Joint synergy and muscle activity in the motion of the ankle–foot complex

The ankle–foot complex (AFC) is a highly integrated system, where joint motions are intricately constrained by various biomechanical factors (Takabayashi et al., 2017; Williams et al., 2023). These constraints include closely arranged skeletal elements, elastic ligaments interconnecting multiple bones, muscles spanning multiple joints, and limitations on the contact surface of the sole (Brockett and Chapman, 2016; Farris et al., 2019; Dygut and Piwowar, 2022). Consequently, the motions of the AFC's joints are not entirely independent but are governed by various coupled relationships. By effectively coordinating these couplings, the AFC demonstrates remarkable flexibility during various complex movements (Pohl et al., 2007). It serves both as a rigid structure, providing weight-bearing support and stability, and as an adaptable entity capable of conforming to uneven terrains (Holowka et al., 2021). Thus, understanding the synergistic patterns and their physiological mechanisms within the AFC is imperative for comprehending the efficient and flexible movements of the foot.

Various methods have been developed to elucidate these synergistic patterns. For instance, Pohl et al. (2007) employed cross-correlation coefficients to assess interangular coupling, revealing synergistic movements between the rearfoot frontal plane and forefoot transverse plane during walking. However, this method often fails to capture nuanced variations within these patterns with time (Chang et al., 2008). Consequently, researchers have adopted vector coding techniques and their modified versions, which use polar angles in angle–angle plots to depict joint synergistic patterns more precisely (Takabayashi et al., 2018; van der Merwe et al., 2020). Such studies indicate that during the early stance phase of walking, coordination is predominantly proximal phase. During the push-off phase, an in-phase coordination pattern emerges, characterized by inversion occurring at multiple foot joints (Arnold et al., 2017; Takabayashi et al., 2017).

Current research on the synergistic movements of the AFC often divides the structure into three sections: forefoot, midfoot and rearfoot. However, this division fails to adequately capture the intricate dynamics of the AFC's 33 joints (Qiu et al., 2011). In response, some researchers have proposed subdividing the forefoot into medial and lateral segments, and even a 26-segment model has been suggested (MacWilliams et al., 2003; Oosterwaal et al., 2016). Nevertheless, such refinements significantly increase the complexity of motion measurement. Moreover, many existing models persist in employing a Cartesian coordinate system to delineate joint motion, computing three degrees of freedom across three orthogonal axes. This methodology does not align well with physiological axes and complicates motion descriptions by including degrees of freedom associated with minute motions. Thus, there exists a necessity to develop a biomimetic multi-segment foot model that mirrors the natural orientation of joint axes and eliminates less significant degrees of freedom.

Existing studies often focus on walking and running gaits. However, AFC movement is typically categorized into open-chain and closed-chain states based on the load conditions of the ankle joint (Karandikar and Vargas, 2011). In the open-chain state, the foot does not contact the ground or other objects, and AFC movement is primarily driven by leg muscles. In the closed-chain state, the foot contacts the ground or other objects, as seen in standing, walking and jumping. Here, AFC movement is influenced by both ground constraints and muscle forces. It is not yet known whether the AFC uses the same synergies in these two distinct mechanical modes or, if different, how the AFC adjusts its synergistic patterns. Studying the joint synergies in both states provides a comprehensive understanding of AFC functionality, encompassing both isolated and interactive status and how it adapts to different constraints.

In addition, current research on the physiological mechanisms underlying motion synergies in the AFC remains incomplete. Muscles drive joint movement, and understanding their biomechanical role is fundamental to comprehending joint synergy (Roberts et al., 2019; Huang et al., 2021). Different types of muscle contractions serve distinct functions: isometric contractions primarily maintain postural stability and support loads; eccentric contractions are predominantly used for braking or resisting movements, aiding in the control of motion speed; while concentric contractions actively move the body or objects in activities such as walking and jumping (Sweeney and Hammers, 2018). Therefore, this study proposed analyzing joint synergy mechanisms by examining the relationship between joint angular velocity and muscle activation, focusing on how different types of muscle contractions contribute to these synergy mechanisms.

