High-Order Characteristics of Upper Limb Intermuscular Coupling in Natural Manipulation

Current analyses of intermuscular coupling (IMC) predominantly rely on pairwise metrics, which may fail to capture high-order interactions (HOIs) essential for understanding complex neuromuscular coordination. This study develops a multi-domain high-order analysis framework for IMC by integrating O-information rate (OIR), frequency-domain O-information rate (fOIR), and $\beta $ -band B-index-rate network analysis to characterize high-order dependencies among muscles across the time domain, frequency domain, and connectivity structure, with a focus on activation and coordination patterns during natural grasping/lifting tasks. The results reveal substantial information redundancy within proximal muscle groups, and synergistic interactions typically emerged from combinations of muscles across different groups. Task- and posture-dependent variations in high-order dependency patterns were identified, with stronger overall muscle redundancy observed during lifting tasks than during gripping tasks. Frequency-domain analysis showed that high-order dependencies were most consistently expressed in the 15-30 Hz range ( $\beta $ band), where redundancy/synergy effects were evident during upper-limb grasping/lifting tasks. The proposed framework to a certain extent reveals task-dependent high-order interactions under partially controlled biomechanical conditions, highlighting redundancy within several muscle groups and synergy across groups. These findings advance the understanding of complex neuromuscular interactions and provide insights for motor control systems and rehabilitation.