Modular Organization of Muscle Synergies to Achieve Movement Behaviors

Muscle synergy has been applied to comprehend how the central nervous system (CNS) controls movements for decades. However, it is not clear about the motion control mechanism and the relationship between motions and muscle synergies. In this paper, we designed two experiments to corroborate the hypothesis: (1) motions can be decomposed to motion primitives, which are driven by muscle synergy primitives and (2) variations of motion primitives in direction and scale are modulated by activation coefficients rather than muscle synergy primitives. Surface electromyographic (EMG) signals were recorded from nine muscles of the upper limb. Nonnegative matrix factorization (NMF) was applied to extract muscle synergy vectors and corresponding activation coefficients. We found that synergy structures of different movement patterns were similar (α=0.05). The motion modulation indexes (MMI) among movement patterns in reaching movements showed apparent differences. Merging coefficients and reconstructed similarity of synergies between simple motions and complex motions were significant. This study revealed the motion control mechanism of the CNS and provided a rehabilitation and evaluation method for patients with motor dysfunction in exercise and neuroscience.


Introduction
A large amount of research has reported that the CNS uses a dimensionality reduction pattern to coactivate a set of motion primitives (MP) to achieve daily activity living (DAL). However, motor control is redundancy and we could achieve a specific motion by combining various activation muscles [1]. How the CNS selects primitives from a vast pool and achieves movement behaviors is a complicated issue in the field of movement neuroscience and neurorehabilitation.
Modularity or muscle synergy as a building block, both structural and computational, exhibited feasibility for achieving motion control [2]. It has been proven in animal experiments, such as in cats, frogs, and monkeys. d'Avella [3] analyzed the movements of frogs during jumping, swimming, and walking in naturalistic conditions and found three shared and two task-specific muscle synergies across behaviors. Research in rhesus macaques showed that the grasping and transporting movements were achieved by modulating the muscle synergies [4,5]. Ting and Macpherson [6] analyzed the postural and balance control of cats and found that muscle synergies were correlated to the movement direction and endpoint force. e modularity of motion control was also found in human motions. e study in various human locomotions, consisting of walking and running at different speeds, walking forward or backward, and walking under different loading conditions and different styles (rectilinear and curvilinear trajectories) [7,8], showed that motions were driven by combining a few muscle synergy primitives. Shared and task-specific muscle synergies were also found in human locomotion [9,10]. And, Barroso found muscle synergies merging in human walking and cycling [11], and cycling synergies are a linear combination of walking synergies. In the clinical research of stroke, decomposing and merging were more evident [12]. Comparing to the lower limb, the upper limb movement is more complicated and exquisite. d'Avella et al. [13,14] analyzed and summarized the movements of point-to-point at different speeds, loads, forearm postures, and via-point movements, showing that the CNS achieved a goal by combining a set of building blocks (muscle synergy primitives). Israely et al. [15] studied the muscle synergy modulation function of hand-reaching tasks from different directions and found a representative set of synergies, which were from the muscle synergies extracted from the center of the reaching space, which could be modulated to achieve motions in different directions. Similar results were found in poststroke [12,15]. However, there was little research on the relationship between movement patterns and muscle synergies. Besides, the relationship between simple motions and complex motions is ambiguous. A deeper understanding of motion control in modularity is necessary.
In this paper, we would mainly analyze the relationship between muscle synergies and motion primitives. Based on the prior research, two hypotheses are tested: (1) any motion can be decomposed to motion primitives, which are driven by muscle synergy primitives and (2) variations of motion primitives in direction and scale are modulated by activation coefficients rather than muscle synergy primitives.

Subjects.
Twenty-eight subjects with no neurological injury (male: eleven, female: seventeen, and age: 23.68 ± 1.74 years) were recruited for the study. All subjects are righthand dominant. ey were informed about the procedure and possible discomfort before giving their informed consent. e research was approved by the ethical committee of the university.