The study aimed to elucidate the physiological mechanisms underlying joint synergy and further clarify the roles of muscles in movement. Considering the biomechanical differences between open-chain and closed-chain movements, we applied hierarchical cluster analysis to identify synergistic patterns and movement primitives in both states. In open-chain movements, our analysis concentrated on the direct impact of muscle actions on joint synergy. Conversely, in closed-chain movements, we examined how muscles and joints adapt to and respond to body weight influences. By correlating movement primitives with muscle activation to identify types of muscle contractions, we clarified the specific roles of muscles in joint motion. This approach enhances our understanding of the underlying mechanisms driving AFC functionality across both dynamic states.

In this study, we employed the OpenSim 4.4 software to simulate human motion, using a musculoskeletal model comprising 10 segments and 23 degrees of freedom (Delp et al., 2007). We modified the structure of the AFC within the model to more accurately reflect joint motion (see Fig. 1A). Given the complexities of anatomy, we simplified the AFC model by consolidating smaller or less mobile skeletal components. The revised AFC model includes eight segments: tibia, talus, calcaneus, navicular, cuboid, medial metatarsals, lateral metatarsals, and phalanges. The ankle joint is formed by the articulation between the tibia and talus, the talonavicular joint connects the talus and navicular, and the subtalar joint involves the articulation between the talus and calcaneus, parallel to the talonavicular joint. Further, the medial tarsometatarsal and metatarsophalangeal joints connect sequentially the navicular, medial metatarsals and phalanges, while the calcaneocuboid and lateral tarsometatarsal joints connect sequentially the calcaneus, cuboid and lateral tarsometatarsals, respectively.

Our model defines joint rotation axes based on the predominant movement direction as established by prior studies (Hicks, 1953; Tweed et al., 2008; Maharaj et al., 2021). Although actual movements between foot segments occur in three orthogonal planes (Nester et al., 2007), these motions are interdependent, and rotations along physiological axes represent the primary direction of joint movement. Moreover, excessive degrees of freedom in the model could lead to sparse data distributions in high-dimensional spaces during feature extraction, which may impact clustering results and feature representation (Steinbach et al., 2004). Consequently, our analysis focuses on these significant motion directions, while disregarding lesser ones. Table 1 details the directions of joint axes, positive joint motion directions, and the ranges of motion for each joint. In practical applications, we scaled the AFC model according to each subject's foot size to ensure adaptability.

Additionally, our analysis of the AFC's joint motion characteristics relies on angular velocity measurements in various rotation directions. Describing motion based purely on the direction of the joint velocity (positive or negative) lacks intuitiveness. Instead, using joint movements defined in Cartesian coordinates – such as dorsiflexion and plantarflexion in the sagittal plane, inversion and eversion in the frontal plane, and abduction and adduction in the transverse plane – offers clearer descriptions (Brockett and Chapman, 2016). Therefore, our study characterizes joint rotation using primary movement components from three orthogonal planes, while the joints still rotate about their physiological axes. For example, when the ankle joint rotates clockwise around its physiological axis, the motion primarily involves plantarflexion, with minor inversion and adduction. Thus, we denote the positive direction of ankle joint rotation as plantarflexion and the negative as dorsiflexion. We describe the angular velocity directions for each joint accordingly: dorsiflexion and plantarflexion for the ankle, medial tarsometatarsal, lateral tarsometatarsal and metatarsophalangeal joints, and inversion and eversion for the subtalar, calcaneocuboid and talonavicular joints.

Eight healthy adult males with no history of gait impairments participated in the experiment (N=8, age: 24±4 years, height: 1.74±0.08 m, mass: 67.0±7.1 kg, mean±s.d.). All participants provided written consent before the experiments.

To accurately capture the joint movements of the AFC, participants were instructed to maintain a barefoot condition throughout the entire experimental process. To minimize the potential effects of standing posture on AFC positioning during static calibration, we utilized masking tape to delineate two parallel lines on the floor, spaced 30 cm apart. Participants were then instructed to put the center of their heels and the second toe on the marked line.

