Voluntary movement requires sensorimotor transformation between extrinsic and intrinsic frames of reference ( Kandel et al., 2012). These results indicate that muscle synergies (i.e., the balance of muscle mechanical impedance) are essential for motor control. 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. 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). 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 formulated muscle synergies as a function of AA sums, positing that muscle synergies are composite units of mechanical impedance. 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. 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. Investigation of neural representation of movement planning has attracted the attention of neuroscientists, as it may reveal the sensorimotor transformation essential to motor control. 7Institute of Neuroscience, University of Newcastle, Newcastle upon Tyne, UK.6Department of Rehabilitation Medicine I, School of Medicine, Fujita Health University, Toyoake, Japan. 5Department of Neurology, University of Maryland School of Medicine, Baltimore, MD, USA.4Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.3Department of Rehabilitation, Senri Chuo Hospital, Toyonaka, Japan.2Department of Neurology, Senri Chuo Hospital, Toyonaka, Japan.1Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan. Fumio Miyazaki 1 Hiroaki Naritomi 2 Keitaro Koba 1 Takanori Oku 1 Kanna Uno 1 Mitsunori Uemura 1 Tomoki Nishi 3 Masayuki Kageyama 3 Hermano Igo Krebs 1,4,5,6,7
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