Based on the idea of synergy to explore the building blocks of movements, this study focused on the muscle space for reaching movements by human upper limbs on a horizontal plane to estimate the relationship among muscle synergies, equilibrium-point (EP) trajectories, and endpoint stiffness in two ways: (1) a novel estimation method that analyzes electromyographic signals under the concept of agonistantagonist (A-A) muscle pairs and (2) a conventional estimation method that uses mechanical perturbations. The experimental results suggest that (1) muscle activities of reaching movements by human upper limbs are represented by only three functional muscle synergies; (2) each muscle synergy balances the coactivations of A-A muscle pairs; (3) two of the muscle synergies are invariant bases that form an EP trajectory described in polar coordinates centered on a shoulder joint, where one is a composite unit for radial movement and the other is for angular movement; and (4) the third muscle synergy is the invariant basis for additional adjustment of the endpoint stiffness and has some influence on the direction and size of the endpoint stiffness ellipse.

Investigation of neural representation of movement planning has attracted the attention of neuroscientists, as it may reveal the sensorimotor transformation essential to motor control. The analysis of muscle synergies based on the activity of agonist–antagonist (AA) muscle pairs may provide insight into such transformations, especially for a reference frame in the muscle space. In this study, we examined the AA concept using the following explanatory variables: the AA ratio, which is related to the equilibrium-joint angle, and the AA sum, which is associated with joint stiffness. We formulated muscle synergies as a function of AA sums, positing that muscle synergies are composite units of mechanical impedance. The AA concept can be regarded as another form of the equilibrium-point (EP) hypothesis, and it can be extended to the concept of EP-based synergies. We introduce, here, a novel tool for analyzing the neurological and motor functions underlying human movements and review some initial insights from our results about the relationships between muscle synergies, endpoint stiffness, and virtual trajectories (time series of EP). Our results suggest that (1) muscle synergies reflect an invariant balance in the co-activation of AA muscle pairs; (2) each synergy represents the basis for the radial, tangential, and null movements of the virtual trajectory in the polar coordinates centered on the specific joint at the base of the body; and (3) the alteration of muscle synergies (for example, due to spasticity or rigidity following neurological injury) results in significant distortion of endpoint stiffness and concomitant virtual trajectories. These results indicate that muscle synergies (i.e., the balance of muscle mechanical impedance) are essential for motor control.

In neuroscience, the idea that motor behaviors are constructed by a combination of building blocks has been supported by a large amount of experimental evidences. The idea has been very attractive as a powerful strategy for solving the motor redundancy problem. While there are some candidates for motor primitives, such as submovements, oscillations, and mechanical impedances, synergies are one of the candidates for motor modules or composite units for motor control. Synergies are usually extracted by applying statistic techniques to explanatory variables, such as joint angles and electromyography (EMG) signals, and by decomposing these variables into fewer units. The results of factor decomposition are, however, not necessarily interpretable with these explanatory variables, even though the factors successfully reduce the dimensionality of movement; therefore, the physical meaning of synergies is unclear in most cases. To obtain insight into the meaning of synergies, this chapter proposes the agonist-antagonist musclepair (A-A) concept and uses other explanatory variables: the A-A ratio, which is related to the equilibrium point (EP), and the A-A sum, which is associated with mechanical stiffness. The A-A concept can be regarded as a form comparable to the EP hypothesis (EPH, model), and it can be extended to the novel concept of EP-based synergies. These explanatory variables enable us to identify muscle synergies from human EMG signals and to interpret the physical meaning of the extracted muscle synergies. This chapter introduces the EMG analysis in hand-force generation of a human upper limb and shows that the endpoint (hand) movement is governed by two muscle synergies for (1) radial movement generation and (2) angular movement generation in a polar coordinate system centered on the shoulder joint. On the basis of the analysis, a synergy-based framework of human motor control is hypothesized, and it can explain the mechanism of the movement control in a simple way.

This paper proposes a novel method for assessment of muscle imbalance based on muscle synergy hypothesis and equilibrium point (EP) hypothesis of motor control. We explain in detail the method for extracting muscle synergies under the concept of agonist-antagonist (AA) muscle pairs and for estimating EP trajectories and endpoint stiffness of human upper limbs in a horizontal plane using an electromyogram. The results of applying this method to the reaching movement of one normal subject and one hemiplegic subject suggest that (1) muscle synergies (the balance among coactivation of AA muscle pairs), particularly the synergies that contributes to the angular directional kinematics of EP and the limb stiffness, are quite different between the normal subject and the hemiplegic subject; (2) the concomitant EP trajectory is also different between the normal and hemiplegic subjects, corresponding to the difference of muscle synergies; and (3) the endpoint (hand) stiffness ellipse of the hemiplegic subject becomes more elongated and orientation of the major axis rotates clockwise more than that of the normal subject. The level of motor impairment would be expected to be assessed from a comparison of these differences of muscle synergies, EP trajectories, and endpoint stiffness among normal and pathological subjects using the method.

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