In the open-chain experiment, participants had their right lower leg suspended, and the right foot executed dorsiflexion and plantarflexion movements (Fig. 1C; Movie 1). Each movement, 2 s per cycle as directed by a metronome, was repeated at least 20 times. At the start of each cycle, participants were instructed to return the right foot to its initial position, ensuring the sole was parallel to the ground. Throughout the experiment, participants were instructed to minimize movement in the right lower leg to reduce the influence of knee joint motion.

In the closed-chain experiment conducted on a treadmill (Fig. 1D; Movie 2), participants completed six conditions: walking at 3 km h⁻¹ with inclinations of −10 deg (downhill10), −5 deg (downhill5), 0 deg (level3), 5 deg (uphill5), 10 deg (uphill10), and walking on level ground at a speed of 4 km h⁻¹ (level4). Each treadmill trial was conducted for 3 min. The initial minute served as an adaptation phase, allowing participants to adjust to the treadmill's slope and speed settings. The subsequent 2 min were utilized for the collection of experimental data.

The experiment utilized compact force plate-instrumented treadmills (AMTI, Watertown, MA, USA) to control slope and walking speed. Three-dimensional kinematic data of the participants were captured with a motion capture system consisting of nine cameras (Vicon, Oxford Metrics, Oxford, UK; 100 Hz). A total of 54 infrared reflective markers were symmetrically positioned on both the left and right sides of the body (Table 2).

Joint angle data were computed using OpenSim software, employing the human musculoskeletal model with modified AFC. Initially, virtual points on the human model were fine-tuned based on marker data obtained from static calibration experiments. Subsequently, each participant's musculoskeletal model was individually scaled to optimize alignment with their anatomical characteristics. Marker point data collected during motion experiments were filtered using a second-order low-pass Butterworth filter with a cutoff frequency of 4 Hz. These filtered marker data were then integrated into the scaled musculoskeletal model to derive joint angle data.

Surface electromyography (EMG) signals from eight muscles in the right lower leg were recorded using the EMG system (SX230, Biometrics, Newport, UK). These muscles included the tibialis anterior, medial soleus, lateral soleus, medial gastrocnemius, lateral gastrocnemius, fibular longus, fibular brevis and the inversion muscle group (Fig. 1B). The EMG sensor for the inversion muscle group was positioned on the posteromedial side of the ankle to capture the activities of the tibialis posterior, flexor digitorum longus and flexor hallucis longus (Otis and Gage, 2001). Despite the proximity of these muscles, making it challenging to isolate individual muscle signals, their collective signal during ankle inversion movements offers valuable insights into the functionality of the inversion muscle group. EMG signals underwent band-pass filtering (20–460 Hz) within the EMG system and were then rectified and filtered using a 4th-order zero-lag Butterworth low-pass filter with a cutoff frequency of 6 Hz to derive linear envelopes in MATLAB software (MathWorks Inc., Natick, MA, USA). Finally, the EMG signals were normalized using each individual's maximum muscle activation observed during level walking at 3 km h⁻¹.

To synchronize joint angle and EMG data with specific motion cycles, we segmented these data accordingly. For walking, the cycle is defined from heel strike to toe-off, focusing our analysis solely on the stance phase to analyze closed-chain movements while disregarding the swing phase. In dorsiflexion/plantarflexion motion, each motion cycle lasted 2 s, initiated 0.5 s before the start of movement. We resampled both EMG and joint angle data to yield 100 evenly distributed points per motion cycle, ensuring consistent and comprehensive data analysis across multiple cycles.

The hierarchical clustering approach was utilized to identify synergistic patterns and movement primitives across the 14 angular velocity directions of the AFC mentioned above. This procedure involves three steps: (1) constructing joint angular velocity matrices in open/closed chains, (2) calculating distances between pairwise angular velocity directions and (3) determining cluster groups and motion primitives within these groups.

For subject S_i under specific movement M_i, joint angle data were extracted from 10 movement cycles for the seven joints, consisting of 100 data points within each cycle. Using the four-point central difference formula and half-wave rectification, these angle data were decomposed into 14 joint angle velocities. Subsequently, a 14×1000 joint angular velocity matrix was constructed under the specific movement.