Experiment Procedures.
Two experiments were designed for corroborating hypotheses. e first experiment (E1) consisted of three simple upper limb motions (SM) and five complex upper limb motions (CM). e simple motions included shoulder flexion/extension, shoulder abduction, and elbow flexion/extension. e complex motions covered touching head in the sagittal plane and the frontal plane, respectively, putting one hand behind the back, and shoulder pushing up in the sagittal plane and the frontal plane, respectively. All participants stood in the anatomic pose. More detailed motion information was illustrated by Pan et al. [12]. All subjects participated in the E1. e second experiment (E2) [16] was carried out in eleven male subjects. e subjects for E2 were instructed to execute reaching movements in six directions and three distances in a horizontal plane in a seating pose. Repeating the procedure six times for every reaching movement, 108 (3 × 6 × 6) trials were performed for every subject.

Data Collecting and Preprocessing.
Surface electromyographic (EMG) signals were recorded (Trigno Wireless EMG System, Delsys, USA) from nine dominant muscles of the right upper limb, including triceps brachii long and lateral head (TriLong and TriLat); pectoralis major (Pecm); deltoid anterior, medial, and posterior (DeltA, DeltM, and DeltP); trapezius upper (TrapUpper); biceps brachii (Bic); and brachioradialis (Brad). Electrodes were placed longitudinally along with the muscle fiber direction on corresponding muscles based on the guidelines of the Surface Electromyography for the Noninvasive Assessment of Muscles (SENIAM) [17].
Before the EMG processing, we eliminated the recordings contaminated due to disturbance and noise. en, raw EMG signals were high-pass filtered (5 th order Butterworth filter, the cutoff frequency of 50 Hz), zero-meaned, rectified, low-pass filtered (5 th order Butterworth filter, the cutoff frequency of 5 Hz), and integrated over 20 ms [3,11,16]. To facilitate comparison across subjects, the EMG envelope was normalized by the average of the top 10 maximum of each muscle from every individual [11].

Extracting Muscle Synergies.
Muscle synergy theory assumes that EMG patterns can be described as a linear combination of a set of muscle synergies (time invariant) activated by corresponding activation coefficients (time variant). It can be described as follows: where E m×t is the preprocessed EMG, m is the number of muscles, and t is the number of sampling. W m×n specifies the spatial profiles of activation, named the muscle synergy matrix, n is the number of muscle synergies. C n×t is the activation coefficient, which is time varying. e m×t is the error of reconstruction. We applied the nonnegative matrix factorization (NMF) [18] to extract muscle synergies. To avoid W and C converge to a local minimum, we repeated 50 times for each synergy.

Determining the Minimum Number of Muscle
Synergy. e NMF algorithm starts with an initialized n. We increased the number of muscle synergy from one to nine. Reconstruction quality was evaluated by calculating the variance accounted for (VAF) [14]. e structure of muscle synergy was affected by the minimum number of synergy. To reconstruct the EMG patterns better and decrease the dimensionality of the muscle synergies, two criteria were applied. Criteria 1: the minimum of muscle synergy was defined as the number that the total VAF was greater than 95% [12] (in the E2, VAF > 90% [19]) and criteria 2: an additional synergy did not contribute more than 5% in the reconstruction of the EMG envelope. e VAF is defined as follows [20]: (2)

Evaluating the Similarity and Merging the Synergies.
Before calculating the synergies similarity, we first matched the muscle synergy vectors from all synergy sets adopting the Hungarian algorithm [21].
e Pearson correlation coefficient (r i,j ) and cosine similarity (s i,j ) were used to assess the similarity of synergy vectors. To identify how the synergies extracted from complex motions were reconstructed by the linear combination of synergies extracted from simple motions, we applied the algorithm proposed by Cheung et al. [22], in where w CM i is the ith synergy vector from a complex motion, w SM k is the kth synergy vector from simple motion, and m i k is a nonnegative coefficient which denotes contributions of the kth synergy vector from simple motion for the structure of ith synergy vector from the complex motion.

