Two APR experiments were conducted in this study. The first experiment was an investigation of the relationship between the lateral balance ability of participants and the characteristics of their muscle synergies quantified by SSI and SCI. The second experiment was a training experiment to explore the plasticity of muscle synergy during training.

The participants in the first experiment were 8 healthy men (mean age 35.1 ± 8 years, mean weight 74 ± 18 kg, mean height 173.5 ± 12 cm). The participants in the second experiment were three out of the eight participants in the first experiment who showed the weakest ability to maintain balance. All participants were right-footed, and had no reported neurological disorders. The protocols of all experiments were approved by the RIKEN ethics committee.

In the experiments, we instructed participants to stand upright in the akimbo position on a movable platform, placing their feet on foot-ground contact sensors located 10 cm apart (Figure 2). We then triggered a lateral displacement of 11 cm with velocity of approximately 6.4 cm/s using the platform. We instructed the participants to make an effort to maintain their balance when the platform was displaced (i.e., avoid body movements other than lateral hip flexion/extension and/or ankle inversion/eversion). The direction and timing of displacement were random and not predictable during the experiment. Before starting the experiment, we asked the participants to practice on the platform for 20 min (approximately 80 platform displacements with various velocities punctuated by some intermittent breaks) to warm up and get used to the experimental environment.

Each participant experienced approximately (mean ± SD: 18 ± 4) leftward and rightward platform displacements and only trials of the leftward displacements were used for analysis in order to avoid any mixing the differences in behavior arising from using the dominant foot as compared with the non-dominant foot (Torres-Oviedo and Ting, 2007).

Electromyography (EMG) wireless surface electrodes (BTC Free EMG, sampled at 1 kHz) were used to record data from six major leg and lower-back muscles of the subject's right side (Konrad, 2005). Muscles include; flexor hallucis longus (FHL), tibialis anterior (TA); which support the ankle strategy in lateral perturbation. In addition to the tensor fasciae latae (TFL), gluteus medius (GM), rectus abdominalis (RA), erector spinae (ES); which support the hip strategy in lateral perturbation (Runge et al., 1999, see Figure 2). EMG Electrodes were placed in accordance to the guidelines of the Surface Electromyography for the Non-Invasive Assessment of Muscles (SENIAM)–European Community project (Hermens et al., 1999).

Since we were interested in the initial stage of the APR, the first recorded 160 ms of muscle activities, after the EMG response onset, were used for synergy calculations. The entire time-series EMG data was rectified and processed with a low-pass filter with a cutoff frequency of 32 Hz. EMGs were normalized by their maximum mean measured during the experiment.

A scoring system was applied to each participant to evaluate his balance skill in responding to the sudden platform displacement. Scores were displayed to the participant throughout the experiment on a front screen, in order to increase motivation to maintain balance. The scores were also used as a reference to associate balance skill with the resulting synergy characteristics of the participants. To estimate the scores, we visually observed each participant responses to each platform displacement and scored the response according to the criteria listed in Table 1.

Although the scores were considered for all the trials, we computed muscle synergy using only the trials of similar quality responses of the subjects (score = +1), to avoid any mixing the differences in behavior arising from using different response strategies such as step strategy or falling. Experimentally, 5 trials were the common number of trials among the subjects that meet this conditions.

An important feature of using muscle synergy is to reduce the dimensions of controlling the muscles. When m muscles are controlled, m commands are generally required.

Let us express the EMG data of m muscles by using the matrix M: (1)M∈Rm × t, where m and t are the number of muscles and the number of sampling data, respectively. The number of commands for controlling m muscles can be reduced by using the following matrix of the muscle synergy W: (2)M=WC+E, Where (3)W∈Rm × n,  C∈Rn × t,  E∈Rm × t and n is the number of control commands.

We assume that W is normalized to satisfy the following conditions: (4)       W=[ W(1)W(2)W(3)⋯W(n) ],|W(i)| = 1, where W⁽ⁱ⁾ denote the vector expressed as (5)W(i)∈Rm.