Each row of the joint angular velocity matrices and corresponds to a cluster. A distance matrix is constructed, where each element represents the correlation distance between a pair of clusters. In this study, correlation distances between pairs of clusters were calculated by subtracting the Spearman's rank correlation (SRC) of the clusters from 1. Based on the defined distance matrix and the average linkage clustering method, the closest clusters are merged. After each merger, the distance matrix is updated to reflect the distances between the newly formed clusters. Clusters are continuously merged until all clusters are combined into a single unified cluster. Finally, the results are visualized using a dendrogram.

Considering the correlations among the angular velocity curves of joints within the same cluster group, we normalized and averaged the angular velocity data within each cluster group to extract their movement primitives.

This study assessed the robustness of hierarchical clustering by analyzing the statistical differences in correlation distances within and across cluster groups. The assumption of a normal distribution of correlation distances was tested using the Jarque–Bera test. Subsequently, an analysis of variance (ANOVA) was performed on the correlation distances to identify significant differences within and across cluster groups. The significance level was set at P=0.05. If the observed significance level in the correlation distances, both within and between clusters, is below 0.05, it indicates statistically significant differences among the synergy groups. Additionally, a power analysis was conducted to assess the statistical power of the study, ensuring it had sufficient capability to detect effects with an accepted power level set at 0.80 or higher. All statistical analyses were performed using MATLAB.

Differences were observed between synergistic patterns in both the open and closed chains. In the open-chain states (Fig. 1A), joint movements were segregated into two distinct clusters. Cluster 1 (C1) encompassed dorsiflexion at the ankle, medial and lateral tarsometatarsal, and metatarsophalangeal joints, accompanied by eversion at the calcaneocuboid, subtalar and talonavicular joints. Cluster 2 (C2) involved plantarflexion at the ankle, medial and lateral tarsometatarsal, and metatarsophalangeal joints, combined with inversion at the calcaneocuboid, subtalar and talonavicular joints. The average correlation distances within C1 and C2 were 0.43 and 0.46, respectively. However, between the clusters, the distance increased to 1.51 (Fig. 2C).

In the closed-chain states (Fig. 2B), Cluster 3 (C3) comprised dorsiflexion at the ankle and medial and lateral tarsometatarsal joints, inversion at the subtalar and talonavicular joints, eversion at the calcaneocuboid joint, and plantarflexion at the metatarsophalangeal joint. Cluster 4 (C4) included plantarflexion at the ankle and medial and lateral tarsometatarsal joints, eversion at the subtalar and talonavicular joints, inversion at the calcaneocuboid joint, and dorsiflexion at the metatarsophalangeal joint. The average correlation distances within C3 and C4 were 0.48 and 0.70, respectively. However, between the clusters, the distance increased to 1.44 (Fig. 2D).

Statistical results indicated that the correlation distances observed both within and between clusters exhibit significant differences in open/closed-chain states (P<0.05, power>0.8).

In open-chain states (Fig. 3), as the AFC underwent dorsiflexion, the ankle joint, medial and lateral tarsometatarsal joints and metatarsophalangeal joint exhibited dorsiflexion, while the subtalar joint, talonavicular joint and calcaneocuboid joint showed eversion. As the AFC underwent plantarflexion, the ankle joint, medial and lateral tarsometatarsal joints and metatarsophalangeal joint exhibited plantarflexion, while the subtalar joint, talonavicular joint and calcaneocuboid joint demonstrated eversion.

In closed-chain states (Fig. 4), the ankle, lateral tarsometatarsal and metatarsophalangeal joints underwent a slight plantarflexion at 0–10% of the gait cycle, while the talonavicular, subtalar, and calcaneocuboid joints exhibited eversion. In the subsequent 10–50% of the gait cycle, the ankle joint and medial and lateral tarsometatarsal joints transitioned to dorsiflexion. The talonavicular and subtalar joints underwent inversion, while the calcaneocuboid joint displayed eversion. The metatarsophalangeal joint underwent plantarflexion followed by dorsiflexion. In the 50–65% of the gait cycle corresponding to the toe-off phase, the ankle joint and medial and lateral tarsometatarsal joints transitioned to plantarflexion, the talonavicular and subtalar joints exhibited eversion and the calcaneocuboid joint displayed inversion. The metatarsophalangeal joint underwent dorsiflexion followed by plantarflexion. As the slope changed from −10 deg to +10 deg, there was an increase in both the plantarflexion angle and angular velocity observed at the ankle joint and metatarsophalangeal joint during the toe-off phase.

