A novel muscle synergy extraction method to explain the equilibrium-point trajectory and endpoint stiffness during human upper-limb movements on a horizontal plane

Abstract

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.

A feasibility study to assess intralimb coordination in stroke rehabilitation: two indices of mechanical impedance by coactivation of agonist muscles

“…Some of the muscle synergies contribute to the displacement of endpoint (hand) equilibrium-point (EP) and the other contributes to modulation of endpoint stiffness. We found that muscle activities during upper limb reaching movements by healthy subjects are represented by three invariant functional synergies [9]. Moreover, the muscle synergies and endpoint stiffness of the reaching movement in a post-stroke subject were different from those of a healthy subject [10].…”

“…See [9] and [11] for more details on dynamic equations and calculation method for the parameters. (a) 2) The analysis of muscle synergy and endpoint stiffness: Human upper limbs on the horizontal plane were simplified as a two-link structure of three pairs of six muscles as shown in Fig.…”

“…Here, u R and u φ are the basis of displacement of the endpoint EP in the polar coordinate system. u R×φ does not contribute to displacement of the EP, but contributes to regulate the limb stiffness under a dynamic condition [9]. Note that, these muscle synergies are quantities determined only by the AA sums.…”

“…We have focused on the activities of agonist-antagonist (AA) muscle pair to examine human voluntary movements, and have proposed muscle synergies that are determined by the balance among the coactivation of AA muscle pairs in relation to joint mechanical impedance [9]. Our muscle synergies are obtained not from statistical analysis but from physical modeling of the human musculoskeletal system.…”

Pilot study on quantitative assessment of muscle imbalance: Differences of muscle synergies, equilibrium-point trajectories, and endpoint stiffness in normal and pathological upper-limb movements

“…Here, the null directional muscle synergy does not contribute to the kinematics of the EP, but contributes to regulate the limb stiffness under a dynamic condition [7]. 4) Endpoint stiffness: In this model, the stiffness of each muscle is proportional to its level of activity [6].…”