Comparison of different state space definitions for local dynamic stability analyses.

Area of Science:

• Biomechanics
• Dynamical Systems Theory
• Motor Control

Background:

• Local dynamic stability quantifies perturbation deviations from motion attractors.
• Reconstructing attractors requires state space definition when equations of motion are unknown.
• Standardized state space methods are lacking in biomechanics.

Purpose of the Study:

• To assess the impact of state space definitions on local divergence exponent (lambda*(s)) calculations.
• To compare lambda*(s) in biomechanical tasks before and after fatigue using various state spaces.
• To provide guidance on selecting appropriate state spaces for biomechanical stability analysis.

Main Methods:

• Evaluated lambda*(s) on the Lorenz attractor with 9 state space definitions.
• Recruited 20 healthy subjects for a repetitive sawing task.
• Assessed shoulder movement stability using 6 state space definitions pre- and post-fatigue.

Main Results:

• Lambda*(s) calculations showed <10% error for 7/9 state spaces on the Lorenz attractor.
• Redundant information in state spaces led to poorer performance.
• Post-fatigue, lambda*(s) decreased across all 6 biomechanical state spaces, with statistical significance in 3.
• Increasing embedding dimension decreased lambda*(s) in both Lorenz and experimental data.

Conclusions:

• Direct numerical comparisons across different state space definitions require caution.
• Trends in local dynamic stability appear consistent across various state space definitions in biomechanics.
• State spaces using positions/velocities or individual state delay reconstruction offer reliable results.