Theoretical Analysis of the Force and Position Synergies in Two-Joint Movements

Central Commands to the Elbow and Shoulder Muscles During Circular Planar Movements of Hand With Simultaneous Generation of Tangential Forces

This study examines some of the non-linear effects of signal transduction in the human motor system, with particular emphasis on muscle hysteresis. The movement tests were analyzed in a group of eight subjects, which were asked to develop tangential force using visual biofeedback while performing slow, externally imposed, circular movements of right hand holding a moving handle operated by a computerized mechatronic system. The positional changes in the averaged EMGs of the elbow and shoulder muscles were compared for all combinations of direction of movement and generated force. Additionally, for one of the subjects, there was carried out MRI identification and 3D printing of the bones of the forelimb, shoulder, scapula and collarbone, which made it possible to reconstruct for him the length and force traces of all the muscles under study. The averaged EMG traces in muscles of both joints show their close correspondence to the related force traces, however, the co-activation patterns of activity in agonists and antagonists were also often encountered. The EMG waves related to the respective force waves were strongly dependent on the predominant direction of the muscle length changes within the correspondent force wave locations: the EMG intensities were higher for the shortening muscle movements (concentric contractions) and lower during muscle lengthening (eccentric contractions). The data obtained allows to suggest that for two-joint movements of the forelimbs, it is sufficient to consider the force and activation synergies (patterns of simultaneous activity in different muscles), ignoring at the first stage the effects associated with kinematic synergy. On the other hand, the data obtained indicate that the movement kinematics has a strong modulating effect on the activation synergy, dividing it into concentric and eccentric subtypes, in accordance with the known non-linear features of the muscle dynamics. It has been shown that the concentric and eccentric differences in the responses of the shoulder muscles are more clearly distinguishable than those in the elbow muscles. The shoulder muscles also have a more pronounced symmetry of the averaged EMG responses with respect to the ascending and descending phases of force waves, while demonstrating a lower degree of antagonist cocontraction. The data obtained suggest that the central commands in two-joint movements are determined mainly by the interdependence of force and activation synergies including both intra- and inter-joint components, while kinematic synergy can be interpreted as a potent modulator of activation synergy.

Hysteresis and Synergy of the Central Commands to Muscles Participating in Parafrontal Upper Limb Movements

The averaged electromyograms (EMGs) were registered from the arm muscles of ten subjects in movements of the right hand performed under visual guidance on the horizontal plane along linear trajectories going parallel to the frontal plane at various distances from the trunk. The tests consisted of the steady movements (speed 4 cm/s) between two points symmetrical about the shoulder axis; the hand moved firstly from left to right, then in the opposite direction. The tests repeated ten times for each of two equal loads (10.2 N) applied to the hand along movement trajectory in the right- (F_r) or leftward (F_l) directions. The elbow and shoulder flexors reacted predominantly on F_r loads; the extensors were mostly activated by F_l loads. Positional changes of the averaged EMGs in both flexor and extensor muscles belonging to different joints demonstrated hysteresis properties; the respective hysteresis loops had counterclockwise direction in flexors and clockwise in extensors. The muscles predominantly opposing the loading forces of a given direction participate in a cocontraction mode as antagonists when the direction of load is changed; in this case, together with a decrease in the amplitude of the hysteresis loops, their direction is also reversed. The multiplication index of synergy (MIS), which is based on multiplication of the respective normalized averaged EMG records, has been proposed to evaluate quantitatively changes in the synergy effects between various muscle groups. For distal shifts of the movement traces, the synergy effects are shown to be changed in different directions, increasing in flexors and decreasing in extensors. The obtained results demonstrate that the muscle hysteresis leads to strong modification of the central commands during movements.

The Force Generation in a Two-Joint Arm Model: Analysis of the Joint Torques in the Working Space

The two-segment model of the human arm is considered; the shoulder and elbow joint torques (JTs) are simulated, providing a slow, steady rotation of the force vector at any end-point of the horizontal working space. The sinusoidal waves describe the JTs, their periods coincide with that of the rotation, and phases are defined by the slopes of the correspondent lines from the joint axes to the end-point. Analysis of the JTs includes an application of the same discrete changes in one joint angle under fixation of the other one and vice versa; the JT pairs are compared for the “shoulder” and “elbow” end-point traces that pass under fixation of the elbow and shoulder angles, respectively. Both shifts between the sinusoids and their amplitudes are unchanged along the “shoulder” traces, whereas these parameters change along the “elbow” ones. Therefore, if we consider a combined action of both JTs acting at the proximal and distal joints, we can assume that for the end-point transitions along the “shoulder,” and “elbow” traces this action possesses isotropic and anisotropic properties, respectively. The model also determines the patterns of the torques of coinciding and opposing directions (TCD, TOD), which would evoke a simultaneous loading of the elbow and shoulder muscles with the coinciding or opposing function (flexors, extensors). For a complete force vector turn, the relationship between the TCD and TOD remains fixed in transitions at the “shoulder” end-point traces, whereas it is changing at the “elbow” ones.