In the open chain, different muscles were activated during dorsiflexion and plantarflexion (Fig. 5). Dorsiflexion movement primarily activated the tibialis anterior, fibular brevis and fibular longus, with normalized EMG peak values above 0.5, while the lateral soleus and inversion muscle group exhibited light activation with normalized EMG peak values above 0.2. The muscle activation curve of the tibialis anterior, the primary driver for dorsiflexion, showed an SRC of −0.77 with ankle joint angle curve and an SRC of 0.73 with movement primitives curve from C1, which encompassed dorsiflexion movements of multiple AFC joints.

Plantarflexion movement mainly activated the medial soleus, lateral soleus, fibular longus, inversion muscle group and fibular brevis, with normalized EMG peak values above 0.5, while the lateral gastrocnemius, medial gastrocnemius and tibialis anterior displayed light activation with normalized EMG peak values above 0.2. The average activation signals of the medial soleus, lateral soleus, fibular longus, inversion muscle group and fibular brevis, the primary driver for plantarflexion, showed an SRC of 0.93 with ankle joint angle curve and an SRC of 0.42 with movement primitives curve from C2, which encompassed plantarflexion movements of multiple AFC joints.

In closed-chain movements, the activating muscles did not change with slope variation, but the amplitude of activation changed (Fig. 4). During the initial contact phase (0–10% of the gait cycle), the tibialis anterior and fibular longus were predominantly activated. During the toe-off phase (50–65% of the gait cycle), the medial gastrocnemius, lateral gastrocnemius, medial soleus, lateral soleus, fibular longus, fibular brevis and inversion muscle group exhibited activation, with normalized EMG peak values above 0.5. Moreover, the EMG peak values of the medial gastrocnemius, lateral gastrocnemius, medial soleus and lateral soleus increased progressively as the slope changed from −10 deg to +10 deg.

During walking, the muscle activation curve of the tibialis anterior showed an SRC of 0.71 with ankle joint angle curve and an SRC of 0.15 with movement primitives curve from C3, which encompassed dorsiflexion movements of the ankle and medial and lateral tarsometatarsal joints. The average activation signals of the medial soleus, lateral soleus, lateral gastrocnemius, medial gastrocnemius, fibular longus, inversion muscle group and fibular brevis showed an SRC of 0.90 with ankle joint angle curve and an SRC of 0.08 with movement primitives curve from C4, which encompassed plantarflexion movements of the ankle and medial and lateral tarsometatarsal joints.

In open-chain movements, muscles directly drive joint actions with minimal external constraints, allowing clear assessment of the roles of anatomical structure and muscle in joint dynamics.

The axes of the AFC joints intersect the Cartesian coordinate planes at oblique angles, leading to coupled movements across three orthogonal planes. For example, the subtalar joint axis inclines at a 16 deg counter-clockwise angle to the sagittal plane and a 42 deg counter-clockwise angle to the horizontal plane, resulting in simultaneous plantarflexion and abduction during subtalar inversion (Manter, 1941). In open-chain AFC plantarflexion movements, subtalar inversion includes a plantarflexion component, thereby extending the range of AFC plantarflexion. This phenomenon probably explains the synergy between ankle plantarflexion and subtalar inversion observed in our cluster analysis of open-chain movements. Similar multi-directional coupling is observed in other joints such as the talonavicular and calcaneocuboid joints, significantly influencing the motion generation of synergistic patterns within the AFC.