Motion Modulation Indexes (MMI).
In the E2, we executed reaching movements in different directions and distances. To assess the modulating extent of activation coefficients among motion patterns, the motion modulation indexes were applied. We applied two indexes, root mean square of modulating signals (RMS-MS) and the VAF of synergy (VAF-Syn). RMS-MS represented an absolute activation degree, and VAF-Synergy (VAF syn i ) showed a relative activation degree. e two indexes could give an objective description of modulation. For one synergy, the VAF syn i is defined as [16] where w i is the ith muscle synergy and c T i is the corresponding activation coefficient. VAF S i and VAF syn i are the VAF and the synergy VAF of the ith muscle synergy, respectively.

Extracting Muscle Synergies.
e VAF is shown in Figure 1. According to the criteria described above, we identified three synergies (2.82 ± 0.40, corresponding VAF is 0.94 ± 0.01) in reaching movement (E2) for further analysis. e cosine similarity (s) and the Pearson correlation coefficient (r) between synergy vectors from all subjects are shown in Table 1. Results showed that the parallel synergy vector in all subjects was relevant. t-test results also illustrated that there was no significant difference among synergy vectors (α � 0.05).

Similarity Analysis in Different Directions and
Distances. To compare the variance of synergy vectors from different directions and distances, t-test was performed. Figure 3 shows the mean p values of the t-test among directions (a) and distances (b). Results showed that all p values were greater than 0.54 in directions (Table 2) and 0.59 in distances (Table 3), indicating that the synergy vectors from all directions and distances were from a population. en, we concatenated the data from all directions and distances, respectively. e t-test results showed that there was also no significant correlation in all directions and distances. For every synergy in six directions (Table 2), the average p values are 0.71 ± 0.21, 0.70 ± 0.21, and 0.73 ± 0.19 (α � 0.05, n � C 2 66 � 2145). And for every synergy in three distances (Table 3), the corresponding average p values are 0.69 ± 0.24, 0.78 ± 0.16, and 0.72 ± 0.19 (α � 0.05, n � C 2 33 � 528), respectively.

Motion Modulation Indexes (MMI).
e MMI for every direction and distance are shown in Figure 4. We found that every synergy was activated mainly in certain directions or distances. For example, the first synergy was activated mainly in 0 and − 45 direction. e second synergy was in the direction of 45, 90, 135, and 180. e third synergy was activated in all directions. In terms of distances, the first     2.43 ± 0.57, and 1.82 ± 0.55. e spatial structure of muscle synergies from every motion pattern is shown in Figure 5. For simple motion, the first synergy mainly activated shoulder abductor (DeltA and DeltM) and TrapUpper, which drove the motion of shoulder abduction. e second synergy primarily stimulated elbow flexor (Bic and Brad), which actuated the motion of elbow flexion. e third synergy drove the shoulder and elbow extension (TriLat, TriLong, DeltM, and DeltP). e forth synergy led to the motion of shoulder flexion (Pecm and DeltA). For every complex motion, every synergy chiefly activated certain muscles also, which actuated similar upper motions. t-test analysis was conducted among the subjects (α � 0.05). e synergy similarity among subjects is shown in Figure 6. e results rejected the null hypothesis (the sample data come from a population). We analyzed the  synergy similarity of all complex motions given in Table 4. A paired synergy is considered significantly correlated if the p is >0.5. We found that the synergy structure exhibited correlations between CM1 and CM2, and CM4 and CM5. However, the first synergy from CM4 and CM5 displayed a negative correlation.

Analysis of Synergy Similarity between Simple Motion and Complex
Motions. e similarity of every extracted synergy between complex motions and the simple motion was computed by cosine similarity (Figure 7). Table 5 shows the average of synergy similarity that every complex motion relates to simple motion. e higher similarity was found between the synergies from the complex motions and synergies from simple motion which composed the complex motion. For instance, touching head in the sagittal plane (CM1) consists of shoulder and elbow flexion. And, we found a greater similarity in the CM1-Syn1 and SM-Syn1, and CM1-Syn3 and SM-Syn2, which was similar in the synergy structure analysis ( Figure 5: complex motion 1). We also found the merging process between simple motion and complex motions. Table 6 demonstrates the merging coefficients (Mer-Coe) and reconstructed similarity (ReSim). We considered that the merging process was significant when the Mer-Coe was higher than 0.3 [11].
e results displayed that all reconstructing similarity was higher than 0.8.

