Quaternion-Based Predictive Framework for Scapulohumeral Coordination

Abstract

Scapulohumeral rhythm (SHR), the coordinated motion between the scapula and humerus during arm elevation, is frequently altered in rotator cuff pathologies, yet the mechanical principles underlying coordination redistribution remain difficult to explain from experimental data alone. This study presents a predictive optimal control framework for investigating scapulohumeral coordination, combining a quaternion-based shoulder model with EMG-informed muscle parameter calibration. The quaternion formulation eliminated kinematic singularities and associated non-physiological activation artifacts observed in the Euler-angle model, while maintaining comparable tracking accuracy. EMG-informed calibration reduced discrepancies between predicted and measured muscle excitations by up to 60% on independent validation tasks. In predictive simulations where only thoracohumeral elevation was prescribed, scapular and clavicular kinematics emerged from musculoskeletal mechanics and minimization of muscular effort, producing SHR values consistent with established experimental ranges. Simulated rotator cuff deficiency resulted in increased reliance on glenohumeral rotation. The proposed framework may serve as a tool for understanding impaired coordination patterns across a broad range of shoulder pathologies, with potential to inform personalized rehabilitation strategies and the design of assistive and prosthetic devices.

Figures (7)

• Figure 1: Overview of the proposed modeling and optimization framework. Green boxes highlight outputs analyzed in the Results section.
• Figure 2: Comparison of computational performance between Euler-angles and quaternion-based models during trajectory tracking simulations.
• Figure 3: Effect of gimbal lock on muscle activation in selected muscle elements in the Euler-angle–based model (black line) during humeral elevation in the frontal plane.
• Figure 4: EMG compared to the resulting muscle excitation with original and adjusted muscle paramaters during a shelf-reaching ADL.
• Figure 5: The resulting joint rotations from the SHR prediction of healthy condition (blue line) and RC-limited condition (red line) compared to the dynamically feasible reference trajectory calculated from experimental data in Section \ref{['main_arxiv:subsec,IK tracking']} (grey line). Only humerus was tracked during these simulations. All angles are measured with respect to thorax. (g),(i) Due to gimbal lock in the YZY sequence of thoracohumeral rotation, values for the first and third axes were zeroed due to gimbal lock instability when elevation was below 8$^\circ$, corresponding segments in the kinematics plots are linearly interpolated and represented by dashed lines.