The calf muscles are the primary drivers of joint motion in the AFC, with their insertion points across multiple joints significantly contributing to joint synergy (Hicks, 1956). For example, the tibialis posterior muscle originates from the posterior aspects of the tibia and fibula (Otis and Gage, 2001; Willegger et al., 2020). Its distal insertions include the tuberosity of the navicular bone, all cuneiform bones, the cuboid bone and the bases of metatarsal bones 2–4. This broad distribution enables it to simultaneously influence movements at the ankle, subtalar, talonavicular and lateral tarsometatarsal joints. Similarly, the fibularis longus muscle, originating from the head and proximal two-thirds of the fibula, attaches to the medial cuneiform and the first metatarsal, impacting the ankle, subtalar, calcaneocuboid and medial tarsometatarsal joints upon activation (Bavdek et al., 2018). During open-chain plantarflexion movements of the AFC, the crossed arrangement of the tibialis posterior and fibularis longus muscles on the foot sole generates an inward pulling force on the bones at both ends of the midfoot when these muscles are activated simultaneously. This force enhances the stiffness of the transverse arch of the midfoot (Dygut and Piwowar, 2022).

Analyzing the relationship between joint motion primitives and muscle activation to discern muscle contraction types significantly enhances our understanding of muscle function during movement. For example, during AFC plantarflexion, primary muscles such as the peroneus, triceps surae and inversion muscles, which are plantarflexors, are activated (Hunt et al., 2001). During the initial 0–50% of the movement cycle, muscle contractions are synchronized with joint rotations, primarily exhibiting concentric contraction to facilitate joint movement. However, in the latter half of the cycle, muscle activation continues even after the direction of joint motion reverses. At this stage, the muscles transition to eccentric contraction, opposing the joint rotation to stabilize the angular velocity as the AFC returns to its original position. This sustained muscle activation is critical because if it ceased following the reversal of joint rotation, the foot would swiftly revert to its natural state, driven by passive forces from ligaments and antagonist muscles. These passive forces become more pronounced as the ankle joint angle nears its limits (Nigg et al., 1990; Bahr et al., 1998; Hoang et al., 2007). Moreover, the strong correlation between muscle activation and ankle angle suggests that a significant portion of muscle force during open-chain movements may be dedicated to counteracting these passive forces within the AFC.

Compared with open-chain movements, closed-chain states transition the movement pattern from proximal fixation to distal fixation. Consequently, the functional role of the calf muscles shifts from providing AFC movement energy to supporting body weight and facilitating oscillations of the body's center of mass. Therefore, in closed-chain movements, our focus is on examining the alterations in joint synergy patterns and their functional differences relative to open-chain movements.

During 0–10% of the gait cycle, ankle plantarflexion demonstrates synergy with subtalar and talonavicular eversion, which differs from the inversion synergy observed in open-chain movements. In this phase, internal rotation of the tibia and fibula leads to eversion at the subtalar and talonavicular joints, influenced by the structural dynamics of the talocrural joint and ground constraints (Sammarco, 2004). From 10% to 50% of the gait cycle, ankle dorsiflexion shows synergy with subtalar and talonavicular inversion, contrasting with eversion in open-chain movements. The subtalar joint initiates inversion, transforming the midfoot into a rigid lever through locking mechanisms at the talonavicular and calcaneocuboid joints, thereby preparing for push-off (Blackwood et al., 2005; Rowe et al., 2022). During the push-off phase, which spans 50–65% of the gait cycle, ankle plantarflexion again aligns with subtalar and talonavicular eversion. Eversion at both the subtalar and talonavicular joints enlarges the sole's contact area with the ground and aids in weight transfer to the contralateral leg (Wang and Gutierrez-Farewik, 2011). Simultaneously, dorsiflexion at the metatarsophalangeal joint initiates the ‘windlass effect’, a biomechanical phenomenon that augments foot compliance and stores elastic energy for propulsion (Welte et al., 2018; Farris et al., 2020; Williams et al., 2022). Additionally, throughout the entire stance phase, the metatarsophalangeal joint consistently engages in negative work, functioning similarly to a damper to regulate movement velocity and enhance overall stability and gait efficiency (Kim et al., 2012).

Furthermore, as the slope increases from −10 deg to +10 deg, the angle of plantarflexion at both the ankle and metatarsophalangeal joints increases during the push-off phase, ensuring sufficient sole contact area for stable foot contact. Concurrently, activity in the plantarflexor muscles increases to compensate for the decrease in gravitational potential energy, thereby elevating the body's center of mass (Kwon and Shin, 2022).