Discussion
e purpose of this study was to investigate the relationship between muscle synergies and motion primitives of the upper limb motions. In previous studies, two muscle synergy models, time-varying synergy and time-invariant synergy, were used to analyze muscle patterns [13,23]. In our study, we extracted time-invariant muscle synergies adopting the NMF algorithm. Two experiments were designed, reaching movements and simple/complex motions. According to the    criteria predefined, we found three synergies were sufficient to explain >90% of the total variability of EMG activity of the nine studied muscles for reaching movements from eleven subjects. In the study of reaching movements of different conditions, three to five time-varying muscle synergies were extracted [24,25]. e results were coincident with the prior study. For simple motion and complex motions, we just selected one or two synergies in the threshold of 0.9, which could not describe the spatiotemporal structure of the synergy. us, the threshold was set to 0.95, and we selected 4, 3, 2, 3, 2, and 2 synergies, respectively. e study discussed the influence of directions and distances to muscle synergy in reaching movements (E2). ttest analysis (Tables 2 and 3) showed that synergies in different directions and distances were irrelevant. In the analysis of MMI, we found that RMS-MS and VAF-Syn exhibited resembled distributions in the radar map (Figure 4). e main performance was that the first synergy was activated mainly in the right and right rear motions. e second synergy mainly involved front, front-left, and left motions. However, the third synergy covered all directions. In the analysis of distance, the first two synergies displayed similar characters, farther distance with greater MMI. However, the third synergy showed an inverse character. We speculated that the third synergy was a shared synergy structure for reaching movements. e conjecture was verified by analyzing the synergy structure ( Figure 2). e results revealed that the CNS controlled the motions in different patterns (directions and distances) by adaptively modulating the corresponding activation coefficients. e E1 mainly analyzed the muscle synergy patterns of the simple motion and complex motions. t-test analysis showed synergy coincidence among subjects. However, there was one case which rejected the null hypothesis in CM3-Syn1, CM3-Syn2, CM3-Syn3, and CM5-Syn1, respectively (n � C 2 28 � 378). Considering the interference and noise of EMG signals, we thought the results were reliable. e CM1 (touching head in the sagittal plane) could be decomposed into shoulder and elbow flexion. And, the CM2 (touching head in the frontal plane) included the simple motions of shoulder abduction and elbow flexion. e analysis of synergy similarity between CM1 and CM2 showed a positive correlation (>0.5) in the corresponding synergy. e synergy structure of the two motions ( Figure 5) also displayed analogy. Semblable results were observed between CM4 and CM5. e results coincided with the conclusion in E2. e similarity of synergy vectors was analyzed between simple motion and complex motions. e results verified that the CNS controlled the motions by recruiting a set of muscle synergy primitives. Combining the study of reaching movements in E2, we knew that every muscle synergy pattern corresponded to a motion primitive.
As a quantitative assessment tool, muscle synergy has been used widely in motor neuroscience and rehabilitation neuroscience. However, the raw EMG signals are contaminated easily, and various preprocessing methods increase the difficulty to compare among researchers. Researchers have reported that experiment conditions have an effect on the envelope of the EMG, including speed, load, and posture [13]. In further work, we could study how the synergy modulates the motion in more conditions.

Conclusions
is study presented the possible patterns of the CNS controlling motions by two experiments, reaching movements in a horizontal plane and simple/complex motions. We applied the NMF to extract muscle synergies. Similarity analysis and t-test in muscle synergies indicated that the CNS modulated activation coefficients to achieve different motion patterns. Besides, for a complex motion, which included several motion primitives, the CNS recruited a set of muscle synergy primitives which drove the corresponding motion to coactivate the motion. Our results provided an interpretable strategy for the CNS controlling the motions.
is would be a potential implication for evaluating and making rehabilitation plans in rehabilitation neuroscience.

Data Availability
e raw data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
ere are no conflicts of interest regarding the publication of this paper.