Cross-Modal Synergy Representation of EMG and Joint Angular Acceleration During Gait in Parkinson’s Disease Using NMF and Multimodal Matrix Factorization

The aims of this research were to characterize neuromuscular control features within the gait cycle in Parkinson's disease (PD) from the perspectives of muscle synergies and cross-modal coupling and to propose a joint representation of the relationship between muscle activation patterns and kinematic dynamic outputs. PD participants (<i>n</i> = 19) were included. Lower-limb surface electromyography (EMG) and kinematic dynamic channels, including pelvic/hip, knee, and ankle angular acceleration, were collected during level-ground natural walking. EMG signals were first decomposed using non-negative matrix factorization (NMF) to extract muscle synergies, and the number of synergies was evaluated using reconstruction performance (R²). Multimodal matrix factorization (MMF) was then applied to jointly decompose the EMG and angular-acceleration channels, yielding a cross-modal synergy representation comprising a shared temporal structure (H) and modality-specific weight structures (W): non-negativity was imposed on EMG weights, whereas kinematic weights were allowed to take positive and negative values to encode directional contributions. Under the current task and muscle set, NMF achieved high EMG reconstruction performance with four synergies (R² = 0.882). The synergy weights showed an ankle-dominant pattern: tibialis anterior (TA) consistently carried high weights across multiple synergies, while lateral gastrocnemius (LG) and soleus (SOL) contributed prominently to another synergy. The synergy activation profiles exhibited phase-dependent fluctuations with multiple rises and falls across the gait cycle, suggesting that synergy output was primarily characterized by continuous modulation rather than single-peak recruitment. MMF further identified eight cross-modal synergies, simultaneously capturing the shared contributions of key muscle groups (e.g., RF, TA, and SOL) and pelvic/hip and knee/ankle angular-acceleration channels within the same decomposition framework and summarizing their descriptive co-variation through the shared temporal structure (H). Overall, A low-dimensional synergy analysis combining EMG-only NMF with cross-modal MMF enables simultaneous characterization of cohort-level modular organization of muscle activity during gait and its descriptive association with pelvis-to-lower-limb dynamic output. This joint framework provides a methodological basis for quantitatively describing gait-related modular organization and temporal modulation patterns in this PD cohort under natural level-ground walking and lays the groundwork for subsequent testing of associations between synergy features and gait phenotypes, clinical severity, and rehabilitation responses.