We set n to be smaller than m. Equation 1 implies that n commands are used to control m muscles by using the muscle synergy W (Figure 3).

C is the matrix containing the n commands to control m muscles as follows: (6)C=[ C(1)C(2)C(3)⋮C(n) ],       C(i)∈Rt

The error between M and WC is expressed as E, which must be small enough that m muscles are controlled by n commands in Equation 1. The magnitude of E is described by an index of similarity L, which is sensitive to both the shape and magnitude of the measured and reconstructed muscle patterns (Torres-Oviedo and Ting, 2007): (7)L=100(1−1m∑i=1m1t∑j=1tEij21t∑j=1tMij′2), where M′=WC, and E_ij and M′_ij are the elements of matrices E and M′,respectively. The range of L is 0 < L < 100. When the magnitude of E becomes smaller, L becomes larger. We considered a value of L > 75% to indicate a good fit with the original data (Torres-Oviedo et al., 2006). This criterion ensured that each muscle would be well reconstructed. A reasonable value of n is chosen by using the index L through the non-negative matrix factorization algorithm (Lee and Seung, 2001).

W⁽ⁱ⁾ in Equation (2) is regarded as the base vectors of the space created by W. We call this space a synergy space. C is the commands moving in the synergy space. We assume that m muscles are controlled in this n-dimensional space to simplify their controls.

To analyze APR behavior based on muscle synergy, we use two indices: SSI and SCI. SSI indicates the similarity in muscle synergy between multiple APRs, and SCI indicates the size of the synergy space.

All subjects successfully completed the assigned tasks. Our next step was to identify the appropriate dimensions of the synergy space of each participant, or in other words, the number of synergies that represent the recorded EMG patterns. To do so, first we used the recorded EMG data to calculate all possible synergies of each participant in each successful trial, and second we reconstructed back muscle activations based on those computed synergies.

Based on the quantitation of Equation 7, Figure 4 shows the similarity L between the recorded and reconstructed muscle activations from the possible computed synergies of participants. The minimum number of synergy space dimensions giving similarity in excess of the threshold value (L > 75%) was two synergies for all the subjects (we have also tested different thresholds to validate our threshold selection; see the supplementary materials for details). Accordingly, we assumed that the collected muscle patterns from the participants could be enough represented by two-dimensional synergy spaces. From the figure, we can note the correlation between the decomposition errors of the subjects and their balance skill, see the scores in Figure 7.

Figure 5 shows an example of the original EMG data of two different trials recorded from a representative good performer. Figure 6 shows an example of the resulting synergies of two representative subjects; good performer and bad performer. From Figures 5 and 6, we can observe that the recorded original EMG data is variable on all subjects regardless the quality of their responses.

During experiments, the 8 participants exhibited various skill levels in response to the displacement of the platform. In each trial, we visually evaluated each participant's response according to the criteria in Table 1. Figure 7 shows the mean of each participants scores across the successful trials. The results show that the participants had various levels of balance skill.

Figures 8A,B shows the relationships of SSI and SSI_c with the participants' scores. Here we see that participants with a high score (low score) showed lower (higher) C stabilities and higher (lower) W stabilities, respectively. Figure 8C shows also the relationships of SCI with the participants' scores. The plots here reveal that participants with a higher score used a smaller size of synergy space to respond to the disturbance, whereas those with a lower score used a larger size. Figures 6A,B show an example of the resulting synergies of higher and lower scores participants, respectively. In the higher score participant, the resulting synergy space in each trial are significantly similar (SSI = 0.95). On the other hand, the stability of the recruiting neural commands are lower (SSI_c = 0.67). The lower score participant, however, showed the opposite, Figure 6B.