In the closed-chain state of the AFC, the correlation between muscle activation and motion primitives diminishes compared with open-chain movements. During the walking process, calf muscles not only facilitate movements within the AFC but also increasingly support variations in the center of mass. From 50% to 70% of the stance phase, despite the dorsiflexion of the ankle joint, plantarflexor muscles exhibit significant activation. These muscles undergo eccentric contraction, opposing the joint's rotation to restrain joint dorsiflexion and limit the descent speed of the center of mass, preparing for its elevation during the subsequent push-off phase. From 70% to 100% of the stance phase, plantarflexor muscle activation corresponds with the joint's rotational direction, where concentric contraction enhances joint plantarflexion, increases arch stiffness, elevates the center of mass and facilitates its forward transfer toward the contralateral leg (Cronin et al., 2013; Kelly et al., 2015).

Additionally, we have compared our findings with existing studies on AFC motion synergy. Some literature suggests that ankle plantarflexion is coupled with subtalar joint eversion during the early stance phase, and dorsiflexion of the tarsometatarsal joint is coupled with subtalar joint eversion, consistent with our cluster C3 findings (Takabayashi et al., 2017; van der Merwe et al., 2020). During the push-off phase, prior research indicates that ankle plantarflexion couples with subtalar joint inversion, observed in our study between 50% and 55% of the gait cycle (Lenz et al., 2021). However, this contrasts with our synergy group because, in our study, each joint rotation is exclusive to only one synergy cluster, with ankle plantarflexion predominantly coupling with subtalar joint eversion throughout the stance phase.

This study has several limitations. Our analysis primarily focused on the extrinsic muscles, which are pivotal in driving AFC movements, while the contributions of intrinsic foot muscles to joint synergy were not discussed (Zelik et al., 2015). Additionally, our identification of joint axes was based on prior literature, which may not accurately reflect individual variation among subjects. The study's sample comprised solely healthy male participants; future research should include both males and females to ensure the generalizability of the results to the broader human population. Moreover, the precision of AFC motion measurements using skin markers might be compromised by skin movement artifacts (Leardini et al., 2021; Schallig et al., 2021). To minimize measurement errors, we employed a model-based approach that closely adheres to the actual physical characteristics of AFC movement. We validated our experimental joint angle data by comparing it with measurements from bi-planar video fluoroscopy and intra-cortical bone pins (Nester et al., 2007; Wang et al., 2023). The ankle, subtalar, tarsometatarsal and metatarsophalangeal joints displayed trends and magnitudes consistent with those reported in the literature. Future studies could adopt these higher-precision methods to further validate our findings.

The AFC exhibits intricately coupled movements, and the synergistic patterns differ between open- and closed-chain states. Hierarchical cluster analysis revealed that in open-chain movements, the plantarflexion of the ankle, tarsometatarsal and metatarsophalangeal joints synergizes with the inversion of the remaining joints. Meanwhile, dorsiflexion aligns with eversion. During closed-chain movements, the synergy groupings are altered. Ankle plantarflexion demonstrates synergy with subtalar and talonavicular joint eversion and metatarsophalangeal joint dorsiflexion. Conversely, ankle dorsiflexion demonstrates synergy with subtalar and talonavicular inversion and metatarsophalangeal joint plantarflexion.

Comparisons of the relationships between motor primitives derived from synergy groups and muscle activation revealed distinct types of muscle contractions and their functional roles during physical activity. When muscle contractions align with joint rotations, they amplify joint movement through concentric contraction. Conversely, when muscle actions counteract joint rotations, they can hinder movement, increase joint stiffness or help maintain stable joint velocity through eccentric contraction. In general, in open-chain movements, synergy patterns influenced by multi-joint muscles crossing oblique joint axes contribute to foot motion. In closed-chain movements, these changes in synergistic patterns enhance the propulsion of the center of mass forward and improve foot arch compliance, facilitating human motion. Our study enhances the understanding of the underlying mechanisms driving AFC functionality in both open- and closed-chain states.