Definition

The term “synergy” literally “working together,” has been used in the motor control literature with various meanings. Here a muscle synergy is defined as the coordinated recruitment of a group of muscles with specific activation balances or specific activation waveforms. Recent experiments have indicated that many motor behaviors are controlled through the flexible combination of a small number of muscle synergies. This mechanism is believed to simplify the selection of the appropriate muscle commands for a given behavioral goal.

Characteristics

To control goal-directed movements the central nervous system (CNS) must map sensory input into motor output. For example, reaching movements usually require selecting the appropriate muscle activation patterns to move the arm to visually specified targets. This transformation is thought to be performed by an internal model implemented in the neural circuits. However, given the complexity of the computations required to select the appropriate activation waveforms of many muscles acting on many articulated body segments, it is not clear what mechanisms allow for an efficient implementation of an internal model. One possibility is that this mapping is simplified by a low-dimensional representation of the motor output. The key idea is that, if all useful muscle patterns can be constructed by the combination of a small number of basic elements, selecting the appropriate muscle pattern for a given goal requires only determining how these elements are combined.

Two Types of Synergies

Muscle synergies are suitable basic elements for constructing a low-dimensional representation of the motor output because they capture a set of features shared by a variety of muscle patterns. Such features can be identified in the spatial domain and in the temporal domain. In the spatial domain, i.e. across muscles, a muscle synergy captures a specific relationship in the muscle activation amplitudes. Considering a set of D muscles, a muscle synergy can be expressed as a D-dimensional vector w of weighting coefficients that specify the activation balance among the muscles (Fig. 1a).

Muscle Synergies. Figure 1
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Generation of muscle patterns by combination of time-invariant synergies. (a) Three different activation balances among five muscles are expressed by three vectors (wi), whose components are represented by horizontal bars of different lengths. (b) Different muscle patterns (1–6) are generated by multiplying the three vectors by three scaling coefficients (ci) and summing them together. (c) A time-varying muscle pattern (m(t)) is generated by combining the synergies with time-varying scaling coefficients (ci(t)). Different patterns can be obtained by changing the scaling coefficient waveforms.

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Different levels of activation may be generated by a single muscle synergy by scaling in amplitude the entire vector:

$${\bf{m}} = c\,{\bf{w}}$$
((1))

where m is a D-dimensional vector that specifies the recruitment level of each muscle and c is a scaling coefficient (Fig. 1b, columns 1–3). More generally, a set of N synergies, {wi}i = 1…N, can generate many distinct muscle patterns by linear combination:

$${\bf{m}} = c_1 {\bf{w}}_1 + c_2 {\bf{w}}_2 + \cdot \cdot \cdot + c_N {\bf{w}}_N = \sum\limits_{i = 1}^N {c_i \ {\bf{w}}_i } $$
((2))

where ci is the scaling coefficient for the i-th synergy (Fig. 1b, rows 4–6).

Since the muscle activation vectors involved in most behaviors are time-dependent, synergistic relationships may also be found in the temporal domain. With respect to time, a synergy may be time-invariant or time-varying. A synergy is time-invariant if the same muscle activation balance, expressed by a vector w, holds at all times, i.e. for all the time-varying activation vectors comprising a muscle patterns. If all the synergies are time-invariant, eq. 2 can be written, taking time into account, as:

$${\bf{m}}(t) = \sum\limits_{i = 1}^N {c_i (t)\, {\bf{w}}_i}$$
((3))

where m(t) is the muscle activation at time t and ci(t) is the scaling coefficient for the i-th synergy at time t (Fig. 1c). Since each time-invariant synergy contributes to the waveform of different muscles with the same ci(t) waveform, the muscle waveforms associated with each synergy are synchronous. In contrast, a time-varying synergy is comprised by a collection of waveforms, each one specific for a muscle, and thus not necessarily synchronous (Fig. 2a).

Muscle Synergies. Figure 2
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Generation of muscle patterns by combination of time-varying synergies. (a) Each one of the two synergies illustrated is composed by a collection of muscle activation waveforms. The profile inside the rectangle below each synergy represents the mean activation waveform for that synergy. (b) A time-varying muscle patterns (m(t)) is generated by multiplying all waveforms of each synergy by a single scaling coefficient (ci), shifting them in time by a single delay (ti), and summing them together. In this example, different patterns are obtained by changing two scaling coefficients and two delays.

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These waveforms can be expressed by a time-varying synergy vector w(t) and eq. 2 can be written as:

$${\bf{m}}(t) = \sum\limits_{i = 1}^N {c_i \ {\bf{w}}_i (t - t_i )}$$
((4))

with one scaling coefficient (ci) and one time delay (ti) for each synergy. In this case, the time dependence of the muscle activation waveforms is captured by the temporal structure of the synergies and by their relative delays (Fig. 2b). Time-varying synergies represent parsimoniously the motor output because, once the synergies are given, a few scaling and delay coefficients are sufficient to specify many muscle patterns.