From these results we may conclude that stability level of C and W could be a possible index to reflect participants' skills to maintain balance against the sudden disturbance. Regardless the variability of original EMG data on all subjects, high scores participants used almost fixed region of the synergy space across trials combined with a variable representation of the neural command C, while low scores participants utilized variable regions of the synergy spaces combined with a fixed representation of the neural command C. Furthermore, high scores participants used smaller size of synergy space than low scores participants.

In the second experiment, we aimed to observe the changes of muscle synergy during training. We asked the participants with the lowest scores (i.e., participants 6, 7, and 8) to continue performing a similar set of experimental trials for additional five sessions. Each session was conducted every two days. At each session, we requested the participants to do additional pre- and post-session practice on the platform for roughly 80 trials interspersed with adequate rest periods. Electrode positions on the participant's body were marked at each session to ensure similar electrode placement in the next experimental session.

Experimental results were as follows. Firstly, regarding the balance scores, participants show improvements in their scores, Figure 9A. Secondly, with respect to SSI and SSI_c, a gradual decrease in the stability of C and a gradual increase in the stability of W occurred, see Figures 9B,C. Thirdly, with respect to SCI, gradual decrease was observed in the synergy size (i.e., an increase in SCI), Figure 9D. From the Figure 9, the scores, SSI, and SCI were associated with one another; thus, the overall relationships were fairly consistent with the outcomes presented in the above experiment.

From this training experiment, we can highlight two main points: (1) synergies seem to be altered through systematic training: the adaptation of W occurs until a proper region is located. This stage occur in conjunction with the adaptation of C. (2) The CNS appears to force the recruitment direction of the muscle synergy to ensure higher coordination between the utilized synergies (i.e., a smaller size of synergy space), which could be the reason for the resulting quality of the subsequent behaviors (Video1, appendix: shows the behavior of a representative subject before and after the training).

These resulting characteristics of SSI, SSI_c, and SCI reveal an important learning methodology of muscles, which we summarized in the following four points:

First, when participants were introduced to the task; if the proper region and size of their synergy space for responding to the task were not yet solved (e.g., in participants with low scores), the CNS tried at each trial to search for the most appropriate synergy space region, evoking various strategies by tuning the value of W. Due to this search stage, low stability of W was observed.

Second, the search criterion that the CNS appeared to rely on in this stage was the size of the synergy space. Narrow space appeared to be the desired target of the CNS. Thus, high SCI was observed in the participants with higher scores. After a number of search trials throughout training, the appropriate coordination of the muscles gradually emerged, and a gradual increase in the stability of W.

Third, during the search stage of W, and to simplify handling of its high temporal variability, the CNS attempted to reduce the degrees of freedom of the resulting motions by restricting the variability of C, and thus, high stability of C was observed. One possible mechanism that might be used by the CNS to manage this stage could be decreasing sensitivity to changes caused by sensory inputs. Such sensitivity reduction can necessitate extra energy from CNS to maintain high stability of C (considering that the inputs were variable in nature).

Fourth, eventually after learning, W was stable in a particular region and smaller in size, and the constraint on the variability of C was gradually eased. Thus, a reduction in the stability of C occurred as a natural response to the variability from the input side.

Our findings could be consistent to some extent with the individual learning stages reported by Bernstein (1967), where individuals learn motor coordination first by temporarily restricting the degrees of freedom that they use. This enables the learner to simplify the dynamics of the involved body parts and the range of movement options when searching for the optimal muscle combinations. Once the individual has gained a certain level of proficiency, the constraint can be relaxed, thereby allowing them to use the full potential of their body (decreased variability of W and increased variability of C).

The resulting variability of W and C in this study could be also associated to the bad and good variability hypothesis discussed by Latash and Anson (2006). This hypothesis mainly indicates that variability is naturally presented in human movements. Thus, bad variability is the one which affects the final performance results of the motor task. Good variability, on the other hand, always works to achieve better outcome. The CNS, therefore, may, in our case, works to decrease the bad variability W and increase the good variability C.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.