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

Abstract

A theoretical approach is proposed to define the force and position singular points (FSPs and PSPs) in the circular, ellipsoidal, and linear planar two-joint movements produced under steady loadings directed along the movement traces. The FSPs coincide with changes in the direction of the force moments acting around the joints; the PSPs show the locations of the extrema at the joint angle trajectories. The force synergy (defined by the location of FSPs) provides a strong influence on the activation synergy; the latter is largely described by correlations between the activities recorded from the muscles participating in the movement. The position synergy (defined by the location of PSPs) is responsible for a hysteresis-related modulation of the activation synergy. Geometrical procedures are proposed to define positions of the FSPs and PSPs along various movement traces; this can provide a general description of the force and position synergies for the movements. The force synergies in the circular movements cover four sectors with diverse loading combinations of the flexor and extensor muscles belonging to different joints. The variability of the synergy effects for changes in the size and position of the circular trajectories is analyzed; the synergy patterns are also considered for ellipsoidal and linear movement traces. A Force Feedback Control Hypothesis is proposed; it allows one to explain the decrease in the number of controlled variables during real multi-joint movements.

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

“…Schematic presentation of various combinations of the activity of flexor and extensor muscles belonging to different joints, as is shown in Figures 3D , 4D , allows us to present in graphical form the changes in the torque patterns (TCD, TOD) for separate transition movements in the joints. As has been shown for two-joint circular movements under a tangential load, central commands to the muscles depend predominantly on positions of the force singular points (FSP), where the JTs change their directions (Kostyukov, 2016 ; Tomiak et al, 2016 ). In the above-cited studies, the torque patterns in two-joint movements are considered through the functions of the simultaneously contracted muscles that belong to different joints.…”

“…One of us proposed a simple geometric method that allows us to define the exact positions of the points where the JTs change sign, which simplifies the determination of these points at various curvilinear movement traces in the working space (Kostyukov, 2016 ). While analyzing two-joint movements, we have also suggested an additional method for marking the sectors of coinciding and opposing synergy along the trajectory of movement (Kostyukov, 2016 ; Tomiak et al, 2016 ). The synergy sectors define the sections of the movement trajectory, in which muscles of the same or different function (flexors, extensors) are simultaneously active.…”

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

“…Earlier, we suggested that the synergy of activation, reflecting the simultaneous activation of muscles belonging to different joints, might be closely related to the patterns of coincidence/opposition in the directions of the torques around the corresponding joints (Kostyukov, 2016; Tomiak et al, 2016; Gorkovenko, 2018; Kostyukov and Tomiak, 2018). Therefore, the existence might be proposed of a close relationship between the activation and force synergies.…”

“…In studying the postural movements, it has been shown that peoples often use muscle cocontraction to stabilize the limb joints in the presence of load disturbances (Milner and Cloutier, 1998). In most cases, people can independently control the relative balance of cocontraction in antagonist muscles, thus varying the stiffness of joints over broad limits (Gribble and Ostry, 1998; Burde et al, 2001; Kostyukov, 2016). In our study, we observed a direction change in EMG hysteresis when the muscles from the active contraction program assisted their antagonists in cocontraction mode.…”

“…In both types of movements, the intensities of EMG activity in the shoulder and elbow muscles are correlated with the respective joint torques, consisting of the positive and negative components, each of which corresponds to the predominant activation of the flexor and extensor muscles, respectively. The methods allowing to evaluate the forces acting on the arm muscles and to define character of the muscle contractions (eccentric vs. concentric) along trajectories of the two-joint movements can be found in earlier studies by our group (Kostyukov, 2016; Lehedza et al, 2016; Lehedza, 2017; Gorkovenko, 2018; Kostyukov and Tomiak, 2018; Vereshchaka et al, 2018a). To distinguish various combinations of activity in muscles acting at different joints, we proposed extracting along the movement paths the segments of coinciding and opposing synergies, with active muscles of different joints belonging to the same (flexor and flexor, extensor and extensor) or opposite (flexor and extensor, extensor and flexor) functionalities, respectively (Tomiak et al, 2015, 2016; Kostyukov and Tomiak, 2018).…”