Muscle Synergy Identification

Muscle synergies provide a useful representation of the motor output if they can generate all muscle patterns observed during the performance of either a task in variety of conditions or multiple tasks. Thus, to test the validity of a synergy model it is necessary to identify a set of synergies from the observed muscle patterns and to show that they capture most of the variability in the data.

The identification of the synergies according to a model that allows for the simultaneous recruitment and combination of multiple synergies (eq. 2) requires a multivariate decomposition algorithm. For time-invariant synergies, the identification of the combination coefficients and synergies of eq. 3 can be obtained with a number of decomposition algorithm such as Principal Component Analysis (PCA), Factor Analysis (FA), Independent Component Analysis (ICA), and Non-negative Matrix Factorization (NMF) [1]. The number of synergies (N) is a free parameter for each decomposition algorithm. While the selection of this parameter is performed with different criteria for each algorithm, in general the goal is to determine the minimum number of synergies that explain all the structured variation in the data, interpreting the remaining unstructured variation as noise. Often this minimum number is determined by inspecting a plot of the reconstruction error as a function of the number of synergies. As the number of synergies increases the reconstruction error decreases and the number at which the error curve changes slope, indicating that additional synergies only explain a small additional amount of variation due to noise, is usually taken as correct number of synergies. The identification of time-varying synergies, according to the model of eq. 4, can be accomplished with the same methods used for time-invariant synergies if the simplifying assumption that the synergies are not time-shifted relatively to each other is introduced [2]. More generally, to identify a set of time-varying synergies that can be time-shifted with respect to each other, it is possible to use an iterative optimization algorithm [3].

Experimental Evidence

Qualitative observations of stereotyped muscle activity patterns in specific tasks, suggestive of a synergistic organization, have long been reported. However, whether muscle synergies are fixed or require task-dependent flexible adjustment has been a controversial issue. Recently, systematic investigations and quantitative analyses of the muscle synergies according to synergy combination models have addressed this issue with a new perspective. Studies conducted on frogs, cats, and humans have provided evidence that the CNS flexibly combines fixed muscle synergies for generating the muscle patterns necessary to perform many motor tasks and behaviors.

Electromyographycal (EMG) activity recorded from many hindlimb muscles of spinalized frogs during withdrawal reflexes [4], decerebrated frogs during spontaneous behavior [5], and intact frogs during defensive kicking [3] and locomotion, has revealed a synergistic organization. These studies have shown that a variety of muscle patterns used in different behaviors are generated by the combination of a small number of time-invariant and time-varying synergies. For example, 90% of the variability in the EMG responses associated with the withdrawal reflexes evoked by skin stimulation at a variety of sites on the frog limb is explained by the combination of four time-invariant synergies.

The study of postural control in cats and humans has also provided evidence for muscle synergies. The activations of cat hindlimb muscles during postural responses to perturbations of the support surface (translations and rotations in multiple directions) are captured by the combination of a five time-invariant synergies [6]. These muscle synergies are associated with specific force vectors applied by the paw against the support, suggesting that they encode task-level biomechanical variables. In humans, the muscle patterns used for shifting the center of pressure during balancing while standing are constructed by combinations of three time-invariant synergies [7].

The muscle patterns in leg and trunk muscles during human locomotion at different speeds and with different fractions of the body weight supported by a harness are accounted by the combination of five time-invariant synergies [8]. The time-varying amplitude scaling coefficients, once the muscle patterns are time-normalized to equal gait cycle duration, have similar waveforms across conditions.

Time-varying muscle synergies have been identified in the patterns of activation of extrinsic and intrinsic hand muscles during fingerspelling [2]. The synergy, identified with PCA, which explains the largest fraction of the data variation has asynchronous waveforms with activity waves unfolding in time across muscles.

Finally, there is evidence that the combinations of time-varying muscle synergies are used for controlling reaching movements in humans [9]. The phasic EMG patterns recorded in arm and shoulder muscles during fast reaching movements to targets arranged in different directions on two vertical planes are generated scaling in amplitude and shifting in time four or five time-varying muscle synergies. The amplitude modulation of the synergy has a simple dependence on the direction of movement, well captured by a cosine function.

In summary, a growing number of studies are unveiling the existence of regularities in the spatiotemporal organization of the muscle patterns observed during the performance of a variety of tasks in many conditions. These regularities are well described by a synergy combination model suggesting that the CNS uses a low-dimensional representation of the motor output and simple combination rules for mastering the complex task of selecting the appropriate muscle pattern for achieving a desired goal.

Postural Synergies