hindlimbs on a treadmill in the tied configuration.

In the tied condition, the left and right belt speeds were the same; in the split-belt condition, the left and right belt speeds were different. Measurements were performed in the following order: multiple trials of the tied condition (tied block); multiple trials of the split-belt condition (split-belt block); and finally multiple trials of the tied condition (wash-out block). To avoid fatigue, one condition was divided into multiple trials, as described in previous studies1,4. A belt speed of 12 m/min was used in the tied condition. In the split-belt condition, the slower belt was run at 12 m/min, and the faster belt was run at 18, 21, or 24 m/min, i.e., the faster belt ran at 1.5x, 1.75x, or 2.0x the speed of the slower belt. One of the speed ratios was used for the split-belt block. Each rat was measured on a separate day for both fast-right and fast-left cases. Each trial lasted 1 min, with 3 min between trials. The measurement conditions for each rat are shown in Table 1.

Table 1.

Measurement conditions.

ID Speed ratio Fast limb Number of trials in a block
Tied Split-belt Wash-out
Rat A 1.5x Left 3 4 4
Right 3 4 4
1.75x Left 3 4 4
Right 3 4 3
2.0x Left 3 5 4
Right 3 4 4
Rat B 1.5x Left 6 4 3
Right 5 4 4
1.75x Left 3 4 4
Right 3 5 2
2.0x Left 3 5 3
Right 4 4 0
Rat C 1.5x Left 4 5 2
Right 3 5 2
1.75x Left 3 4 2
Right 3 5 2
2.0x Left 3 6 2
Right 3 5 1
Rat D 1.5x Left 3 5 2
Right 3 4 2
1.75x Left 3 5 2
Right 3 5 2
2.0x Left 3 5 1
Right 4 2 1
Rat E 1.5x Left 3 6 2
Right 2 4 2
1.75x Left 3 5 2
Right 3 5 2
2.0x Left 3 4 2
Right 4 5 1
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Motion capture

A 3D-motion capture system (Oqus300+, Qualisys, Sweden) was used to measure the left and right hindlimb motions of rats. Markers were attached to the skin of the hip and hindlimb landmarks: left and right iliac crest, greater trochanter, knee, external ankle, and fourth metatarsal head, with a measurement frequency of 500 Hz.

Calculation of kinematics

As the skin over the rat’s knee stretches during walking, the position obtained from the markers will deviate slightly from the actual knee position. Therefore, we first estimated the length of the femur and tibia from the position of the greater trochanter, the knee, and the ankle, and corrected the knee position based on these bone lengths. The measurement data for femur and tibia lengths were calculated at each time point in each trial for each rat, and the mode was used as the estimate of the femur and tibia lengths. Based on the estimated femur and tibia lengths for each rat, the knee position was estimated and corrected by constrained least squares using the positions of the greater trochanter and ankle as constraints.

The time series data of the measured positions of the left and right iliac crest, greater trochanter, external ankle, and fourth metatarsal head markers and the corrected position of the knee were low-pass filtered at 20 Hz and then used to calculate elevation angles of the pelvis, thigh, shank and foot in the sagittal plane (Fig. 1c).

Locomotor parameters

Walking on a split-belt treadmill requires coordinated leg motions, and many previous studies have used duty factor, double support duration, stride length, and step length as indexes of these motions4,13,24. To facilitate inter-study comparisons, these four parameters were used here. The definitions of each parameter are; duty factor, the ratio of the stance phase duration relative to one gait cycle; stride length, the distance from the touchdown position to the lift-off position of the foot for each leg; step length, the distance between the foot positions of the two legs at the touchdown of one leg along the direction of belt movement (fast/slow step length indicates the step length at the touchdown of the fast/slow leg). The touchdown and lift-off positions were determined by setting a threshold for the vertical positions of the fourth metatarsal head.

Kinematic synergy analysis

Kinematic synergy analysis is a method that allows motion to be decomposed into temporal and spatial components, and approaches the mechanism of motion control from the changes in these components in response to conditions. The kinematic synergy of each limb was calculated from the elevation angle Inline graphic during each locomotor cycle. The time scale Inline graphic of the data for one locomotor cycle was normalized to phase Inline graphic, and the average of the postures for that cycle was calculated according to the following equation: 

graphic file with name d33e1238.gif 1

where Inline graphic is averaged posture angle of Inline graphic (Inline graphic pelvis, thigh, shank, and foot). Then, the kinematic synergy of each locomotor cycle was calculated based on singular value decomposition as follows

graphic file with name d33e1269.gif 2

where N is the number of synergies, Inline graphic is the ith temporal component, Inline graphic is the ith singular values, and Inline graphic is the ith spatial component (i = 1, 2, …, N). The contribution rate Inline graphic (i = 1, 2, …, N) is calculated by

graphic file with name d33e1310.gif 3

and the cumulative contribution rate is calculated by

graphic file with name d33e1316.gif 4

When the cumulative contribution ratio exceeded 90%, synergies up to that number were included in the subsequent analyses.

Statistical analysis

Based on previous studies13,24 and due to the inclusion of multiple trials within each condition, locomotor parameters and kinematic synergies were sampled from the first five steps of each trial, and statistical analyses were performed on these data. Firstly, the data from the five steps were averaged, and then gathered for each sampled block under the same speed conditions. The differences between fast and slow sides were statistically analyzed for the four locomotor parameters. The contribution rates of the synergies were analyzed directly. For the temporal component of the kinematic synergy, the peak phases were extracted and analyzed statistically. To account for repeated measures within subjects, linear mixed models were applied for the above data. For each dependent variable, we fitted a model including belt condition, speed ratio, and their interaction as fixed effects, and animal subject as a random intercept to account for repeated measurements within individuals as follows:

graphic file with name d33e1333.gif 5

where Inline graphic is belt condition (Inline graphic = tied, split-belt, and wash-out), Inline graphic is speed ratio (Inline graphic = 1.5x, 1.75x, and 2.0x), and Inline graphic represents a single-trial observation of the dependent variable measured from subject Inline graphic in belt condition Inline graphic at speed ratio Inline graphic. Inline graphicrepresents the overall intercept, and Inline graphic represent the fixed effects of belt condition, speed ratio, and their interaction, respectively. Random effects and residual errors were assumed to be normally distributed with mean zero, Inline graphic and Inline graphic, representing between-subject variability and within-subject noise, respectively. Fixed-effect parameters were summarized as regression estimates (β), standard errors (SE), t-values, denominator degrees of freedom, associated p-values, and 95% confidence intervals (CF). The degrees of freedom were estimated using the Satterthwaite approximation. The random effects were characterized by estimating variance components for both subject-level variability and residual error, allowing quantification of between- and within-subject variance. Effect sizes were quantified using marginal and conditional R² values, representing the variance explained by fixed effects alone and by the full model, respectively38. The overall significance of fixed effects was tested using omnibus F-tests from analysis of variance (ANOVA). When significant main or interaction effects were observed, post-hoc pairwise comparisons were conducted using estimated marginal means (EMMs) with Tukey’s adjustment. Statistical significance was set at α = 0.05.

For the spatial component of kinematic synergy, to account for correlations among multiple dependent variables, a multivariate linear mixed model was fitted:

graphic file with name d33e1395.gif 6

where Inline graphic is belt condition (Inline graphic = tied, split-belt, and wash-out) and Inline graphic is speed ratio (Inline graphic = 1.5x, 1.75x, and 2.0x), and Inline graphic represents the four dependent variables (pelvis, thigh, shank, and foot of spatial component) measured from subject Inline graphic in belt condition Inline graphic at speed ratio Inline graphic. Inline graphic denotes vectors of fixed-effect coefficients for each dependent variable. The random effects and residual errors were assumed to be multivariate normally distributed with mean zero and covariance matrices Inline graphic and Inline graphic. Marginal and conditional R² values were computed separately for each dependent variable. Fixed effects were evaluated using omnibus ANOVA tests on the fitted model, testing whether regression coefficients jointly differed from zero across outcomes. Following significant omnibus multivariate effects, post-hoc pairwise comparisons were conducted using estimated marginal means for each dependent variable. Because outcomes were modeled jointly, Holm correction was applied to control the family-wise error rate across multiple comparisons and correlated measures. Statistical significance was set at α = 0.05.

Data analysis was performed using MATLAB (MATLAB R2021b; The MathWorks, Natick, MA, USA) and R (4.5.2).

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

Supplementary Material 1 (240.5KB, docx)
Supplementary Material 2 (11.4MB, mp4)
Supplementary Material 3 (7.6MB, mp4)
Supplementary Material 4 (9.3MB, mp4)
Supplementary Material 5 (9.5MB, mp4)
Supplementary Material 6 (11.8MB, mp4)

Acknowledgements

The authors thank Dr. Meiko Asaka for her technical and administrative support.

Author contributions

D.Y. and T.F. conceptualized and supervised the study. R.S. performed the experiments. S.F. and R.S. performed the analyses. S.F. and D.Y. prepared the manuscript. All the authors reviewed the manuscript.

Funding

This work was supported by JSPS KAKENHI Grant Numbers JP23K21610 (to D.Y.) and JP20KK0226 (to D.Y.).

Data availability

The data generated or analyzed during the current study are available via Zenodo (10.5281/zenodo.17310509).

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

These authors contributed equally to this work: Soichiro Fujiki and Ryutaro Sakai.

References

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Associated Data

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Supplementary Materials

Supplementary Material 1 (240.5KB, docx)
Supplementary Material 2 (11.4MB, mp4)
Supplementary Material 3 (7.6MB, mp4)
Supplementary Material 4 (9.3MB, mp4)
Supplementary Material 5 (9.5MB, mp4)
Supplementary Material 6 (11.8MB, mp4)

Data Availability Statement

The data generated or analyzed during the current study are available via Zenodo (10.5281/zenodo.17310509).

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